writing mathematical expressions with latex978-1-4842-3913-1/1.pdf · 538 with ipython notebook in...

537© Fabio Nelli 2018 F. Nelli, Python Data Analytics, https://doi.org/10.1007/978-1-4842-3913-1

APPENDIX A

Writing Mathematical Expressions with LaTeXLaTeX is extensively used in Python. In this appendix there are many examples that can

be useful to represent LaTeX expressions inside Python implementations. This same

information can be found at the link http://matplotlib.org/users/mathtext.html.

With matplotlibYou can enter the LaTeX expression directly as an argument of various functions that can

accept it. For example, the title() function that draws a chart title.

import matplotlib.pyplot as plt

%matplotlib inline

plt.title(r'$\alpha > \beta$')

With IPython Notebook in a Markdown CellYou can enter the LaTeX expression between two '$$'.

$$c = \sqrt{a^2 + b^2}$$

c = a +b2 2

https://doi.org/10.1007/978-1-4842-3913-1

http://matplotlib.org/users/mathtext.html

538

With IPython Notebook in a Python 2 CellYou can enter the LaTeX expression within the Math() function.

from IPython.display import display, Math, Latex

display(Math(r'F(k) = \int_{-\infty}^{\infty} f(x) e^{2\pi i k} dx'))

Subscripts and SuperscriptsTo make subscripts and superscripts, use the ‘_’ and ‘^’ symbols:

r'$\alpha_i > \beta_i$'

a bi i>

This could be very useful when you have to write summations:

r'$\sum_{i=0}^\infty x_i$'

i=0

¥

åxi

Fractions, Binomials, and Stacked NumbersFractions, binomials, and stacked numbers can be created with the \frac{}{}, \binom{}{},

and \stackrel{}{} commands, respectively:

r'$\frac{3}{4} \binom{3}{4} \stackrel{3}{4}$'

3

4

3

4

3

4æ

èç

ö

ø÷

Fractions can be arbitrarily nested:

51

4

-x

Appendix A Writing MAtheMAticAl expressions With lAtex

539

Note that special care needs to be taken to place parentheses and brackets around

fractions. You have to insert \left and \right preceding the bracket in order to inform the

parser that those brackets encompass the entire object:

51

4

-x

æ

è

ççç

ö

ø

÷÷÷

RadicalsRadicals can be produced with the \sqrt[]{} command.

r'$\sqrt{2}$'

2

FontsThe default font is italics for mathematical symbols. To change fonts, for example with

trigonometric functions as sin:

s t = Asin 2 t( ) ( )w

The choices available with all fonts are

from IPython.display import display, Math, Latex

display(Math(r'\mathrm{Roman}'))

display(Math(r'\mathit{Italic}'))

display(Math(r'\mathtt{Typewriter}'))

display(Math(r'\mathcal{CALLIGRAPHY}'))


540

AccentsAn accent command may precede any symbol to add an accent above it. There are long

and short forms for some of them.

\acute a or \'a

\bar a

\breve a

\ddot a or \"a

\dot a or \.a

\grave a or \`a

\hat a or \^a

\tilde a or \~a

\vec a

\overline{abc}

SymbolsYou can also use a large number of the TeX symbols.

