references - springer978-3-540-85130-1/1.pdf · 138 references 17. carpenter ... d.m.: neural...

Retract

ed

References

1. Adeli, H., Hung, S.L.: Machine Learning Neural Networks, Genetic Algorithms and FuzzySystems. John Wiley and Sons, New York (1995)

2. Aleksander, I., Morton, H.: An Introduction to Neural Computing. Chapman and Hall, Lon-don (1990)

3. Amari, S.: Learning Patterns and Pattern Sequences by Self Organizing Nets of ThresholdElements. IEEE Transactions on Computers C-21, 1197–1206 (1972)

4. Anzai, Y.: Pattern Recognition and Machine Learning. Academic Press, Englewood Cliffs(1992)

5. Bajaj, R., Chaudhury, S.: Signature Verification Using Multiple Neural Classifiers. PatternRecognition 30(1), 1–7 (1997)

6. Benedetto, J.J., Frazier, M.W. (eds.): Wavelets, Mathematics and Applications. CRC Press,Boca Raton (1994)

7. Brigham, E.O.: The Fast Fourier Transform. Prentice-Hall, Englewood Cliffs (1978)8. Burrus, C.S., Gopinath, R.H., Guo, H.: Introduction to Wavelets and Wavelet Transforms.

In: A Primer, Prentice-Hall, Englewood Cliffs (1998)9. Looney, C.G.: Pattern Recognition Using Neural Networks: Theory and Algorithms for

Engineers and Scientists (1997)10. Carpenter, G.A., Grossberg, S., Markuzon, N., Reynolds, J., Rosen, D.B.: Fuzzy ARTMAP:

A Neural-Network Architecture for Incremental Supervised Learning of Analog Multidi-mensional Maps. IEEE Trans. Neural Networks 3, 698–713 (1992)

11. Carpenter, A., Tan, H.A.: Rule Extraction: From Neural Architecture to Symbolic Repre-sentation. Connection Sci. 7(1), 3–27 (1995)

12. Carpenter, G.A., Milenova, B.L., Noeske, B.W.: Distributed ARTMAP: A Neural Networkfor Fast Distributed Supervised Learning. Neural Network 11(4), 793–813 (1998)

13. Carpenter, G.A., Gjaja, M.: Fuzzy ART Choice Functions, Technical Report CAS CNS-TR-93-060, Boston University. In: Proceedings of the World Congress on Neural Networks(WCNN 1994) (1994)

14. Carpenter, G.A., Grossberg, S. (eds.): Pattern Recognition by Self Organizing Neural Net-works. MIT Press, Cambridge (1991)

15. Carpenter, G.A., Grossberg, S., Reynolds, J.H.: ARTMAP: Supervised Real-Time Learningand Classification of Non-stationary Data by a Self organizing Neural Network. NeuralNetworks 4, 565–588 (1991)

16. Carpenter, G.A., Grossberg, S., Rosen, D.B.: Fuzzy ART: Fast Stable Learning and Cat-egorization of Analog Patterns by an Adaptive Resonance System. Neural Networks 4,759–771 (1991)

Retract

ed

138 References

17. Carpenter, G.A., Grossberg, S., Rosen, D.B.: A Neural Network Realization of Fuzzy ART,Technical Report CAS CNS-TR-91-021, Boston University (1991)

18. Carpenter, G.A., Grossberg, S.: The Art of Adaptive Pattern Recognition by a Self Orga-nizing Neural Network. IEEE Computer Magazine 21(3), 77–88 (1988)

19. Carpenter, G.A., Grossberg, S., Rosen, D.B.: ART 2A: An Adaptive Resonance Algorithmfor Rapid Category Learning and Recognition. Neural Networks 4, 493–504 (1991)

20. Casagrande, A.: Classification and identification of soils. Trans. ASCE 113, 60–64 (1498)21. Castillo, E., Ruiz–Cobo, R.: Functional Equations and Modeling in Science and Engineer-

ing. Marcel Dekker, New York (1992)22. Castillo, E.: Functional Networks. Neural Processing Letters 7, 151–159 (1998)23. Chakravarty, D., Misra, B.: Application of Neural Networks for the Rock Property Pre-

diction. In: Proceedings of National Conference on Neural Networks and Fuzzy Systems,Anna University, Chennai, July 23-25, pp. 166–172 (1997)

24. Chen, R.M., Huang, Y.M.: Multiconstraint Task Scheduling in Multiprocessor System byNeural Network. In: Proceedings of the IEEE Tenth International Conference on Tools withArtificial Intelligence, pp. 288–294 (1998)

25. Christian, B.: Wavelets – a Primer. Universities Press Pvt. Ltd., Hyderabad (2003)26. Coifman, R.R., Wickerhauser, M.V.: Wavelets and Adapted Waveform Analysis, A Toolkit

for Signal Processing and Numerical Analysis. In: Proceedings of Symposia in AppliedMathematics, vol. 47, pp. 119–153 (1993)

27. Coifman, R.R., Wickerhauser, M.V.: Wavelets and Adapted Wave-form Analysis, pp. 399–424 (1991)

28. Daubechies, I.: Orthonormal Bases of Compactly Supported Wavelets Communication onPure and Applied Mathematics, vol. 41, pp. 909–996 (1988)

29. Daubechies, I. (ed.): Different Perspectives on Wavelets. AMS, Providence (1993)30. Daubechies, I.: Ten Lectures on Wavelets. SIAM, Philadelphia (1992)31. Dixon, M.X., Cole, G.R., Bellgard, M.I.: Using the Hopfield Network with Mean Field An-

nealing to Solve the Shortest Path Problem in a Communication Network. In: InternationalConference on Neural Networks, vol. 5, pp. 2652–2657 (1995)

32. Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press,Boston (1980)

33. Duric, Z., Li, F., Wechsler, H.: Recognition of Arm Movements. In: Fifth IEEE Internationalconference on Automatic Face and Gesture Recognition, P 0348 (2002)

34. Gose, E., Johnsonbaugh, R., Jost, S.: Pattern Recognition and Image Analysis. Prentice Hallof India, New Delhi (2000)

35. Gomez-Sanchez, E., Dimitriadis, Y.A., Cano Izquierdo, J.M., Coronado, J.L.: μ ARTMAPUse of Mutual Information for Category Reduction in Fuzzy ARTMAP. IEEE Transactionson Neural Networks 13(1), 58–69 (2002)

36. Revuelta, F.F., Garcıa Chamizo, J.M., Pico, F.I.: Hand Gesture Recognition based on Mor-phologic Features. In: IX simposium Nacional de Reconoimiento de Formas Y Analisis deImagenes, Benicassim Mayo (2001)

37. Freeman, J.A., Skapura, D.M.: Neural Networks Algorithms, Applications and Program-ming Techniques. Addison-Wesley, Reading (1991)

38. Limin, F.: Neural Networks in Computer Intelligence. McGraw Hill Inc., New York (1994)39. Fukumi, M., Omatu, S., Takeda, F., Kosaka, T.: Rotation Invariant Neural Pattern Recog-

nition System with Application to Coin Recognition. IEEE Transactions on Neural Net-works 3(2), 241–251 (1992)

40. Gader, P., et al.: Fuzzy and Crisp Handwritten Character Recognition Using Neural Net-works. In: Conference Proceedings of the 1992 Artificial Neural Networks in EngineeringConference, vol. 3, pp. 421–424 (1992)

Retract

ed

References 139

41. Carpenter, G.A., Grossberg, S.: Fuzzy Adaptive Resonance Theory – Advanced ResearchProjects Agency ARPA, the office of Naval Research (ONR N00014-91-J-4100)

42. Goldberg, D.E.: Genetic Algorithms in Search: Optimization and Machine Learning.Addison-Wesley, Reading (1989)

43. Gomez-Sanchez, E., Gago-Gonzalez, Y.A., Dimitriadis, Y.A., Canolzquierdo, J.M., Coro-nado, J.I.: Experimental Study of a Novel Neuro Fuzzy System for On Line HandwrittenRecognition. Pattern Recognition Lett. 19(3), 357–364 (1998)

44. Gupta, M.M., Rao, D.H. (eds.): Neuro-Control Systems: Theory and Applications. IEEEPress, NY (1994)

45. Guyon, I., Albrecht, P., Cun, Y.L., Denker, J., Hubbard, W.: Design of a Neural NetworkCharacter Recognizer for a Touch Terminal. Pattern Recognition 24(2), 105–117 (1991)

46. Hans Raj, K., Mangla, P., Srivatsav, S., Patvardhan, C.: A Neural Network Based ProcessAdvisor for Hot Extrusion of Steel. In: Proceedings of International Conference on Cogni-tive Systems, ICCS 1997, New Delhi, pp. 767–777 ( December 1997)

47. Hecht-Neilsen, R.: Neuro Computing. Addison Wesley, Reading (1990)48. Hopfield, J.J., Tank, D.W.: Computing with Neural Circuits: A Model. Science 233, 625–

633 (1986)49. Hopfield, J.J.: Neural Networks and Physical Systems with Emergent Collective Computa-

tional Abilities. Proc. of the National Academy of Sciences 79, 2554–2558 (1982)50. Hopfield, J.J., Tank, D.W.: Neural Computation of Decision in Optimization Problems.

Biol. Cybernet 52, 141–152 (1985)51. Hu, M.K.: Visual Pattern Recognition by Moment Invariants. IRE Trans. Inf. Theory 8,

179–187 (1962)52. Ibarra Pico, F.: Memorias Associativas Ortogonales Y sus applicaciones en analisis de lec-

tura. Institut de Cultura Juan Gil – Albert ISBN: 84-7784-258-2 (1997) (with English trans-lation)

53. Walker, J.S.: A Primer on Wavelets and their Scientific Applications. Chapman and Hall,Boca Raton (1999)

54. Chandran, J.S.: Statistics for Business and Economics. Vikas Publishing House, New Delhi(2000)

55. Kartalopoulos, S.: Understanding Neural Networks and Fuzzy Logic. IEEE Press, NY(1996)

56. Tom, K.: Simplified Fuzzy ARTMAP, AI Expert, pp. 18–25 (November 1993)57. Klir, J., Folger, T.A.: Fuzzy Sets, Uncertainty and Information. Prentice Hall, New York

(1988)58. Klir, G.J., Bo, Y.: Fuzzy Sets and Fuzzy Logic. Prentice Hall of India, New Delhi (1997)59. Kohonen, T.: Self-organized Formation of Topologically Correct Feature Maps. Biol. Cy-

bernet 43, 59–69 (1982)60. Kohonen, T.: Self-organization and Associative Memory, 3rd edn. Springer, Berlin (1989)61. Kohonen, T.: Correlation Matrix Memories. IEEE Transactions on Computers 21, 353–359

(1972)62. Kohonen, T.: The Self Organizing Map. Proc. IEEE 78(9), 1464–1480 (1990)63. Bart, K.: Fuzzy Engineering. Prentice Hall International, Englewood Cliffs (1997)64. Bart, K.: Neural Networks and Fuzzy Systems: A Dynamical Systems Approach to Ma-

chine Intelligence. Prentice-Hall, New York (1992)65. Kosko, B.: Fuzzy Entropy and Conditioning. Information Sciences 40(2), 165–174 (1986)66. Murakami, K., Taguchi, H.: Gesture Recognition Using Recurrent Neural Networks. Jour-

nal of the ACM 1(1), 237–242 (1991)67. Lee, K., Takefuji, Y., Funabiki, N.: A Parallel Improvement Algorithm for the Bipartite

Subgraphy Problem. Case Western Reserve University, CAISR Technical Report TR91-105(1991)

Retract

ed

140 References

68. Lee, J.S., Sun, Y.N., Chen, C.H.: Multi-scale Corner Detection by Using Wavelet Trans-forms. IEEE Trans. Image Processing 4(1), 100–104 (1995)

69. Liang, K.C., Kuo, C.C.J.: Waveguide: A Joint Wavelet-Based Image Representation andDescription System. IEEE Trans. Image Processing 8(11), 1619–1629 (1991)

70. Mallat, S.: A Wavelet Tour of Signal Processing. Academic Press, New York (1998)71. Mallat, S.: A theory for multiresolution signal decomposition, the wavelet representation.

IEEE Pattern Analysis and Machine Intelligence 11, 674–693 (1989)72. Martin, G.L., Pittman, J.A.: Recognizing Hand Printed Letters and Digits Using Back Prop-

agation Learning. Neural Computation 3(2), 258–267 (1991)73. Merino, E.P., Dimitriadis, Y.A., Garefa, R.G., Lopez, J.C.: A Dictionary Based Neural

network Scheme for On-Line Handwriting Recognition. In: Simner, M., Leedham, C.,Thomassen, A. (eds.) Handwriting and Drawing Research: Basic and Applied, pp. 343–358. IOS Press, Amsterdam (1996)

74. Meyer, Y.: Wavelets and Operators. Cambridge University Press, Cambridge (1992)75. Meyer, Y.: Wavelets: Algorithms and Applications. SIAM, Philadelphia (1993)76. Moore, B.: ART 1 and Pattern Clustering. In: Touretzky, D., Hinton, G., Sejnowski, T.

(eds.) Proceedings of the 1988 Connectionist Models Summer School, pp. 174–185. Mor-gan Kaufmann Publishers, San Francisco (1989)

77. Nellis, J., Stonham, T.J.: A Neural Network Character Recognition System that Dynami-cally Adapts to an Author’s Writing Style. In: Conference Proceedings of the 1992 ArtificialNeural Networks in Engineering Conference, vol. 3, pp. 975–979 (1992)

78. Pal, S.K., Majumdar, D.K.D.: Fuzzy Mathematical Approach to Pattern Recognition. WileyEastern Ltd., New Delhi (1986)

79. Papoulis, A.: Probability, Random Variables and Stochastic Processes, 3rd edn. McGrawHill, New York (1991)

80. Parado-Hernandez, E., Gomez-Sanehez, E., Dimitriadis, Y.A.: Study of Distributed Learn-ing as a Solution to Category Proliferation in Fuzzy ARTMAP Based Neural Systems.Neural Networks 16(7), 1039–1057 (2003)

81. Patterson, D.W.: Artificial Neural Networks: Theory and Applications. Prentice Hall, En-glewood Cliffs (1996)

82. Maes, P., Darell, T., Blumberg, B., Penland, A.: The Alive System: Full-Body Interactionwith Autonomous Agents. In: Computer Animation 1995 Conference. IEEE Press, Geneva(1995)

83. Punmia, B.C., Jain, A.K.: Soil Mechanics and Foundations. Laxmi Publications (2005)84. Gonzalez, R.C., Woods, R.E.: Digital Image Processing, 2nd edn. Pearson Education, Lon-

don (2004)85. Rajasekaran, S., Suresh, D., Vijayalakshmi Pai, G.A.: Application of Sequential Learning

Neural Networks to Civil Engineering Problems. Engineering with Computers 18, 138–147(2002)

86. Rajasekaran, S., Vijayalakshmi Pai, G.A.: Simplified fuzzy ARTMAP as pattern recognizer.Comput. Civil Engg., ASCE 14(2), 92–99 (2000)

87. Rajasekaran, S., Vijayalakshmi Pai, G.A.: Image Recognition Using Simplified FuzzyArtmap Augmented With a Moment Based Feature Extractor. Pattern Recognition, Artif.Intell. 14(8), 1081–1094 (2000)

88. Rajasekaran, S., Vijayalakshmi Pai, G.A.: Neural Networks, Fuzzy Logic and Genetic Al-gorithms. Prentice Hall India Pvt. Ltd., New Delhi (2004)

89. Sharma, R., Vladimir, L.P., Huang, T.S., et al.: Speech / Gesture Interface to a Visual Com-puting Environment. IEEE Computer Graphics and Applications 20(2), 29–37 (2000)

90. Raghuveer, R.M., Ajit, B.S.: Wavelet Transforms – Introduction to Theory and Applica-tions. Pearson Education Limited, Singapore (1998)

Retract

ed

References 141

91. Watson, R.: A Survey of Gesture Recognition Techniques., Technical Report TCD – CS –93 – 11, Department of Computer Science, Trinity College, Dublin, Ireland (1993)

92. Rosenblatt, F.: Principles of Neurodynamics. Spartan Books (1962)93. Chen, R.M., Huang, Y.-M.: Competitive Neural Network to Solve Scheduling Problems.

Neuro Computing 37, 177–196 (2001)94. Salzberg, S.L.: Learning with Nested Generalized Exemplars. Kluwer Academic Publish-

ers, Dordrecht (1990)95. Robert, S.: Digital Image Processing and Computer Vision. John Wiley and Sons Inc.,

Chichester (1989)96. Robert, S.: Pattern Recognition – Statistical Structural and Neural Approaches. John Wiley

and Sons Inc., Chichester (1992)97. Simpson, P.: Fuzzy Min-Max Classification with Neural Networks. Heuristics: The Journal

of Knowledge Engineering 4, 1–9 (1991)98. Soman, K.P., Ramachandran, K.I.: Insight Into Wavelets From Theory To Practice. Prentice

Hall of India, New Delhi (2004)99. Takagi, H., Konda, T., Kojima, Y.: Neural Network Design on Approximate Reasoning and

its Applications to Pattern Recognition. In: Proc. of the Intl. Conf. of Fuzzy Logic andNeural Networks, Iizuka, Japan, pp. 671–674 (July 1990)

100. Takeda, M., Goodman, J.W.: Neural Networks for Computation: Number Representationand Programming Complexity. Appl. Opt. 25, 3033–3046 (1986)

101. Baudel, T., Beaudounin, M.: Lafon CHARADE: Remote control of Objects using FreeHand Gestures. Communications of the ACM 36(7), 28–35 (1993)

102. Darell, T.J., Penland, A.P.: Space – time gestures. In: IEEE Conference on Vision and Pat-tern Recognition, New York (June 1993)

103. Rao, V., Rao, H.: C++ Neural Networks and Fuzzy Logic. MIS Press, New York (2000)104. Verzi, S.J., Heileman, G.L., Georgiopaulos, M., Healy, M.J.: Boosted ARTMAP. In: Proc.

IEEE World Congr. Comput. Intell., WCCI 1998, Anchorage, AK, pp. 395–400 (May 1998)105. Pavlovis, V.L., Sharma, R., Huang, T.S.: Visual Interpretation of Hand Gestures For Hu-

man Computer Interaction: A Review. IEEE Transactions on Pattern Analysis and MachineIntelligence 19(7), 677–695 (1997)

106. Wasserman, Philip, D.: Advanced Methods in Neural Computing. Van Nostrand Reinhold,New York (1993)

107. Wasserman, Philip, D.: Neural Computing. Van Nostrand Reinhold, New York (1989)108. Whang, B.: Elasto Plastic Orthotropic Plates and Shells. In: Proceedings of the Sympo-

sium on Application for Finite Element Methods in Civil Engineering, ASCE, pp. 481–515(November 1969)

109. Williamson, J.: Gaussian ARTMAP: A Neural Network for Fast Incremental Learning ofNoisy Multidimensional Maps. Neural Network 9(5), 881–897 (1996)

110. Willems, T.M., Rooda, T.E.: Neural networks for job-shop scheduling. Control Eng. Prac-tice 2(1), 31–39 (1994)

111. Yager, R. (ed.): Fuzzy Sets and Applications: Selected Papers by L.Z. Zadeh. Wiley-Interscience, New York (1987)

112. Yager, R.R.: Modeling and Formulating Fuzzy Knowledge Bases using Neural Networks.Neural Networks 7(8), 1273–1283 (1994)

113. Yamakawa, T., Tomoda, S.: A Fuzzy Neuron and its Application to Pattern Recognition. In:Proc. Third Intl. Fuzzy System Association Congress, Japan, pp. 30–38 (1989)

114. You, J., Bhattacharya, P.: A Wavelet-Based Course-to-Fine Image Matching Scheme ina Parallel Virtual Machine Environment. IEEE Trans. Image Processing 9(9), 1547–1559(2000)

Retract

ed

142 References

115. Huang, Y.-M., Chen, R.-M.: Scheduling Multiprocessor Job with Resource and TimingConstraints using Neural Network. IEEE Trans. System Man Cybernet, Part B 29(4), 490–502 (1999)

116. Zadeh, L.: Fuzzy Sets. Information and Control 8, 338–353 (1965)117. Zadeh, L.A.: The Role of Fuzzy Logic in the Management of Uncertainty in Expert Sys-

tems. In: Gupta, Kandel, Bandler, Kiszka (eds.) Approximate Reasoning in Expert System.Elsevier, NY (1985)

118. Zhang, J., Morris, A.J.: A Sequential Learning approach for single hidden layer neuralnetworks. Neural Networks 11(1), 65–80 (1998)

119. Zimmermann, H.J.: Fuzzy Sets: Decision Making and Expert Systems. Kluwer AcademicPublishers, Boston (1987)

Websites

ftp : //wuarchive.wustl.edu:/doc/techreports/wustl.edu/math/wawa.ps.Zhttp : //en.wikipedia.org/wiki/Wavelethttp : //wavelet tutorial/rabipolikar/rowan(tutorials)http : //www.amara.com/IEEE Wave/IEEEWavelet.html.http : //www.amara.com/current/wavelet.html.http : //www.amara.com/concurrent/wavelet.htmlhttp : //perso.wanadoo.fr/polyvalens/clemens/wavelets/wavelets(tutorials)http : //www.wavelet.org.

Retract

ed

Appendix A: MicroARTMAP MATLABImplementation

MicroARTMAP has two modes of operation:

TRAINING: input/output pairs are provided to learn the relation between them, andthis knowledge is stored in weight matrices.

TEST: input is provided, together with weight matrices, and the output is estimated.

Parameters of MicroARTMAP

beta rho beta rho 1 2 rho----A--- ----B--- entropy step

parameter mic=[1.0 0.0 1.0 1.0 0 0.08 0.02]’;

MicroARTMAP admits the following commands:

MAINTENANCE

MicroARTMAP(‘create’, TAG, PAR, WA, WB, WAB)MicroARTMAP(‘destroy’, TAG)LIST=MicroARTMAP(‘list’)MicroARTMAP(‘set parameters’, TAG, PAR)PAR=MicroARTMAP(‘get parameters’, PAR)MicroARTMAP(‘set weights’, TAG, WA, WB, WAB)[WA WB WAB]= MicroARTMAP(‘get weights’, TAG)USED=MicroARTMAP(’get used’, TAG)

OPERATION

MicroARTMAP(’train’, TAG, C, INP, OUT)OUT=MicroARTMAP(’test’, TAG, INP)

DOCUMENTATION

MicroARTMAP(’ver’)

Parameters are as follows:

TAG is a string of at most 10 characters.PAR is the parameters vector.

V.K. David and S. Rajasekaran: Pattern Recog. Using Neural & Funct. Net., SCI 160, pp. 143–154.springerlink.com c© Springer-Verlag Berlin Heidelberg 2009

Retract

ed

144 MicroARTMAP MATLAB Implementation

WA, WB and WAB are weights matrices.INP is a matrix with input data, each row a pattern.OUT is a matrix with the output data, each row a pattern.LIST is a character arrayUSED is [Na Nb], the number of units used in ARTa and ARTb

The input matrix INP and the output matrix OUT contain a pattern in each row,and therefore have the same number of rows. Also all input and output elements arenormalised to [0,1].

If NaN are present in matrix INP in either test or incremental learning modes, corre-sponding entry in matrix OUT will be NaN. Also unpredicted samples will be a row ofNaN in matrix OUT.

WA contains weights of input module, and it is an M by N matrix where N must betwo times the number of columns of INP, and M is the maximum number of memoryunits.

WB contains weights of output module, and it is an M by N matrix where N must betwo times the number of columns of OUT, and M is the maximum number of memoryunits.

WAB contains weights of inter-ART map, and it is matrix of Ma, the number ofrows in WA, by Mb, the number of rows in WB. It contains frequencies of associationsbetween ARTa and ARTb categories.

All weights are initialised to 1 before first learning.PAR is a column vector containing the following eight parameters:

input module: BETA : learning rate (w,v weights) [0,1]

RHO : vigilance factor [0,1]

output module: BETA : learning rate (w,v weights) [0,1]

RHO : vigilance factor [0,1]

control or error: h max : maximum contribution to entropy [0,infty]

H max : maximum entropy [0,infty]

RHOstep: step for incrementing RHO [0,1]

TAG can have any values, only ‘all’ is reserved.MICRO(‘destroy’, ‘all’) clears all networks from memory.MICRO(‘ver’) prints MEX file versionMICRO is case sensitive to commands and tags.