Lowercase Greek

\alpha \beta \chi \delta \digamma

\epsilon \eta \gamma \iota \kappa

\lambda \mu \nu \omega \phi

\pi \psi \rho \sigma \tau

\theta \upsilon \varepsilon \varkappa \varphi

\varpi \varrho \varsigma \vartheta \xi

\zeta


541

Uppercase Greek

\delta \gamma \lambda \omega \phi \pi

\psi \sigma \theta \Upsilon \xi \mho

\nabla

Hebrew

\aleph \beth \daleth \gimel

Delimiters

/ [ \downarrow \Uparrow \Vert \backslash

\downarrow \langle \lceil \lfloor \llcorner \lrcorner

\rangle \rceil \rfloor \ulcorner \uparrow \urcorner

\vert \{ \| \} ] |

Big Symbols

\bigcap \bigcup \bigodot \bigoplus \bigotimes

\biguplus \bigvee \bigwedge \coprod \int

\oint \prod \sum


542

Standard Function Names

\pr \arccos \arcsin \arctan

\arg \cos \cosh \cot

\coth \csc \deg \det

\dim \exp \gcd \hom

\inf \ker \lg \lim

\liminf \limsup \ln \log

\max \min \sec \sin

\sinh \sup \tan \tanh

Binary Operation and Relation Symbols

\Bumpeq \cap \cup

\doteq \Join \subset

\supset \Vdash \Vvdash

\approx \approxeq \ast

\asymp \backepsilon \backsim

\backsimeq \barwedge \because

\between \bigcirc \bigtriangledown

\bigtriangleup \blacktriangleleft \blacktriangleright

\bot \bowtie \boxdot

\boxminus \boxplus \boxtimes

\bullet \bumpeq \cap

\cdot \circ \circeq

\coloneq \cong \cup

\curlyeqprec \curlyeqsucc \curlyvee

\curlywedge \dag \dashv

(continued)


543

\ddag \diamond \div

\divideontimes \doteq \doteqdot

\dotplus \doublebarwedge \eqcirc

\eqcolon \eqsim \eqslantgtr

\eqslantless \equiv \fallingdotseq

\frown \geq \geqq

\geqslant \gg \ggg

\gnapprox \gneqq \gnsim

\gtrapprox \gtrdot \gtreqless

\gtreqqless \gtrless \gtrsim

\in \intercal \leftthreetimes

\leq \leqq \leqslant

\lessapprox \lessdot \lesseqgtr

\lesseqqgtr \lessgtr \lesssim

\ll \lll \lnapprox

\lneqq \lnsim \ltimes

\mid \models \mp

\nVdash \nVdash \napprox

\ncong \ne \neq

\neq \nequiv \ngeq

\ngtr \ni \nleq

\nless \nmid \notin

\nparallel \nprec \nsim

(continued)


544

\nsubset \nsubseteq \nsucc

\nsupset \nsupseteq \ntriangleleft

\ntrianglelefteq \ntriangleright \ntrianglerighteq

\nvdash \nvdash \odot

\ominus \oplus \oslash

\otimes \parallel \perp

\pitchfork \pm \prec

\precapprox \preccurlyeq \preceq

\precnapprox \precnsim \precsim

\propto \rightthreetimes \risingdotseq

\rtimes \sim \simeq

\slash \smile \sqcap

\sqcup \sqsubset \sqsubset

\sqsubseteq \sqsupset \sqsupset

\sqsupseteq \star \subset

\subseteq \subseteqq \subsetneq

\subsetneqq \succ \succapprox

\succcurlyeq \succeq \succnapprox

\succnsim \succsim \supset

\supseteq \supseteqq \supsetneq

\supsetneqq \therefore \times

\top \triangleleft \trianglelefteq

\triangleq \triangleright \trianglerighteq

\uplus \vdash \varpropto

\vartriangleleft \vartriangleright \vdash

\vee \veebar \wedge

\wr


545

Arrow Symbols

\downarrow \leftarrow

\leftrightarrow \lleftarrow

\longleftarrow \longleftrightarrow

\longrightarrow \lsh

\nearrow \nwarrow

\rightarrow \rrightarrow

\rsh \searrow

\swarrow \Uparrow

\Updownarrow \circlearrowleft

\circlearrowright \curvearrowleft

\curvearrowright \dashleftarrow

\dashrightarrow \downarrow

\downdownarrows \downharpoonleft

\downharpoonright \hookleftarrow

\hookrightarrow \leadsto

\leftarrow \leftarrowtail

\leftharpoondown \leftharpoonup

\leftleftarrows \leftrightarrow

\leftrightarrows \leftrightharpoons

\leftrightsquigarrow \leftsquigarrow

\longleftarrow \longleftrightarrow

\longmapsto \longrightarrow

\looparrowleft \looparrowright

\mapsto \multimap

\nleftarrow \nleftrightarrow

\nrightarrow \nearrow

\nleftarrow \nleftrightarrow

(continued)