EXAMPLE

INP=[...]; OUT=[...];PAR=[1.0 0.0 1.0 0.9 0.0 0.1 0.02]’;[Mi Ni]=size(INP);[Mo No]=size(OUT);UnitsA=501;UnitsB=501;

Retract

ed

MicroARTMAP MATLAB Implementation 145

WA=ones(UnitsA, 2*Ni);WB=ones(UnitsB, 2*No);WAB=ones(UnitsA,1);Create NETMICRO(‘create’, ‘net1’, WA, WB, WAB);List existing networkslist=MICRO(‘list’)Train networkMICRO(‘train’, ‘net1’, INP, SUP)Get weights[WA WB WAB]=MICRO(‘get weights’, ‘net1’);Test on some inputINP=[...];OUT=MICRO(‘test’, ‘net1’, INP);Destroy networkMICRO(‘destroy’, ‘net1’)Clear MEX fileclear micro

handpgm1.m

A = [0 0 1 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1;1 0 1 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1;0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1;0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1;0 0 1 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1;0 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1;0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1;0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1;0 0 1 0 0 0 1 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1;0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1];

B = [1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0;0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0;1 0 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0;1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0;1 1 1 0 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0;1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0;1 1 1 1 0 0 0 0 0 1 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0;1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0;1 1 1 1 0 1 0 1 0 1 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0;1 1 1 1 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0];

C = [0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0;1 1 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0;0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0;0 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0;

Retract

ed


0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0;0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0;0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0;0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0;0 1 1 1 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0;0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0];

D = [1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0;0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0;1 0 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0;1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0;1 1 1 0 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0;1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0;1 1 1 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0;1 1 1 1 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0;1 1 1 1 0 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0;1 1 1 1 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0];

E = [1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1;0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1;1 0 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1;1 1 0 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1;1 1 1 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1;1 1 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1;1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1;1 1 1 1 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1;1 1 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1;1 1 1 1 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1];

F = [1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0;0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0;1 0 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0;1 1 0 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0;1 1 1 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0;1 1 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0;1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0;1 1 1 1 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0;1 1 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0;1 1 1 1 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0];

G = [0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0;1 1 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0;0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0;0 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0;0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0;

Retract

ed


0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0;0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0;0 1 1 1 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0;0 1 1 1 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0;0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0];

H = [1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1;0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1;1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1;1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1;1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1;1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1;1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1;1 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1;1 0 0 0 1 1 0 1 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1;1 0 0 0 1 1 0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1];

I = [1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 1 1;0 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 1 1;1 0 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 1 1;1 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 1 1;1 1 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 1 1;1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 1 1;1 1 1 1 1 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 1 1;1 1 1 1 1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 1 1;1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 1 1;1 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 1 1];

J = [1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0;0 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0;1 0 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0;1 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0;1 1 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0;1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0;1 1 1 1 1 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0;1 1 1 1 1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0;1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0;1 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0];

K = [1 0 0 1 0 1 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0;0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0;1 1 0 1 0 1 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0;1 0 1 1 0 1 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0;1 0 0 0 0 1 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0;1 0 0 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0;1 0 0 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0;

Retract

ed


1 0 0 1 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0;1 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0;1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0];

L = [1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1;0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1;1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1;1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1;1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1;1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1;1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1;1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1;1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1;1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1];

M = [1 0 0 0 1 1 1 0 1 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1;0 0 0 0 1 1 1 0 1 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1;1 1 0 0 1 1 1 0 1 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1;1 0 1 0 1 1 1 0 1 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1;1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1;1 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1;1 0 0 0 1 0 1 0 1 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1;1 0 0 0 1 1 0 0 1 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1;1 0 0 0 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1;1 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1];

N = [0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0;1 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0;0 1 0 0 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0;0 0 1 0 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0;0 0 0 1 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0;0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0;0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0;0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0;0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0;0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0];

O = [0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0;1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0;0 0 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0;0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0;0 1 1 0 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0;0 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0;0 1 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0;0 1 1 1 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0;

Retract

ed


0 1 1 1 0 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0;0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0];

P = [1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0;0 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0;1 0 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0;1 1 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0;1 1 1 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0;1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0;1 1 1 1 1 0 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0;1 1 1 1 1 1 1 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0;1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0;1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0];

Q = [0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1;1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1;0 0 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1;0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1;0 1 1 0 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1;0 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1;0 1 1 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1;0 1 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1;0 1 1 1 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1;0 1 1 1 0 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1];

R = [1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0;0 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0;1 0 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0;1 1 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0;1 1 1 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0;1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0;1 1 1 1 1 0 0 0 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0;1 1 1 1 1 1 1 0 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0;1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0;1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0];

S = [0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0;1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0;0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0;0 1 0 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0;0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0;0 1 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0;0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0;0 1 1 1 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0;0 1 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0;0 1 1 1 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0];

Retract

ed


T = [1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0;0 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0;1 0 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0;1 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0;1 1 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0;1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0;1 1 1 1 1 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0;1 1 1 1 1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0;1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0;1 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0];

U = [1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0;0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0;1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0;1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0;1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0;1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0;1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0;1 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0;1 0 0 0 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0;1 0 0 0 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0];

V = [0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0;1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0;0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0;0 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0;0 0 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0;0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0;0 0 0 0 0 1 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0;0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0;0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0];

W = [1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0 1;0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0 1;1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0 1;1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0 1;1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0 1;1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0 1;1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0 1;1 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0 1;1 0 0 0 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0 1;1 0 0 0 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0 1];

Retract

ed


X = [1 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1;0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1;1 1 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1;1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1;1 0 0 1 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1;1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1;1 0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1;1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1;1 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1;1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1];

Y = [1 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0;0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0;1 1 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0;1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0;1 0 0 1 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0;1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0;1 0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0;1 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0;1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0;1 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0];

Z = [1 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;1 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;1 1 0 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;1 1 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;1 1 1 1 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;1 1 1 1 1 0 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;1 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0];

PA = [1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1;0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1;1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1;1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1;1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1;1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1;1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1;1 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1;1 0 0 0 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1;1 0 0 0 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1];

Retract

ed


MA = [1 0 1 1 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1;0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1;1 1 1 1 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1;1 0 0 1 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1;1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1;1 0 1 1 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1;1 0 1 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1;1 0 1 1 1 1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1;1 0 1 1 1 1 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1;1 0 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1];

YA = [1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1;0 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1;1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1;1 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1;1 0 1 1 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1;1 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1;1 0 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1;1 0 1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1;1 0 1 0 1 1 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1;1 0 1 0 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1];

LA = [1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1;0 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1;1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1;1 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1;1 0 1 1 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1;1 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1;1 0 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1;1 0 1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1;1 0 1 0 1 1 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1;1 0 1 0 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1];

INP = [A’ B’ C’ D’ E’ F’ G’ H’ I’ J’ K’ L’ M’ N’ O’ P’ Q’ R’ S’ T’ U’ V’W’ X’ Y’ Z’ PA’ MA’ YA’ LA’]’;a1 = [0 0 0 0 1; 0 0 0 0 1; 0 0 0 0 1; 0 0 0 0 1; 0 0 0 0 1; 0 0 0 0 1; 0 0 00 1; 0 0 0 0 1; 0 0 0 0 1; 0 0 0 0 1];a2 = [0 0 0 1 0; 0 0 0 1 0; 0 0 0 1 0; 0 0 0 1 0; 0 0 0 1 0; 0 0 0 1 0; 0 0 01 0; 0 0 0 1 0; 0 0 0 1 0; 0 0 0 1 0];a3 = [0 0 0 1 1; 0 0 0 1 1; 0 0 0 1 1; 0 0 0 1 1; 0 0 0 1 1; 0 0 0 1 1; 0 0 01 1; 0 0 0 1 1; 0 0 0 1 1; 0 0 0 1 1];a4 = [0 0 1 0 0; 0 0 1 0 0; 0 0 1 0 0; 0 0 1 0 0; 0 0 1 0 0; 0 0 1 0 0; 0 0 10 0; 0 0 1 0 0; 0 0 1 0 0; 0 0 1 0 0];a5 = [0 0 1 0 1; 0 0 1 0 1; 0 0 1 0 1; 0 0 1 0 1; 0 0 1 0 1; 0 0 1 0 1; 0 0 10 1; 0 0 1 0 1; 0 0 1 0 1; 0 0 1 0 1];

Retract

ed


a6 = [0 0 1 1 0; 0 0 1 1 0; 0 0 1 1 0; 0 0 1 1 0; 0 0 1 1 0; 0 0 1 1 0; 0 0 11 0; 0 0 1 1 0; 0 0 1 1 0; 0 0 1 1 0];a7 = [0 0 1 1 1; 0 0 1 1 1; 0 0 1 1 1; 0 0 1 1 1; 0 0 1 1 1; 0 0 1 1 1; 0 0 11 1; 0 0 1 1 1; 0 0 1 1 1; 0 0 1 1 1];a8 = [0 1 0 0 0; 0 1 0 0 0; 0 1 0 0 0; 0 1 0 0 0; 0 1 0 0 0; 0 1 0 0 0; 0 1 00 0; 0 1 0 0 0; 0 1 0 0 0; 0 1 0 0 0];a9 = [0 1 0 0 1; 0 1 0 0 1; 0 1 0 0 1; 0 1 0 0 1; 0 1 0 0 1; 0 1 0 0 1; 0 1 00 1; 0 1 0 0 1; 0 1 0 0 1; 0 1 0 0 1];a10 = [0 1 0 1 0; 0 1 0 1 0; 0 1 0 1 0; 0 1 0 1 0; 0 1 0 1 0; 0 1 0 1 0; 0 1 01 0; 0 1 0 1 0; 0 1 0 1 0; 0 1 0 1 0];a11 = [0 1 0 1 1; 0 1 0 1 1; 0 1 0 1 1; 0 1 0 1 1; 0 1 0 1 1; 0 1 0 1 1; 0 1 01 1; 0 1 0 1 1; 0 1 0 1 1; 0 1 0 1 1];a12 = [0 1 1 0 0; 0 1 1 0 0; 0 1 1 0 0; 0 1 1 0 0; 0 1 1 0 0; 0 1 1 0 0; 0 1 10 0; 0 1 1 0 0; 0 1 1 0 0; 0 1 1 0 0];a13 = [0 1 1 0 1; 0 1 1 0 1; 0 1 1 0 1; 0 1 1 0 1; 0 1 1 0 1; 0 1 1 0 1; 0 1 10 1; 0 1 1 0 1; 0 1 1 0 1; 0 1 1 0 1];a14 = [0 1 1 1 0; 0 1 1 1 0; 0 1 1 1 0; 0 1 1 1 0; 0 1 1 1 0; 0 1 1 1 0; 0 1 11 0; 0 1 1 1 0; 0 1 1 1 0; 0 1 1 1 0];a15 = [0 1 1 1 1; 0 1 1 1 1; 0 1 1 1 1; 0 1 1 1 1; 0 1 1 1 1; 0 1 1 1 1; 0 1 11 1; 0 1 1 1 1; 0 1 1 1 1; 0 1 1 1 1];a16 = [1 0 0 0 0; 1 0 0 0 0; 1 0 0 0 0; 1 0 0 0 0; 1 0 0 0 0; 1 0 0 0 0; 1 0 00 0; 1 0 0 0 0; 1 0 0 0 0; 1 0 0 0 0];a17 = [1 0 0 0 1; 1 0 0 0 1; 1 0 0 0 1; 1 0 0 0 1; 1 0 0 0 1; 1 0 0 0 1; 1 0 00 1; 1 0 0 0 1; 1 0 0 0 1; 1 0 0 0 1];a18 = [1 0 0 1 0; 1 0 0 1 0; 1 0 0 1 0; 1 0 0 1 0; 1 0 0 1 0; 1 0 0 1 0; 1 0 01 0; 1 0 0 1 0; 1 0 0 1 0; 1 0 0 1 0];a19 = [1 0 0 1 1; 1 0 0 1 1; 1 0 0 1 1; 1 0 0 1 1; 1 0 0 1 1; 1 0 0 1 1; 1 0 01 1; 1 0 0 1 1; 1 0 0 1 1; 1 0 0 1 1];a20 = [1 0 1 0 0; 1 0 1 0 0; 1 0 1 0 0; 1 0 1 0 0; 1 0 1 0 0; 1 0 1 0 0; 1 0 10 0; 1 0 1 0 0; 1 0 1 0 0; 1 0 1 0 0];a21 = [1 0 1 0 1; 1 0 1 0 1; 1 0 1 0 1; 1 0 1 0 1; 1 0 1 0 1; 1 0 1 0 1; 1 0 10 1; 1 0 1 0 1; 1 0 1 0 1; 1 0 1 0 1];a22 = [1 0 1 1 0; 1 0 1 1 0; 1 0 1 1 0; 1 0 1 1 0; 1 0 1 1 0; 1 0 1 1 0; 1 0 11 0; 1 0 1 1 0; 1 0 1 1 0; 1 0 1 1 0];a23 = [1 0 1 1 1; 1 0 1 1 1; 1 0 1 1 1; 1 0 1 1 1; 1 0 1 1 1; 1 0 1 1 1; 1 0 11 1; 1 0 1 1 1; 1 0 1 1 1; 1 0 1 1 1];a24 = [1 1 0 0 0; 1 1 0 0 0; 1 1 0 0 0; 1 1 0 0 0; 1 1 0 0 0; 1 1 0 0 0; 1 1 00 0; 1 1 0 0 0; 1 1 0 0 0; 1 1 0 0 0];a25 = [1 1 0 0 1; 1 1 0 0 1; 1 1 0 0 1; 1 1 0 0 1; 1 1 0 0 1; 1 1 0 0 1; 1 1 00 1; 1 1 0 0 1; 1 1 0 0 1; 1 1 0 0 1];a26 = [1 1 0 1 0; 1 1 0 1 0; 1 1 0 1 0; 1 1 0 1 0; 1 1 0 1 0; 1 1 0 1 0; 1 1 01 0; 1 1 0 1 0; 1 1 0 1 0; 1 1 0 1 0];a27 = [1 1 0 1 1; 1 1 0 1 1; 1 1 0 1 1; 1 1 0 1 1; 1 1 0 1 1; 1 1 0 1 1; 1 1 01 1; 1 1 0 1 1; 1 1 0 1 1; 1 1 0 1 1];

Retract

ed


a28 = [1 1 1 0 0; 1 1 1 0 0; 1 1 1 0 0; 1 1 1 0 0; 1 1 1 0 0; 1 1 1 0 0; 1 1 10 0; 1 1 1 0 0; 1 1 1 0 0; 1 1 1 0 0];a29 = [1 1 1 0 1; 1 1 1 0 1; 1 1 1 0 1; 1 1 1 0 1; 1 1 1 0 1; 1 1 1 0 1; 1 1 10 1; 1 1 1 0 1; 1 1 1 0 1; 1 1 1 0 1];a30 = [1 1 1 1 0; 1 1 1 1 0; 1 1 1 1 0; 1 1 1 1 0; 1 1 1 1 0; 1 1 1 1 0; 1 1 11 0; 1 1 1 1 0; 1 1 1 1 0; 1 1 1 1 0];OUT = [a1’ a2’ a3’ a4’ a5’ a6’ a7’ a8’ a9’ a10’ a11’ a12’ a13’ a14’ a15’ a16’a17’ a18’ a19’ a20’ a21’ a22’ a23’ a24’ a25’ a26’ a27’ a28’ a29’ a30’]’

ticTAG=(‘SALO1’);PAR=[1.0 0.0 1.0 1.0 0 0.08 0.002]’;[Mi Ni]=size(INP);[Mo No]=size(OUT);

UnitsA=3;UnitsB=3;WA=ones(UnitsA, 2*Ni);WB=ones(UnitsB, 2*No);WAB=(ones(UnitsA,UnitsB));MICRO(‘create’, TAG, PAR, WA, WB, WAB)

LIST=MICRO(‘list’)MICRO(‘train’, TAG, INP, OUT)OUT=MICRO(‘test’, TAG , INP);for i=1:4INP1=input(‘enter the leter code’);OUT1=MICRO(‘test’, TAG , INP1)

endtoc

Retract

ed

Appendix B: DWT on db1 Wavelets - number.m

Inputs to MicroArtMap using DWT on db1 wavelet on handwritten numbers

zer=[1 0 1 1 1 1 0 0 1 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 00 0 1 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0;

1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 00 1 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0;

1 0 0 1 1 1 0 0 1 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 00 1 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0;

1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 00 1 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0;

1 0 1 1 0 1 0 0 1 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 00 1 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0];

one=[0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 10 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0;

0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 00 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0;

0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 00 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 00 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0;

0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 00 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0;]

two=[ 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 00 1 1 0 0 0 1 0 0 0 1 1 0 0 1 1 1 0 1 1 0 0 0 1 1 1 1 0 0;

0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 01 1 0 0 0 1 0 0 0 1 1 0 0 1 1 1 0 1 1 0 0 0 1 1 1 1 0 0;

0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 01 1 0 0 0 1 0 0 0 1 1 0 0 1 1 1 0 1 1 0 0 0 1 1 1 1 0 0;

0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0


Retract

ed

156 DWT on db1 Wavelets - number.m

1 1 0 0 0 1 0 0 0 1 1 0 0 1 1 1 0 1 1 0 0 0 1 1 1 1 0 0;0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0

1 1 0 0 0 1 0 0 0 1 1 0 0 1 1 1 0 1 1 0 0 0 1 1 1 1 0 0;]

thr=[0 1 1 1 1 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 00 1 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0;

0 0 1 1 1 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 01 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0;

0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 01 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0;

0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 01 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0;

0 1 1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 01 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0];

fou=[ 0 1 1 1 1 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 00 1 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0;

0 0 1 1 1 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 01 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0;

0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 01 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0;

0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 01 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0;

0 1 1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 01 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0];

fiv=[0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 11 1 1 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1;

0 0 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 1 11 1 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1;

0 1 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 1 11 1 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1;

0 1 1 0 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 1 11 1 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1;

0 1 1 1 0 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 1 11 1 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1];

six=[0 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 0 0 1 1 00 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0;

0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 0 0 1 1 0 00 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0;

0 0 0 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 0 0 1 1 0 00 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0;

0 0 1 0 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 0 0 1 1 0 00 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0;

Retract

ed

DWT on db1 Wavelets - number.m 157

0 0 1 1 0 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 0 0 1 1 0 00 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0];

sev=[0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 01 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0;

0 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 11 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0;

0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 11 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0;

0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 11 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0;

0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 11 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0];

eig=[0 1 1 1 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 11 1 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 0 0 0 0 1 1 1 1 0 0;

0 0 1 1 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 11 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 0 0 0 0 1 1 1 1 0 0;

0 1 0 1 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 11 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 0 0 0 0 1 1 1 1 0 0;

0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 11 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 0 0 0 0 1 1 1 1 0 0;

0 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 11 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 0 0 0 0 1 1 1 1 0 0];

nin=[0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 1 1 01 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 0 0;

0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 11 0 0 0 1 1 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 0 0;

0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 11 0 0 0 1 1 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 0 0;

0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 11 0 0 0 1 1 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 0 0;

0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 11 0 0 0 1 1 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 0 0];

INP=[zer’ one’ two’ thr’ fou’ fiv’ six’ sev’ eig’ nin’]’for i=1:50

Y=INP(i,1:64);[ca1 cd]=dwt(Y,‘db1’);

[ca2 cd]=dwt(ca1,‘db1’);[ca3 cd]=dwt(ca2,‘db1’);INP1(i,1:8)=ca3;

end

Retract

ed

158 DWT on db1 Wavelets - number.m

zer1=[0 0 0 0 1; 0 0 0 0 1; 0 0 0 0 1; 0 0 0 0 1; 0 0 0 0 1];one1=[0 0 0 1 0; 0 0 0 1 0; 0 0 0 1 0; 0 0 0 1 0; 0 0 0 1 0];two1=[0 0 0 1 1; 0 0 0 1 1; 0 0 0 1 1; 0 0 0 1 1; 0 0 0 1 1];thr1=[0 0 1 0 0; 0 0 1 0 0; 0 0 1 0 0; 0 0 1 0 0; 0 0 1 0 0];fou1=[0 0 1 0 1; 0 0 1 0 1; 0 0 1 0 1; 0 0 1 0 1; 0 0 1 0 1];fiv1=[0 0 1 1 0; 0 0 1 1 0; 0 0 1 1 0; 0 0 1 1 0; 0 0 1 1 0];six1=[0 0 1 1 1; 0 0 1 1 1; 0 0 1 1 1; 0 0 1 1 1; 0 0 1 1 1];sev1=[0 1 0 0 0; 0 1 0 0 0; 0 1 0 0 0; 0 1 0 0 0; 0 1 0 0 0];eig1=[0 1 0 0 1; 0 1 0 0 1; 0 1 0 0 1; 0 1 0 0 1; 0 1 0 0 1];nin1=[0 1 0 1 0; 0 1 0 1 0; 0 1 0 1 0; 0 1 0 1 0; 0 1 0 1 0];

OUT=[zer1’ one1’ two1’ thr1’ fou1’ fiv1’ six1’ sev1’ eig1’ nin1’]’ticTAG=(‘SALO1’);PAR=[1.0 0.0 1.0 1.0 0 0.08 0.002]’;[Mi Ni]=size(INP1);[Mo No]=size(OUT);UnitsA=3;UnitsB=3;WA=ones(UnitsA, 2*Ni);WB=ones(UnitsB, 2*No);WAB=(ones(UnitsA,UnitsB));MICRO(‘create’, TAG, PAR, WA, WB, WAB)

LIST=MICRO(‘list’)MICRO(‘train’, TAG, INP1, OUT)OUT=MICRO(‘test’, TAG , INP1)

INP2=[1.7678 1.7678 1.0607 0.7071 0.7071 1.0607 1.4142 1.3];

OUT1=MICRO(‘test’, TAG , INP2)toc

Retract

ed

Appendix C: Inputs to ARTMAP for Signatures

Eight features obtained for each sample signature by Block Processing

I=imread(‘E:\sample of vasantha(wavwmenu)\sample n\n1’);a=imresize(I,[200,200],’nearest’);imshow(I);figure;imshow(a);

BW = im2bw(I,0.8);imshow(BW);i1=BW(1:100,1:50);i2=BW(1:100,51:100);i3=BW(1:100,101:150);i4=BW(1:100,151:200);i5=BW(101:200,1:50);i6=BW(101:200,51:100);i7=BW(101:200,101:150);i8=BW(101:200,151:200);figure;imshow(i1);figure;imshow(i2);figure;imshow(i3);figure;imshow(i4);figure;imshow(i5);figure;imshow(i6);figure;imshow(i7);figure;imshow(i8);

c1=0;c2=0;c3=0;c4=0;c5=0;c6=0;c7=0;c8=0;


Retract

ed

160 Inputs to ARTMAP for Signatures

for i=1:100for j=1:50

if i1(i,j)==0c1=c1+1;

endend

endfor i=1:100

for j=1:50if i2(i,j)==0

c2=c2+1;end

endendfor i=1:100

for j=1:50if i3(i,j)==0

c3=c3+1;end

endendfor i=1:100

for j=1:50if i4(i,j)==0c4=c4+1;

endend

endfor i=1:100

for j=1:50if i5(i,j)==0

c5=c1+1;end

endendfor i=1:100

for j=1:50if i6(i,j)==0

c6=c2+1;end

endendfor i=1:100

for j=1:50if i7(i,j)==0

Retract

ed

Inputs to ARTMAP for Signatures 161

c7=c3+1;end

endendfor i=1:100

for j=1:50if i8(i,j)==0

c8=c4+1;end

endend

c1c2c3c4c5c6c7c8

Inputs to MicroARTMAP by Block Processing for Signatures

a = [151 200 601 628 152 201 602 629];b = [ 0 0 469 518 1 1 470 0 ];c = [3 3 511 764 4 4 512 768];d = [ 0 0 402 450 1 1 403 451];e = [150 187 717 578 151 188 718 579];f = [0 18 590 517 1 19 591 0];g = [ 82 52 621 893 83 53 622 894];h = [ 1 108 668 611 2 109 669 612];INP = [a’ b’ c’ d’ e’ f’ g’ h’]’;a1 = [0 0 0 0 1];b1 = [0 0 0 1 0];c1 = [0 0 0 1 1];d1 = [0 0 1 0 0];e1 = [0 0 1 0 1];f1 = [0 0 1 1 0];g1 = [0 0 1 1 1];h1 = [0 1 0 0 0];

OUT = [a1’ b1’ c1’ d1’ e1’ f1’ g1’ h1’]’;

ticTAG=(‘SALO1’);PAR=[1.0 0.0 1.0 1.0 0 0.08 0.002]’;

Retract

ed

162 Inputs to ARTMAP for Signatures

[Mi Ni]=size(INP);[Mo No]=size(OUT);UnitsA=3;UnitsB=3;WA=ones(UnitsA, 2*Ni);WB=ones(UnitsB, 2*No);WAB=(ones(UnitsA,UnitsB));MICRO(‘create’, TAG, PAR, WA, WB, WAB)LIST=MICRO(‘list’)MICRO(‘train’, TAG, INP, OUT)OUT=MICRO(‘test’, TAG , INP);INP1=[1 108 668 611 2 109 669 612];OUT1=MICRO(‘test’, TAG , INP1)toc

Retract

ed

Appendix D: The Competitive Hopfield Neural Network

# include <stdio.h># include <math.h># include <conio.h># include <time.h># include <stdlib.h># include <dos.h># include <string.h>

/* STEP 1 - INITIAL VALUE SETTING*/

int c2 = 4, c3 = 1, c5 = 3, c6 = 1;/*resource request matrix (Table 6)*/int r[5][4] = {{1, 0, 0, 0},{0, 1, 0, 0},{0, 0, 1, 0},{0, 0, 0, 1},{1, 0, 0, 1}};/* timing constraint matrix (Table 7)*/int T1[5][2]= {{2, 3},{5, 8},{3, 4},{4, 8},{2, 5}};/*initial state matrix (Table 8)*//*int V[2][5][8] ={{