546

\nrightarrow \nwarrow

\rightarrow \rightarrowtail

\rightharpoondown \rightharpoonup

\rightleftarrows \rightleftarrows

\rightleftharpoons \rightleftharpoons

\rightrightarrows \rightrightarrows

\rightsquigarrow \searrow

\swarrow \to

\twoheadleftarrow \twoheadrightarrow

\uparrow \updownarrow

\updownarrow \upharpoonleft

\upharpoonright \upuparrows

Miscellaneous Symbols

\$ \AA \Finv

\game \im \p

\re \s \angle

\backprime \bigstar \blacksquare

\blacktriangle \blacktriangledown \cdots

\checkmark \circledr \circleds

\clubsuit \complement \copyright

\ddots \diamondsuit \ell

\emptyset \eth \exists

\flat \forall \hbar

\heartsuit \hslash \iiint

(continued)


547

\iint \iint \imath

\infty \jmath \ldots

\measuredangle \natural \neg

\nexists \oiiint \partial

\prime \sharp \spadesuit

\sphericalangle \ss \triangledown

\varnothing \vartriangle \vdots

\wp \yen



APPENDIX B

Open Data Sources

Political and Government DataData.gov

http://data.gov

This is the resource for most government-related data.

Socrata

http://www.socrata.com/resources/

Socrata is a good place to explore government-related data. Furthermore, it provides

some visualization tools for exploring data.

US Census Bureau

http://www.census.gov/data.html

This site provides information about US citizens covering population data, geographic

data, and education.

UN3ta

https://data.un.org/

UNdata is an Internet-based data service which brings UN statistical databases.

European Union Open Data Portal

http://open-data.europa.eu/en/data/

This site provides a lot of data from European Union institutions.

https://doi.org/10.1007/978-1-4842-3913-1

http://data.gov/

http://www.socrata.com/resources/

http://www.census.gov/data.html

https://data.un.org/

http://open-data.europa.eu/en/data/

550

Data.gov.uk

http://data.gov.uk/

This site of the UK Government includes the British National Bibliography: metadata

on all UK books and publications since 1950.

The CIA World Factbook

https://www.cia.gov/library/publications/the-world-factbook/

This site of the Central Intelligence Agency provides a lot of information on history,

population, economy, government, infrastructure, and military of 267 countries.

Health DataHealthdata.gov

https://www.healthdata.gov/

This site provides medical data about epidemiology and population statistics.

NHS Health and Social Care Information Centre

http://www.hscic.gov.uk/home

Health data sets from the UK National Health Service.

Social DataFacebook Graph

https://developers.facebook.com/docs/graph-api

Facebook provides this API which allows you to query the huge amount of

information that users are sharing with the world.

Topsy

http://topsy.com/

Topsy provides a searchable database of public tweets going back to 2006 as well as

several tools to analyze the conversations.

Appendix B Open dAtA SOurceS

http://data.gov.uk/

https://www.cia.gov/library/publications/the-world-factbook/

https://www.healthdata.gov/

http://www.hscic.gov.uk/home

https://developers.facebook.com/docs/graph-api

http://topsy.com/

551

Google Trends

http://www.google.com/trends/explore

Statistics on search volume (as a proportion of total search) for any given term,

since 2004.

Likebutton

http://likebutton.com/

Mines Facebook’s public data—globally and from your own network—to give an

overview of what people “Like” at the moment.

Miscellaneous and Public Data SetsAmazon Web Services public datasets

http://aws.amazon.com/datasets

The public data sets on Amazon Web Services provide a centralized repository of

public data sets. An interesting dataset is the 1000 Genome Project, an attempt to build

the most comprehensive database of human genetic information. Also a NASA database

of satellite imagery of Earth is available.

DBPedia

http://wiki.dbpedia.org

Wikipedia contains millions of pieces of data, structured and unstructured, on

every subject. DBPedia is an ambitious project to catalogue and create a public, freely

distributable database allowing anyone to analyze this data.

Freebase

http://www.freebase.com/

This community database provides information about several topics, with over 45

million entries.


http://www.google.com/trends/explore

http://likebutton.com/

http://aws.amazon.com/datasets#http://aws.amazon.com/datasets

http://wiki.dbpedia.org/

http://www.freebase.com/

552

Gapminder

http://www.gapminder.org/data/

This site provides data coming from the World Health Organization and World Bank

covering economic, medical, and social statistics from around the world.

Financial DataGoogle Finance

https://www.google.com/finance

Forty years’ worth of stock market data, updated in real time.