{1, 1, 1, 0, 1, 0, 0, 0, 1, 0},

{1, 2, 0, 1, 0, 1, 0, 1, 0, 0},

{1, 3, 1, 0, 0, 0, 1, 1, 1, 1},

{1, 4, 0, 1, 1, 0, 1, 0, 0, 0},

{1, 5, 0, 1, 0, 1, 0, 1, 0, 1},

{2, 1, 1, 0, 1, 0, 1, 0, 1, 1},

{2, 2, 1, 0, 1, 0, 0, 1, 0, 0},

{2, 3, 0, 1, 0, 1, 0, 1, 0, 1},

{2, 4, 1, 0, 0, 0, 0, 0, 1, 0},

{2, 5, 0, 0, 0, 0, 1, 1, 1, 1}

}};*/


Retract

ed

164 The Competitive Hopfield Neural Network

int V[2][10][8] ={ {{1, 0, 1, 0, 0, 0, 1, 0}

{0, 1, 0, 1, 0, 1, 0, 0}

{1, 0, 0, 0, 1, 1, 1, 1}

{0, 1, 1, 0, 1, 0, 0, 0}

{0, 1, 0, 1, 0, 1, 0, 1}

{1, 0, 1, 0, 1, 0, 1, 1}

{1, 0, 1, 0, 0, 1, 0, 0}

{0, 1, 0, 1, 0, 1, 0, 1}

{1, 0, 0, 0, 0, 0, 1, 0}

{0, 0, 0, 0, 1, 1, 1, 1}

}};

int RxRi[10][10], Wxyzijl[5][5][5][5][5][5];/*N - Jobs, M - Machines, T - Time, F - resource*/int N, M, T, F;int x, i, s, y, z, j, k, l, yy, zz, i1, j1, k1,S;int resource, sum;float ec2, ec5, ec6, ec3, EA,Theta[5][5][5];int result[5][5][5], G[5][5][5];int deltax, deltaxy, deltaxz;int Net[5][5][5], Netxyz[5][5][5], Max;

/* ENERGY*/int energy(){

ec2=0;

ec5=0;

ec6=0;

ec3=0;

/* ec2 calculation*/for(i=1;i<=N;i++)

for(j=1;j<=M;j++)for (k=1;k<=T;k++)

for(j1=1;j1<=M;j1++)for(k1=1;k1<=T;k++)

if (j1 <= j)ec2 = ec2 + V[i][j][k] * V[i][j1][k1];

/* ec5 calculation */for (i=1;i<=N;i++)

Retract

ed

The Competitive Hopfield Neural Network 165


ec5 = ec5 + V[i][j][k] * (G[i][j][k] * G[i][j][k]) * result[i][j][k];

/* ec6 calculation */for (i=1;i<=N;i++)


for (i1=1;i1<=N;i1++)for (j1=1;j1<=M;j1++)

for (S=1;S<=F;S++)if ((i1 <= i) && (j1 <= j))

ec6 = ec6 + V[i][j][k] * r[i][S] * V[i1][j1][k] * r[i1][S];

/* ec3 calculation */for(i=1;i<=N;i++){

sum =0;for(j=1;j<=M;j++)

for (k=1;k<=T;k++)sum = sum + V[i][j][k];

ec3 = ec3 + (sum-T1[i][1])*(sum-T1[i][1]);}

ec2 = (c2/2) * ec2;ec5 = (c5/2) * ec5;ec6 = (c6/2) * ec6;ec3 = (c3/2) * ec3;

EA = ec2 + ec3 + ec5 + ec6;return EA;}

/*DELTA FUNCTION */int delta(int b, int c){

int a;if (b == c)

a = 1;else

a = 0;return a;

}

Retract

ed


/*HEVISIDE FUNCTION */int Hevi(b){

int a;if (b > 1)

a = 1;else

a = 0;return a;

}

void main(){

printf("Enter No. of jobs");scanf("%d",&N);printf("Enter No. of Machines");scanf("%d",&M);printf("Enter No. of resources");scanf("%d",&F);printf("Enter Time");scanf("%d",&T);

/* calculation of weight and theta matrix starts here(step 2)*/

/*the following loops computes the resource RxRi*/for(x=1;x<=N;x++)

{for (i=1;i<=N;i++)

{resource=0;for(S=1;S<=F;S++)

{RxRi[x][i] = resource + r[x][S] * r[i][S];resource = RxRi[x][i];

}}

}

/* CALCULATION OF WEIGHT MATRIX */for(x=1;x<=N;x++)

{for(y=1;y<<=M;y++)

{for(z=1;z<<=T;z++)

{for(i=1;i<<=N;i++)

Retract

ed

The Competitive Hopfield Neural Network 167

{for(j=1;j<<<=M;j++)

{for(l=1;l<<=T;l++)

{delta_x = delta(x,i);delta_y = delta(y,j);delta_z = delta(z,k);

}Wxyzijl[x][y][z][i][j][l] = -c2*delta_x * (1- delta_y) - c3 *

delta_x - c6*(1-delta_x)*(1-delta_y) * delta_z * RxRi[x][i];printf("Wxyzijk value is %d", Wxyzijl[x][y][z][i][j][l]);printf("press any key ...");getche();

}}

}}

}

/* CALCULATION OF THETA(x, y, z) - equation 7 */for (y=1;y<=M;y++)

{for (x=1;x<=N;x++)

{for(z=1;z<=T;z++)

{G[x][y][z]=z-T1[x][2]+1; /* T1(x,2) is deadline of jobs*/result[x][y][z] = Hevi(G[x][y][z]); /* heavside function */Theta[x][y][z]= -

c3*T1[x][1]+(c5/2)*(G[x][y][z]*G[x][y][z])* result[x][y][z];printf("Theta[x][y][z] %d= ",Theta[x][y][z]);printf("press any key ...");getche();

}}

}

/* STEP 3 recalling *//* initial energy value based on initial neuron states*/

EA = energy();/* calculate net output eqn 4 and adjust neuron state*/while ( abs(EA)<.0000001){ /* while loop starts here */for (yy=1;yy<=M;y++)

Retract

ed


for (zz=1;zz<=T;z++){ /* loop of zz starts here */for(x=1;x<=N;x++)for(y=1;y<=M;y++)for(z=1;z<=T;z++)

{Net[x][y][z] = 0;Netxyz[x][y][z] = 0;for(j=1;j<=M;j++)for(i=1;i<=N;i++)for(l=1;l<=T;l++)Netxyz[x][y][z] = Wxyzijl[x][y][z][i][j][l] * V[i][j][l] + Netxyz[x][y][z];Net[x][y][z] = Netxyz[x][y][z] - Theta[x][y][z];}

/* PICK LARGEST NET VALUE */Max=1; /* always 1*/for(x=2;x<=N;x++)if(Net[Max][yy][zz]<Net[x][yy][zz])Max=x;/* update the neuron states based onthe winner take it*/for(x=1;x<=N;x++)if (x == Max)V[x][yy][zz]=1;elseV[x][yy][zz] = 0;} /* loop of zz ends here *//*energy value based on updated neuron states */EA = energy();printf("Energy value =printf(’Press any key ...");getch();} /* while loop ends here */}

Retract

ed

Appendix E:Moment Invariants for Handwritten Characters

The characteristics obtained for samples using the program HPGMomout.m

φ1 φ2 φ3 φ4 φ5 φ6 φ7

.49175E+00 .13667E+00 .29460E-01 .15069E+00 .13739E-01 .55703E-01 -.17347E-17

.50320E+00 .14848E+00 .37433E-01 .16274E+00 .17352E-01 .62808E-01 .22835E-02

.49017E+00 .14221E+00 .36228E-01 .15100E+00 .14939E-01 .56930E-01 .13444E-02

.48652E+00 .13733E+00 .29446E-01 .14694E+00 .13640E-01 .54421E-01 .28189E-17

.50320E+00 .14848E+00 .37433E-01 .16274E+00 .17352E-01 .62808E-01 -.22835E-02

.47823E+00 .13061E+00 .27640E-01 .13883E+00 .11980E-01 .50226E-01 .71265E-03

.51654E+00 .15068E+00 .34829E-01 .17461E+00 .18480E-01 .67780E-01 .28790E-03

.46086E+00 .12242E+00 .26619E-01 .12471E+00 .96889E-02 .43607E-01 -.12143E-16

.47823E+00 .13061E+00 .27640E-01 .13883E+00 .11980E-01 .50226E-01 -.71265E-03

.52128E+00 .15567E+00 .40689E-01 .18011E+00 .20236E-01 .71057E-01 -.13573E-02

.47844E+00 .16473E+00 .55689E-01 .14866E+00 .18808E-01 .60172E-01 .00000E+00

.48329E+00 .16441E+00 .54477E-01 .15207E+00 .19304E-01 .61551E-01 -.34543E-02

.49262E+00 .16460E+00 .51448E-01 .15941E+00 .20118E-01 .64518E-01 -.13417E-02

.49418E+00 .16467E+00 .51349E-01 .16068E+00 .20242E-01 .65033E-01 .95577E-03

.48796E+00 .16446E+00 .53943E-01 .15569E+00 .19676E-01 .63005E-01 .31332E-02

.47561E+00 .16269E+00 .55137E-01 .14588E+00 .18239E-01 .58735E-01 -.36103E-02

.50273E+00 .18440E+00 .67334E-01 .17317E+00 .26059E-01 .74183E-01 -.28948E-02

.47844E+00 .16473E+00 .55689E-01 .14866E+00 .18808E-01 .60172E-01 .00000E+00

.44624E+00 .14686E+00 .48145E-01 .12159E+00 .12960E-01 .46458E-01 -.42772E-03

.49340E+00 .18460E+00 .70760E-01 .16567E+00 .24933E-01 .71007E-01 .46357E-02

.81576E+00 .56646E+00 .41498E+00 .78047E+00 .62240E+00 .58328E+00 .24980E-15

.77632E+00 .52787E+00 .37902E+00 .67917E+00 .48605E+00 .49044E+00 .61755E-01

.86265E+00 .57994E+00 .41078E+00 .89727E+00 .75618E+00 .67782E+00 -.63833E-01

.86343E+00 .57973E+00 .40304E+00 .89931E+00 .75174E+00 .67882E+00 .58997E-01

.84414E+00 .58579E+00 .42931E+00 .85444E+00 .72283E+00 .64915E+00 .18574E+00

.77632E+00 .52787E+00 .37902E+00 .67917E+00 .48605E+00 .49044E+00 .61755E-01

.86265E+00 .57994E+00 .41078E+00 .89727E+00 .75618E+00 .67782E+00 -.63833E-01

.86343E+00 .57973E+00 .40304E+00 .89931E+00 .75174E+00 .67882E+00 .58997E-01

.84414E+00 .58579E+00 .42931E+00 .85444E+00 .72283E+00 .64915E+00 .18574E+00

.79964E+00 .52625E+00 .37300E+00 .72515E+00 .52706E+00 .52359E+00 -.14237E+00

.89198E+00 .69288E+00 .57509E+00 .10280E+01 .11149E+01 .85092E+00 -.13677E+00


Retract

ed

170 Moment Invariants for Handwritten Characters

.73162E+00 .46798E+00 .31636E+00 .56895E+00 .33975E+00 .38619E+00 .68783E-02

.73113E+00 .46806E+00 .31670E+00 .56767E+00 .33907E+00 .38586E+00 -.14218E-01

.74328E+00 .46617E+00 .30882E+00 .58817E+00 .35212E+00 .39946E+00 -.40686E-01

.60128E+00 .25114E+00 .10084E+00 .29189E+00 .69518E-01 .14592E+00 .17347E-16

.61393E+00 .25680E+00 .10224E+00 .30864E+00 .76458E-01 .15620E+00 -.14023E-01

.62641E+00 .25779E+00 .96425E-01 .32470E+00 .80127E-01 .16452E+00 -.55759E-02

.62912E+00 .25810E+00 .96162E-01 .32832E+00 .80940E-01 .16642E+00 .33134E-02

.62207E+00 .25737E+00 .10081E+00 .31902E+00 .78779E-01 .16155E+00 .11735E-01

.58904E+00 .24247E+00 .96952E-01 .27471E+00 .62494E-01 .13505E+00 -.11489E-01

.63835E+00 .28736E+00 .12662E+00 .35085E+00 .10284E+00 .18764E+00 -.11993E-01

.55444E+00 .21877E+00 .84470E-01 .23064E+00 .44752E-01 .10758E+00 -.12884E-02

.55949E+00 .21933E+00 .83267E-01 .23584E+00 .45995E-01 .11016E+00 -.36919E-02

.62967E+00 .28709E+00 .13147E+00 .33937E+00 .99291E-01 .18144E+00 .17772E-01

.53850E+00 .23888E+00 .10981E+00 .22171E+00 .48501E-01 .10783E+00 .97145E-16

.54938E+00 .24361E+00 .11338E+00 .23378E+00 .53274E-01 .11483E+00 -.79068E-02

.55876E+00 .24220E+00 .10748E+00 .24292E+00 .54806E-01 .11893E+00 -.31033E-02

.55944E+00 .24211E+00 .10659E+00 .24363E+00 .54767E-01 .11923E+00 .29739E-02

.55144E+00 .24327E+00 .11083E+00 .23573E+00 .53252E-01 .11570E+00 .91064E-02

.53475E+00 .24660E+00 .12095E+00 .22009E+00 .50463E-01 .10899E+00 .14056E-01

.57110E+00 .27280E+00 .13606E+00 .26577E+00 .71100E-01 .13823E+00 -.64409E-02

.50028E+00 .21024E+00 .91887E-01 .17906E+00 .32271E-01 .81669E-01 .55492E-03

.49978E+00 .21028E+00 .92056E-01 .17860E+00 .32206E-01 .81516E-01 -.10775E-02

.50561E+00 .20980E+00 .90333E-01 .18322E+00 .33103E-01 .83584E-01 -.29418E-02

.53472E+00 .20262E+00 .92534E-01 .20414E+00 .38256E-01 .92844E-01 -.23469E-01

.56446E+00 .23453E+00 .12591E+00 .24034E+00 .58655E-01 .11894E+00 -.36004E-01

.57661E+00 .22978E+00 .11233E+00 .25285E+00 .58213E-01 .12312E+00 -.31285E-01

.57418E+00 .22243E+00 .10160E+00 .24919E+00 .52953E-01 .11869E+00 -.27686E-01

.55718E+00 .21296E+00 .93616E-01 .22976E+00 .44568E-01 .10655E+00 -.24037E-01

.52559E+00 .20471E+00 .90596E-01 .19813E+00 .35786E-01 .89794E-01 -.18932E-01

.58925E+00 .25688E+00 .14029E+00 .27524E+00 .75056E-01 .14176E+00 -.47279E-01

.47841E+00 .16286E+00 .66910E-01 .14682E+00 .19810E-01 .59709E-01 -.13032E-01

.48003E+00 .16505E+00 .69729E-01 .14831E+00 .20752E-01 .60890E-01 -.13439E-01

.49143E+00 .16920E+00 .72468E-01 .15773E+00 .23202E-01 .65738E-01 -.13819E-01

.64691E+00 .33424E+00 .17825E+00 .38051E+00 .13910E+00 .21913E+00 .87723E-02

.63205E+00 .32932E+00 .17992E+00 .35777E+00 .12761E+00 .20489E+00 .30829E-01

.66602E+00 .32396E+00 .15835E+00 .40455E+00 .14290E+00 .22909E+00 -.10370E-01

.66942E+00 .32465E+00 .15579E+00 .40970E+00 .14467E+00 .23227E+00 .17046E-01

.65824E+00 .32718E+00 .16708E+00 .39366E+00 .14179E+00 .22448E+00 .43035E-01

.64247E+00 .32726E+00 .17455E+00 .37123E+00 .13192E+00 .21178E+00 -.26864E-01

.68643E+00 .38530E+00 .22716E+00 .45912E+00 .21001E+00 .28381E+00 -.25579E-01

.59429E+00 .29012E+00 .14734E+00 .29745E+00 .87413E-01 .15964E+00 .10266E-01

.59201E+00 .28990E+00 .14758E+00 .29474E+00 .86338E-01 .15816E+00 .33665E-02

.59950E+00 .28909E+00 .14408E+00 .30316E+00 .88770E-01 .16250E+00 -.39003E-02

.53902E+00 .16358E+00 .33180E-01 .19826E+00 .23619E-01 .80183E-01 .62884E-17

Retract

ed

Moment Invariants for Handwritten Characters 171

.53570E+00 .16635E+00 .40896E-01 .19567E+00 .24633E-01 .79983E-01 .26074E-02

.52035E+00 .15349E+00 .31315E-01 .17865E+00 .19448E-01 .69997E-01 .49542E-03

.51646E+00 .15124E+00 .30375E-01 .17475E+00 .18562E-01 .67937E-01 -.34694E-17

.52035E+00 .15349E+00 .31315E-01 .17865E+00 .19448E-01 .69997E-01 -.49542E-03

.53570E+00 .16635E+00 .40896E-01 .19567E+00 .24633E-01 .79983E-01 -.26074E-02

.56337E+00 .17981E+00 .40355E-01 .22657E+00 .31431E-01 .96147E-01 .62226E-03

.50091E+00 .14130E+00 .26786E-01 .15916E+00 .15237E-01 .59813E-01 .47250E-04

.49703E+00 .13905E+00 .25998E-01 .15548E+00 .14511E-01 .57957E-01 -.12143E-16

.50091E+00 .14130E+00 .26786E-01 .15916E+00 .15237E-01 .59813E-01 -.47250E-04

.72593E+00 .67568E+00 .59691E+00 .64475E+00 .58152E+00 .52940E+00 .29143E-15

.73745E+00 .74530E+00 .70100E+00 .69585E+00 .71085E+00 .60058E+00 -.96497E-01

.75931E+00 .72382E+00 .66336E+00 .73139E+00 .74225E+00 .62155E+00 -.64862E-01

.76660E+00 .71714E+00 .65099E+00 .74383E+00 .75256E+00 .62896E+00 .24980E-15

.75931E+00 .72382E+00 .66336E+00 .73139E+00 .74225E+00 .62155E+00 .64862E-01

.73745E+00 .74530E+00 .70100E+00 .69585E+00 .71085E+00 .60058E+00 .96497E-01

.67795E+00 .55236E+00 .44112E+00 .51062E+00 .35181E+00 .37900E+00 .30219E-01

.66330E+00 .56163E+00 .45287E+00 .49119E+00 .33752E+00 .36766E+00 .12733E-01

.80305E+00 .81042E+00 .78387E+00 .86594E+00 .10390E+01 .77851E+00 -.36082E-15

.66330E+00 .56163E+00 .45287E+00 .49119E+00 .33752E+00 .36766E+00 -.12733E-01

.75507E+00 .77854E+00 .77234E+00 .74469E+00 .83655E+00 .65772E+00 -.19750E+00

.78858E+00 .93890E+00 .10323E+01 .88075E+00 .12479E+01 .85766E+00 -.40880E+00

.81404E+00 .89942E+00 .96553E+00 .92517E+00 .12848E+01 .88020E+00 -.40248E+00

.81944E+00 .88274E+00 .92976E+00 .93316E+00 .12678E+01 .87803E+00 -.33124E+00

.80478E+00 .88740E+00 .92440E+00 .90319E+00 .12057E+01 .85093E+00 -.21590E+00

.77006E+00 .91736E+00 .95038E+00 .84066E+00 .11059E+01 .80403E+00 -.81273E-01

.68691E+00 .59386E+00 .51620E+00 .54284E+00 .42657E+00 .41814E+00 -.85303E-01

.67088E+00 .60823E+00 .53541E+00 .52200E+00 .41353E+00 .40718E+00 -.90634E-01

.86034E+00 .99928E+00 .11152E+01 .10935E+01 .17669E+01 .10946E+01 -.43421E+00

.67671E+00 .61017E+00 .54534E+00 .53127E+00 .42988E+00 .41535E+00 -.11052E+00

.59242E+00 .35781E+00 .22487E+00 .31969E+00 .12196E+00 .18963E+00 -.69389E-17

.59491E+00 .33320E+00 .20477E+00 .31476E+00 .11256E+00 .17944E+00 -.16690E-01

.56884E+00 .35768E+00 .22826E+00 .29221E+00 .10839E+00 .17359E+00 -.21426E-02

.57613E+00 .35546E+00 .22683E+00 .29949E+00 .11187E+00 .17740E+00 -.14747E-01

.56019E+00 .35255E+00 .23339E+00 .27886E+00 .10180E+00 .16545E+00 .41659E-01

.62860E+00 .34653E+00 .21453E+00 .36035E+00 .13942E+00 .21043E+00 -.61747E-01

.64506E+00 .41887E+00 .28643E+00 .41098E+00 .20145E+00 .26381E+00 -.14097E-01

.53725E+00 .30532E+00 .17880E+00 .24207E+00 .72119E-01 .13271E+00 -.22027E-02

.64198E+00 .42037E+00 .28795E+00 .40758E+00 .19871E+00 .26147E+00 .33890E-01

.56446E+00 .29825E+00 .16770E+00 .26731E+00 .80146E-01 .14506E+00 -.17795E-01

.81159E+00 .65449E+00 .74029E+00 .79060E+00 .88875E+00 .65180E+00 .79900E+00

.72222E+00 .43028E+00 .42081E+00 .51711E+00 .33902E+00 .34942E+00 .26351E+00

.82562E+00 .74857E+00 .82120E+00 .87398E+00 .10803E+01 .76185E+00 .81931E+00

.83565E+00 .71949E+00 .72921E+00 .89155E+00 .10409E+01 .75690E+00 .71706E+00

.86265E+00 .69018E+00 .62899E+00 .95117E+00 .10525E+01 .78523E+00 .62908E+00

Retract

ed


.90664E+00 .66684E+00 .52785E+00 .10640E+01 .11112E+01 .85560E+00 .52656E+00

.82756E+00 .61248E+00 .71031E+00 .81365E+00 .90884E+00 .64777E+00 .85827E+00

.76466E+00 .61456E+00 .62343E+00 .67852E+00 .63877E+00 .53843E+00 .51441E+00

.77469E+00 .59223E+00 .55562E+00 .69383E+00 .61946E+00 .53769E+00 .46783E+00

.80170E+00 .56968E+00 .47798E+00 .74512E+00 .63194E+00 .56302E+00 .44419E+00