Climatic DataNational Climatic Data Center

http://www.ncdc.noaa.gov/data-access/quick-links#loc-clim

Huge collection of environmental, meteorological, and climate data sets from the US

National Climatic Data Center. The world’s largest archive of weather data.

WeatherBase

http://www.weatherbase.com/

This site provides climate averages, forecasts, and current conditions for over 40,000

cities worldwide.

Wunderground

http://www.wunderground.com/

This site provides climatic data from satellites and weather stations, allowing you to

get all information about the temperature, wind, and other climatic measurements.


http://www.gapminder.org/data/

https://www.google.com/finance

http://www.ncdc.noaa.gov/data-access/quick-links#loc-clim

http://www.weatherbase.com/

http://www.wunderground.com/

553

Sports DataPro-Football-Reference

http://www.pro-football-reference.com/

This site provides data about football and several other sports.

Publications, Newspapers, and BooksNew York Times

http://developer.nytimes.com/docs

Searchable, indexed archive of news articles going back to 1851.

Google Books Ngrams

http://storage.googleapis.com/books/ngrams/books/datasetsv2.html

This source searches and analyzes the full text of any of the millions of books

digitized as part of the Google Books project.

Musical DataMillion Song Data Set

http://aws.amazon.com/datasets/6468931156960467

Metadata on over a million songs and pieces of music. Part of Amazon Web Services.


http://www.pro-football-reference.com/

http://developer.nytimes.com/docs#http://developer.nytimes.com/docs

http://storage.googleapis.com/books/ngrams/books/datasetsv2.html

http://aws.amazon.com/datasets/6468931156960467


Index

AAccents, LaTeX, 540–547Advanced Data aggregation

apply() functions, 225transform() function, 226

Anaconda, 24, 88Anderson Iris Dataset, see Iris flower

datasetArray manipulation

joining arrayscolumn_stack() and row_stack(), 72hstack() function, 71vstack() function, 71

splitting arrayshsplit() function, 72split() function, 73–74vsplit() function, 72

Artificial intelligence, 5, 350schematization of, 352

Artificial neural networksbiological networks, 361edges, 356hidden layer, 357input and output layer, 357multi layer perceptron, 360nodes, 356schematization of, 355–356SLP (see Single layer perceptron (SLP))weight, 356

BBar chart

3D, 306–307error bars, 281horizontal, 281–282matplotlib, 278multiserial, 282–284multiseries stacked bar, 286–290pandas DataFrame, 285–286representations, 291stacked bar charts, 290x-axis, 280xticks() function, 279

Bayesian methods, 4Big Data, 353Bigrams, 498Biological neural networks, 361Blending operation, 520

CCaffe2, 355Chart typology, 267Choropleth maps

D3 library, 459geographical representations, 459HTML() function, 461–462jinja2, 462–463JSON and TSV, 463

https://doi.org/10.1007/978-1-4842-3913-1

556

JSON TopoJSON, 460require.config(), 461results, 464US population, 2014

data source census.gov, 467file TSV, codes, 466HTML() function, 468jinja2.Template, 469pop2014_by_county

dataframe, 465–466population.csv, 467–468render() function, 470–471SUMLEV values, 464

Classification and regression trees, 12Classification models, 12Climatic data, 552Clustered bar chart

IPython Notebook, 454–455jinja2, 455, 457–458render() function, 458–459

Clustering models, 4, 11–12Collocations, 498Computer vision, 507Concatenation

arrays, 188combining, 191, 193concat() function, 189–190dataframe, 191keys option, 190pivoting, 193

hierarchical indexing, 193long to wide format, 195stack() function, 194unstack() function, 194

removing, 196Correlation, 129–131Covariance, 129–131

Cross-validation, 13Cython, 22

DData aggregation

apply() functions, 226, 228–229GroupBy, 217

groupby() function, 219operations, 218output of, 220SPLIT-APPLY-COMBINE, 218

hierarchical grouping, 220–221merge(), 226numeric and string values, 219price1 column, 219transform() function, 225

Data analysischarts, 2data visualization, 2definition, 1deployment phase, 2information, 6knowledge, 6knowledge domains

computer science, 3disciplines, 3fields of application, 5machine learning and artificial

intelligence, 5mathematics and statistics, 4problems of, 3

open data, 15–16predictive model, 2process

data sources, 9deployment, 13exploration/visualization, 10–11

Choropleth maps (cont.)