.57376E+00 .18627E+00 .41024E-01 .24007E+00 .34786E-01 .10335E+00 .16480E-16

.58420E+00 .19418E+00 .47181E-01 .25341E+00 .39592E-01 .11156E+00 -.14767E-02

.54481E+00 .17099E+00 .38516E-01 .20680E+00 .26612E-01 .85193E-01 .10875E-02

.54092E+00 .16901E+00 .37925E-01 .20266E+00 .25605E-01 .82960E-01 .29490E-16

.54481E+00 .17099E+00 .38516E-01 .20680E+00 .26612E-01 .85193E-01 -.10875E-02

.58420E+00 .19418E+00 .47181E-01 .25341E+00 .39592E-01 .11156E+00 .14767E-02

.60862E+00 .21121E+00 .51768E-01 .28674E+00 .50579E-01 .13161E+00 -.24347E-02

.62522E+00 .22064E+00 .52666E-01 .30995E+00 .57930E-01 .14543E+00 -.67508E-03

.52378E+00 .15628E+00 .32235E-01 .18337E+00 .20473E-01 .72160E-01 .00000E+00

.62522E+00 .22064E+00 .52666E-01 .30995E+00 .57930E-01 .14543E+00 .67508E-03

.52202E+00 .19586E+00 .72119E-01 .19291E+00 .31777E-01 .85197E-01 -.44309E-02

.53337E+00 .18441E+00 .62908E-01 .19860E+00 .30625E-01 .85616E-01 -.11046E-01

.51442E+00 .16358E+00 .45956E-01 .17630E+00 .22084E-01 .71395E-01 -.49529E-02

.50810E+00 .15622E+00 .39571E-01 .16921E+00 .19397E-01 .66833E-01 -.18258E-02

.51442E+00 .16126E+00 .42080E-01 .17600E+00 .21140E-01 .70591E-01 .86578E-03

.53337E+00 .17977E+00 .54950E-01 .19799E+00 .28444E-01 .83892E-01 .55177E-02

.53086E+00 .21744E+00 .92778E-01 .20744E+00 .40065E-01 .96537E-01 .73211E-02

.48283E+00 .15582E+00 .47450E-01 .14923E+00 .17536E-01 .58863E-01 -.39685E-02

.47651E+00 .14885E+00 .42209E-01 .14280E+00 .15492E-01 .54982E-01 -.19067E-02

.48283E+00 .15428E+00 .44980E-01 .14903E+00 .17042E-01 .58390E-01 -.26208E-03

.62847E+00 .26337E+00 .10091E+00 .32927E+00 .83957E-01 .16861E+00 .69389E-17

.61393E+00 .25680E+00 .10224E+00 .30864E+00 .76458E-01 .15620E+00 .14023E-01

.65086E+00 .26641E+00 .93698E-01 .35959E+00 .92699E-01 .18536E+00 -.11516E-01

.65719E+00 .26760E+00 .90400E-01 .36887E+00 .95025E-01 .19047E+00 .11449E-15

.65086E+00 .26641E+00 .93698E-01 .35959E+00 .92699E-01 .18536E+00 .11516E-01

.61393E+00 .25680E+00 .10224E+00 .30864E+00 .76458E-01 .15620E+00 -.14023E-01

.57919E+00 .22756E+00 .83375E-01 .25914E+00 .53250E-01 .12331E+00 .33343E-02

.57485E+00 .22683E+00 .84212E-01 .25429E+00 .52010E-01 .12079E+00 -.13878E-16

.57919E+00 .22756E+00 .83375E-01 .25914E+00 .53250E-01 .12331E+00 -.33343E-02

.66351E+00 .30241E+00 .13187E+00 .39072E+00 .12371E+00 .21448E+00 .22267E-01

.48203E+00 .14853E+00 .56470E-01 .14491E+00 .17575E-01 .56679E-01 -.54432E-02

.50347E+00 .17243E+00 .79972E-01 .16621E+00 .26751E-01 .70928E-01 -.76641E-02

.51617E+00 .17274E+00 .73876E-01 .17752E+00 .27607E-01 .75383E-01 -.48798E-02

.51780E+00 .16869E+00 .67529E-01 .17844E+00 .25956E-01 .74514E-01 -.43819E-02

.50836E+00 .16004E+00 .60188E-01 .16876E+00 .22144E-01 .68340E-01 -.52380E-02

.48785E+00 .14820E+00 .52578E-01 .14998E+00 .17321E-01 .58197E-01 -.62253E-02

.52138E+00 .18151E+00 .82787E-01 .18467E+00 .31296E-01 .80326E-01 -.10990E-01

.43713E+00 .12125E+00 .41214E-01 .10819E+00 .96076E-02 .38110E-01 -.33964E-02

.43599E+00 .12224E+00 .42956E-01 .10762E+00 .98518E-02 .38138E-01 -.34340E-02

Retract

ed


.44262E+00 .12604E+00 .45504E-01 .11249E+00 .10892E-01 .40548E-01 -.30245E-02

.50895E+00 .17974E+00 .61828E-01 .17705E+00 .25896E-01 .74918E-01 .53088E-02

.50944E+00 .18643E+00 .70216E-01 .17874E+00 .28055E-01 .77300E-01 .10783E-01

.51280E+00 .16970E+00 .50571E-01 .17777E+00 .23503E-01 .72961E-01 .11796E-02

.51852E+00 .17216E+00 .51183E-01 .18324E+00 .24911E-01 .75836E-01 .46476E-02

.51555E+00 .17372E+00 .55428E-01 .18072E+00 .25417E-01 .75321E-01 .79364E-02

.50544E+00 .18138E+00 .63731E-01 .17471E+00 .25607E-01 .74179E-01 .23298E-03

.52286E+00 .19267E+00 .69918E-01 .19351E+00 .31461E-01 .84562E-01 .89060E-04

.48111E+00 .16464E+00 .56411E-01 .15031E+00 .19333E-01 .60977E-01 .55599E-02

.47694E+00 .16343E+00 .55886E-01 .14704E+00 .18594E-01 .59362E-01 .41116E-02

.47911E+00 .16287E+00 .54320E-01 .14861E+00 .18596E-01 .59843E-01 .27183E-02

.45996E+00 .15485E+00 .56835E-01 .13201E+00 .15851E-01 .52107E-01 -.77522E-02

.47325E+00 .16759E+00 .68897E-01 .14383E+00 .20090E-01 .59459E-01 -.11683E-01

.48262E+00 .16523E+00 .62782E-01 .15059E+00 .20249E-01 .61612E-01 -.10459E-01

.48331E+00 .16247E+00 .58339E-01 .15083E+00 .19398E-01 .60982E-01 -.89396E-02

.47531E+00 .15925E+00 .55611E-01 .14439E+00 .17736E-01 .57628E-01 -.71717E-02

.45862E+00 .15649E+00 .55303E-01 .13209E+00 .15651E-01 .52176E-01 -.50996E-02

.49086E+00 .18330E+00 .77231E-01 .16176E+00 .25334E-01 .69745E-01 -.13938E-01

.42411E+00 .13244E+00 .44960E-01 .10389E+00 .98458E-02 .37852E-01 -.47657E-02

.42361E+00 .13341E+00 .46326E-01 .10367E+00 .10015E-01 .37982E-01 -.50714E-02

.42944E+00 .13486E+00 .47115E-01 .10728E+00 .10628E-01 .39594E-01 -.54865E-02

.56671E+00 .25019E+00 .11228E+00 .25333E+00 .59849E-01 .12636E+00 .58981E-16

.55670E+00 .24339E+00 .10989E+00 .24059E+00 .54822E-01 .11846E+00 .10197E-01

.58355E+00 .24986E+00 .10651E+00 .27133E+00 .64407E-01 .13530E+00 -.89732E-02

.58908E+00 .24949E+00 .10311E+00 .27752E+00 .65536E-01 .13822E+00 -.45103E-16

.55393E+00 .26278E+00 .13233E+00 .24426E+00 .61532E-01 .12482E+00 .11280E-01

.56695E+00 .25180E+00 .11733E+00 .25368E+00 .61168E-01 .12715E+00 .15912E-01

.59462E+00 .28861E+00 .14597E+00 .29708E+00 .86980E-01 .15923E+00 -.15018E-01

.52561E+00 .21821E+00 .92689E-01 .20311E+00 .39109E-01 .94601E-01 .24579E-02

.52172E+00 .21834E+00 .93786E-01 .19969E+00 .38391E-01 .93026E-01 .12143E-16

.52561E+00 .21821E+00 .92689E-01 .20311E+00 .39109E-01 .94601E-01 -.24579E-02

.69138E+00 .61179E+00 .56685E+00 .56255E+00 .48245E+00 .43889E+00 .24286E-16

.72222E+00 .81217E+00 .82650E+00 .69957E+00 .81172E+00 .63013E+00 -.14941E+00

.76622E+00 .76521E+00 .78053E+00 .76727E+00 .87998E+00 .67023E+00 -.53558E-01

.78089E+00 .75149E+00 .76572E+00 .79213E+00 .90267E+00 .68536E+00 .16306E-15

.76622E+00 .76521E+00 .78053E+00 .76727E+00 .87998E+00 .67023E+00 .53558E-01

.72222E+00 .81217E+00 .82650E+00 .69957E+00 .81172E+00 .63013E+00 .14941E+00

.62346E+00 .42809E+00 .34105E+00 .38810E+00 .21280E+00 .25281E+00 .13103E-01

.59799E+00 .44153E+00 .35485E+00 .36014E+00 .19882E+00 .23842E+00 -.22009E-02

.82222E+00 .86028E+00 .92925E+00 .93907E+00 .13009E+01 .86933E+00 -.59674E-15

.59799E+00 .44153E+00 .35485E+00 .36014E+00 .19882E+00 .23842E+00 .22009E-02

.69274E+00 .28223E+00 .89521E-01 .42640E+00 .11664E+00 .22608E+00 -.25500E-15

.69031E+00 .27759E+00 .92937E-01 .42003E+00 .11461E+00 .22147E+00 -.19014E-01

.66461E+00 .27335E+00 .95544E-01 .38120E+00 .10139E+00 .19904E+00 .96801E-02

Retract

ed


.65972E+00 .27119E+00 .94573E-01 .37365E+00 .98206E-01 .19425E+00 -.69389E-16

.66461E+00 .27335E+00 .95544E-01 .38120E+00 .10139E+00 .19904E+00 -.96801E-02

.69031E+00 .27759E+00 .92937E-01 .42003E+00 .11461E+00 .22147E+00 .19014E-01

.69274E+00 .28223E+00 .89521E-01 .42640E+00 .11664E+00 .22608E+00 -.25500E-15

.63824E+00 .24422E+00 .75854E-01 .33472E+00 .74420E-01 .16523E+00 .41261E-02

.63336E+00 .24206E+00 .75387E-01 .32769E+00 .71993E-01 .16101E+00 .30358E-16

.63824E+00 .24422E+00 .75854E-01 .33472E+00 .74420E-01 .16523E+00 -.41261E-02

.69184E+00 .28170E+00 .13874E+00 .42520E+00 .11875E+00 .22480E+00 -.11102E-15

.70873E+00 .29693E+00 .14913E+00 .45427E+00 .14318E+00 .24891E+00 -.31433E-02

.66484E+00 .25251E+00 .91637E-01 .37301E+00 .86894E-01 .18769E+00 .55500E-02

.65021E+00 .23964E+00 .75628E-01 .34876E+00 .73678E-01 .17063E+00 -.90206E-16

.66484E+00 .25251E+00 .91637E-01 .37301E+00 .86894E-01 .18769E+00 -.55500E-02

.70873E+00 .29693E+00 .14913E+00 .45427E+00 .14318E+00 .24891E+00 .31433E-02

.69258E+00 .30106E+00 .18724E+00 .42911E+00 .14674E+00 .23767E+00 .25983E-01

.60265E+00 .20882E+00 .80215E-01 .27856E+00 .48735E-01 .12729E+00 -.18186E-02

.58802E+00 .19594E+00 .68790E-01 .25785E+00 .40467E-01 .11411E+00 -.34694E-17

.60265E+00 .20882E+00 .80215E-01 .27856E+00 .48735E-01 .12729E+00 .18186E-02

.57376E+00 .18627E+00 .41024E-01 .24007E+00 .34786E-01 .10335E+00 -.87278E-16

.56467E+00 .18249E+00 .45948E-01 .22900E+00 .33048E-01 .97812E-01 .55292E-03

.55853E+00 .18213E+00 .44301E-01 .22290E+00 .31785E-01 .95005E-01 .22384E-02

.55464E+00 .18015E+00 .43586E-01 .21849E+00 .30624E-01 .92593E-01 -.32960E-16

.55853E+00 .18213E+00 .44301E-01 .22290E+00 .31785E-01 .95005E-01 -.22384E-02

.56467E+00 .18249E+00 .45948E-01 .22900E+00 .33048E-01 .97812E-01 -.55292E-03

.59559E+00 .20179E+00 .48917E-01 .26916E+00 .44443E-01 .12051E+00 -.28337E-02

.53681E+00 .16488E+00 .35617E-01 .19682E+00 .23921E-01 .79839E-01 .86776E-03

.53292E+00 .16290E+00 .35093E-01 .19270E+00 .23006E-01 .77694E-01 .29924E-16

.53681E+00 .16488E+00 .35617E-01 .19682E+00 .23921E-01 .79839E-01 -.86776E-03

.83563E+00 .62965E+00 .49421E+00 .85395E+00 .78583E+00 .67581E+00 -.12212E-14

.81822E+00 .63769E+00 .55466E+00 .81364E+00 .77407E+00 .65061E+00 -.28852E+00

.78858E+00 .59843E+00 .47332E+00 .73532E+00 .61938E+00 .56754E+00 .73632E-01

.78009E+00 .60056E+00 .47793E+00 .71917E+00 .60307E+00 .55587E+00 -.72164E-15

.78858E+00 .59843E+00 .47332E+00 .73532E+00 .61938E+00 .56754E+00 -.73632E-01

.81822E+00 .63769E+00 .55466E+00 .81364E+00 .77407E+00 .65061E+00 .28852E+00

.77160E+00 .50474E+00 .34738E+00 .65770E+00 .44411E+00 .46622E+00 .80602E-01

.93556E+00 .77702E+00 .67650E+00 .11930E+01 .15222E+01 .10486E+01 -.22893E+00

.73765E+00 .51134E+00 .36880E+00 .59711E+00 .39956E+00 .42575E+00 .00000E+00

.93556E+00 .77702E+00 .67650E+00 .11930E+01 .15222E+01 .10486E+01 .22893E+00

.81847E+00 .74101E+00 .75519E+00 .86816E+00 .97296E+00 .74592E+00 -.29143E-15

.79861E+00 .88341E+00 .97308E+00 .88258E+00 .11876E+01 .83015E+00 -.47761E+00

.74889E+00 .63819E+00 .60789E+00 .67433E+00 .61994E+00 .53772E+00 .52100E-01

.73689E+00 .64413E+00 .61042E+00 .65457E+00 .60074E+00 .52424E+00 .12143E-15

.74889E+00 .63819E+00 .60789E+00 .67433E+00 .61994E+00 .53772E+00 -.52100E-01

.79861E+00 .88341E+00 .97308E+00 .88258E+00 .11876E+01 .83015E+00 .47761E+00

.73822E+00 .51993E+00 .45629E+00 .60174E+00 .43032E+00 .43289E+00 .53704E-01

Retract

ed


.69022E+00 .53978E+00 .47905E+00 .52747E+00 .37914E+00 .38663E+00 .21511E-15

.96007E+00 .10550E+01 .12551E+01 .14205E+01 .25879E+01 .14567E+01 .22086E+00

.73822E+00 .51993E+00 .45629E+00 .60174E+00 .43032E+00 .43289E+00 -.53704E-01

.52202E+00 .19586E+00 .72119E-01 .19291E+00 .31777E-01 .85197E-01 -.44309E-02

.53086E+00 .22413E+00 .10541E+00 .20832E+00 .43145E-01 .98963E-01 -.19417E-01

.56096E+00 .22094E+00 .86651E-01 .23735E+00 .47525E-01 .11155E+00 -.15060E-01

.57099E+00 .21967E+00 .78780E-01 .24783E+00 .48433E-01 .11590E+00 -.71637E-02

.56096E+00 .21760E+00 .80117E-01 .23691E+00 .45590E-01 .11019E+00 .12149E-02

.53086E+00 .21744E+00 .92778E-01 .20744E+00 .40065E-01 .96537E-01 .73211E-02

.48283E+00 .15428E+00 .44980E-01 .14903E+00 .17042E-01 .58390E-01 -.26208E-03

.46388E+00 .15240E+00 .48457E-01 .13487E+00 .15225E-01 .52502E-01 -.12101E-02

.45756E+00 .15239E+00 .50208E-01 .13048E+00 .14764E-01 .50815E-01 -.20392E-02

.59105E+00 .25454E+00 .10812E+00 .28150E+00 .68628E-01 .14158E+00 -.40092E-02

.64161E+00 .24627E+00 .73690E-01 .34095E+00 .76726E-01 .16862E+00 .11276E-15

.63238E+00 .23417E+00 .70161E-01 .32413E+00 .68642E-01 .15664E+00 -.12763E-01

.62529E+00 .24791E+00 .85011E-01 .32003E+00 .74103E-01 .15897E+00 .77158E-02

.62140E+00 .24647E+00 .84712E-01 .31473E+00 .72237E-01 .15584E+00 .69389E-17

.62529E+00 .24791E+00 .85011E-01 .32003E+00 .74103E-01 .15897E+00 -.77158E-02

.63238E+00 .23417E+00 .70161E-01 .32413E+00 .68642E-01 .15664E+00 .12763E-01

.64161E+00 .24627E+00 .73690E-01 .34095E+00 .76726E-01 .16862E+00 .11276E-15

.60174E+00 .22223E+00 .67364E-01 .28260E+00 .54976E-01 .13294E+00 .38213E-02

.59785E+00 .22079E+00 .67339E-01 .27766E+00 .53554E-01 .13018E+00 -.17347E-17

.60174E+00 .22223E+00 .67364E-01 .28260E+00 .54976E-01 .13294E+00 -.38213E-02

.40181E+00 .11507E+00 .32060E-01 .87791E-01 .65013E-02 .29707E-01 -.56389E-03

.40045E+00 .11408E+00 .32759E-01 .86694E-01 .64251E-02 .29266E-01 -.18125E-02

.39289E+00 .11448E+00 .33160E-01 .83093E-01 .60953E-02 .28037E-01 -.18648E-16

.41140E+00 .11380E+00 .29187E-01 .92641E-01 .67265E-02 .31177E-01 -.66197E-03

.40899E+00 .11340E+00 .29235E-01 .91253E-01 .65887E-02 .30648E-01 -.56379E-17

.40132E+00 .11292E+00 .30613E-01 .87044E-01 .62749E-02 .29178E-01 .59433E-03

.41425E+00 .12558E+00 .38269E-01 .96936E-01 .82489E-02 .34291E-01 -.18579E-02

.38214E+00 .10535E+00 .28422E-01 .75799E-01 .49122E-02 .24538E-01 -.12829E-03

.42521E+00 .12549E+00 .35322E-01 .10328E+00 .87147E-02 .36487E-01 -.84163E-03

.38180E+00 .10559E+00 .28818E-01 .75661E-01 .49300E-02 .24531E-01 -.63979E-03

.41343E+00 .11596E+00 .30804E-01 .94179E-01 .70553E-02 .32018E-01 .11641E-02

.40824E+00 .11062E+00 .27964E-01 .90177E-01 .62676E-02 .29918E-01 -.36006E-03

.40527E+00 .11727E+00 .33734E-01 .89974E-01 .69122E-02 .30786E-01 .17325E-02

.42206E+00 .11331E+00 .27028E-01 .98423E-01 .70492E-02 .33080E-01 .10847E-02

.40439E+00 .11619E+00 .32671E-01 .89395E-01 .67130E-02 .30399E-01 .55087E-03

.41054E+00 .11385E+00 .31136E-01 .91783E-01 .68532E-02 .31039E-01 .24985E-02

.42494E+00 .12454E+00 .34680E-01 .10292E+00 .85674E-02 .36215E-01 .13497E-03

.39256E+00 .10650E+00 .28058E-01 .80986E-01 .53727E-02 .26404E-01 .12011E-02

.43876E+00 .12675E+00 .33636E-01 .11172E+00 .95303E-02 .39690E-01 .15038E-02

.39168E+00 .10573E+00 .27325E-01 .80465E-01 .52421E-02 .26111E-01 .59224E-03

.37975E+00 .10366E+00 .27660E-01 .74359E-01 .47099E-02 .23870E-01 .22652E-03

Retract

ed


.40824E+00 .11062E+00 .27964E-01 .90177E-01 .62676E-02 .29918E-01 -.36006E-03

.40527E+00 .11727E+00 .33734E-01 .89974E-01 .69122E-02 .30786E-01 .17325E-02

.42206E+00 .11331E+00 .27028E-01 .98423E-01 .70492E-02 .33080E-01 .10847E-02

.40439E+00 .11619E+00 .32671E-01 .89395E-01 .67130E-02 .30399E-01 .55087E-03

.41054E+00 .11385E+00 .31136E-01 .91783E-01 .68532E-02 .31039E-01 .24985E-02

.42494E+00 .12454E+00 .34680E-01 .10292E+00 .85674E-02 .36215E-01 .13497E-03

.39256E+00 .10650E+00 .28058E-01 .80986E-01 .53727E-02 .26404E-01 .12011E-02

.43876E+00 .12675E+00 .33636E-01 .11172E+00 .95303E-02 .39690E-01 .15038E-02

.39168E+00 .10573E+00 .27325E-01 .80465E-01 .52421E-02 .26111E-01 .59224E-03

Retract

ed

Appendix F: Pattern.cpp

// pattern1.cpp// Kohonen map for pattern recognition

#include “e:\bujji\layerk.cpp"

#define INPUT_FILE “e:\\bujji\\input.dat"#define OUTPUT_FILE “e:\\bujji\\kohonen.dat"#define dist_tol 0.001#define wait_cycles 10000 // creates a pause to

// view the character mapsvoid main(){

int neighborhood_size, period;float avg_dist_per_cycle=0.0;float dist_last_cycle=0.0;float avg_dist_per_pattern=100.0; // for the latest cyclefloat dist_last_pattern=0.0;float total_dist;float alpha;unsigned startup;int max_cycles;int patterns_per_cycle=0;

int total_cycles, total_patterns;int i;

// create a network objectKohonen_network knet;

FILE * input_file_ptr, * output_file_ptr;

// open input file for readingif ((input_file_ptr=fopen(INPUT_FILE,“r"))==NULL)


Retract

ed

178 Pattern.cpp

{cout << “problem opening input file\n";exit(1);}// open writing file for writingif ((output_file_ptr=fopen(OUTPUT_FILE,“w"))==NULL){cout << “problem opening output file\n";exit(1);}

// -----------------------------------------// Read in an initial values for alpha, and the// neighborhood size.// Both of these parameters are decreased with// time. The number of cycles to execute before// decreasing the value of these parameters is// called the period. Read in a value for the// period.// -----------------------------------------

cout << “ Please enter initial values for:\n";cout << “alpha (0.01-1.0),\n";cout << “and the neighborhood size (integer between 0 and 50)\n";cout << “separated by spaces, e.g. 0.3 5 \n ";

cin >> alpha >> neighborhood_size ;

cout << “Now enter the period, which is the\n";cout << “number of cycles after which the values\n";cout << “for alpha the neighborhood size are decremented\n";cout << “choose an integer between 1 and 500 , e.g. 50 \n";

cin >> period;

// Read in the maximum number of cycles// each pass through the input data file is a cyclecout << “Please enter the maximum cycles for the simulation\n";cout << “A cycle is one pass through the data set.\n";cout << “Try a value of 500 to start with\n";

cin >> max_cycles;

Retract

ed

Pattern.cpp 179

// the main loop//// continue looping until the average distance is less than// the tolerance specified at the top of this file// , or the maximum number of// cycles is exceeded;

// initialize counterstotal_cycles=0; // a cycle is once through all the input datatotal_patterns=0; // a pattern is one entry in the input data

// get layer informationknet.get_layer_info();

// set up the network connectionsknet.set_up_network(neighborhood_size);

// initialize the weights

// randomize weights for the Kohonen layer// note that the randomize function for the// Kohonen simulator generates// weights that are normalized to length = 1knet.randomize_weights();

// write header to output filefprintf(output_file_ptr,

“cycle\tpattern\twin index\tneigh_size\tavg_dist_per_pattern\n");

fprintf(output_file_ptr,“------------------------------------------------\n");

// main loop

startup=1;total_dist=0;

while ((avg_dist_per_pattern > dist_tol)&& (total_cycles < max_cycles)

|| (startup==1))

Retract

ed

180 Pattern.cpp

{startup=0;dist_last_cycle=0; // reset for each cyclepatterns_per_cycle=0;// process all the vectors in the datafile

while (!feof(input_file_ptr)){knet.get_next_vector(input_file_ptr);

// now apply it to the Kohonen networkknet.process_next_pattern();

dist_last_pattern=knet.get_win_dist();

// print result to output filefprintf(output_file_ptr,“%i\t%i\t%i\t\t%i\t\t%f\n",total_cycles,total_patterns,knet.get_win_index(),neighborhood_size,avg_dist_per_pattern);

// display the input character and the// weights for the winner to see match

knet.display_input_char();knet.display_winner_weights();cout << “Press any key ...";char patrec;cin >> patrec;

// pause for a while to view the// character mapsfor (i=0; i<wait_cycles; i++)

{;}

total_patterns++;

// gradually reduce the neighborhood size// and the gain, alphaif (((total_cycles+1) % period) == 0)

{if (neighborhood_size > 0)

neighborhood_size –;knet.update_neigh_size(neighborhood_size);

Retract

ed

Pattern.cpp 181

if (alpha>0.1)alpha -= (float)0.1;

}patterns_per_cycle++;dist_last_cycle += dist_last_pattern;knet.update_weights(alpha);dist_last_pattern = 0;

}

avg_dist_per_pattern= dist_last_cycle/patterns_per_cycle;total_dist += dist_last_cycle;total_cycles++;

fseek(input_file_ptr, 0L, SEEK_SET); // reset the file pointer// to the beginning of// the file

} // end main loop

cout << “\n\n\n\n\n\n\n\n\n\n\n";cout << “---------------------------------------------\n";cout << “ done \n";

avg_dist_per_cycle= total_dist\total_cycles;

cout << “\n";cout << “---->average dist per cycle = " << avg_dist_per_cycle << " <---\n";cout << “---->dist last cycle = " << dist_last_cycle << " <---\n";cout << “->dist last cycle per pattern= " << avg_dist_per_pattern << " <---\n";cout << “------------>total cycles = " << total_cycles << " <---\n";cout << “------------>total patterns = " << total_patterns << “ <---\n";cout << “---------------------------------------------------\n";// close the input filefclose(input_file_ptr);}

Retract

ed

Appendix G: handpgm2.m

Refer to the input (INP) and output (OUT) from the program handpgm1.m

tic

TAG=(‘SALO1’);PAR=[0.5 0.0 0.5 1.0 0 0.08 0.002]’;[Mi Ni]=size(INP);[Mo No]=size(OUT);UnitsA=3;UnitsB=3;WA=ones(UnitsA, 2*Ni);WB=ones(UnitsB, 2*No);WAB=(ones(UnitsA,UnitsB));MICRO(‘create’, TAG, PAR, WA, WB, WAB)

LIST=MICRO(‘list’)MICRO(‘train’, TAG, INP, OUT)OUT=MICRO(‘test’, TAG , INP);INP1=[1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1

1 1 0];OUT1=MICRO(‘test’, TAG, INP1)

toc

V.K. David and S. Rajasekaran: Pattern Recog. Using Neural & Funct. Net., SCI 160, p. 183.springerlink.com c© Springer-Verlag Berlin Heidelberg 2009

references - springer978-3-540-85130-1/1.pdf · 138 references 17. carpenter ... d.m.: neural...

Documents