Index

557

extraction, 9–10model validation, 13planning phase, 9predictive modeling, 12preparation, 10problem definition, 8stages, 6–8

purpose of, 1Python and, 17quantitative and qualitative, 14types

categorical data, 6numerical data, 6

DataFramepandas

definition, 103–105nested dict, 111operations, 121structure, 103transposition, 111

structure, 102Data manipulation

aggregation (see Data aggregation)concatenation, 188discretization and binning, 204group iteration, 222permutation, 210phases of, 181preparation (see Data preparation)string (see String manipulation)transformation, 197

Data preparation, 181DataFrame, 182merging operation, 182pandas.concat(), 182pandas.DataFrame.combine_

first(), 182

pandas.merge(), 182procedures of, 181

Data structures, operationsDataFrame and series, 121–122flexible arithmetic

methods, 120–121Data transformation

drop_duplicates() function, 199mapping

adding values, 201axes, 202dict objects, 199replacing values, 199

remove duplicates, 198–199Data visualization

adding textaxis labels, 251–252informative label, 254mathematical expression, 254–255modified of, 252text() function, 253

bar chart (see Bar chart)chart typology, 267contour plot/map, 297–299data analysis, 2313D surfaces, 302, 304grid, 256grids, subplots, 309handling date values, 264–267histogram, 277–278installation, 233IPython and IPython

QtConsole, 233, 235kwargs

figures and axes, 249horizontal subplots, 249–250linewidth, 248

Index

558

plot() function, 249vertical subplots, 250–251

legendchart of, 258legend() function, 257, 258multiseries chart, 259upper-right corner, 257

line chart (see Line chart)matplotlib architecture and

NumPy, 247matplotlib library (see matplotlib

library)mplot3d, 302multi-panel plots

grids, subplots, 309, 311subplots, 307–309

pie charts, 292axis() function, 293modified chart, 294pandas Dataframe, 296pie() function, 292shadow kwarg, 295

plotting windowbuttons of, 241commands, 241matplotlib and NumPy, 246plt.plot() function, 242, 243properties, 243QtConsole, 241–242

polar chart, 299, 301pyplot module, 239saving, charts

HTML file, 262–263image file, 264source code, 260–261

scatter plot, 3D, 304–305Decision trees, 11

Deep learning, 349, 532artificial (see Artificial neural

networks)artificial intelligence, 350data availability, 353machine learning, 351neural networks and GPUs, 352Python

frameworks, 354programming language, 354

schematization of, 352TensorFlow (see TensorFlow)

Digits datasetdefinition, 475digits.images array, 477digit.targets array, 478handwritten digits, 477handwritten number images, 475matplotlib library, 477scikit-learn library, 476

Discretization and binning, 204any() function, 210categorical type, 206cut() function, 205–206, 208–209describe() function, 209detecting and filtering

outliers, 209qcut(), 208–209std() function, 210value_counts() function, 206

Django, 17Dropping, 117–118

EEclipse (pyDev), 41–42Element-wise computation, 47Expression-oriented programming, 33

Data visualization (cont.)

Index

559

FFinancial data, 552Flexible arithmetic methods, 120–121Fonts, LaTeX, 539

GGradient theory, 523Graphics Processing Unit (GPU), 353Grouping, 11Group iteration

chain of transformations, 222, 224functions on groups

mark() function, 224–225quantiles() function, 224

GroupBy object, 222

HHandwriting recognition

digits dataset, 475–478handwritten digits, matplotlib

library, 478learning and predicting, 478, 480, 482OCR software, 473scikit-learn, 474–475svc estimator, 480TensorFlow, 480validation set, six digits, 479

Health data, 550Hierarchical indexing

arrays, 136–137DataFrame, 135reordering and sorting levels, 137–138stack() function, 136statistic levels, 138structure, 134two-dimensional structure, 134

IIDEs, see Interactive development

environments (IDEs)Image analysis

concept of, 521convolutions, 523definition, 507edge detection, 522, 525

blackandwhite.jpg image, 526–529, 531

black and white system, 525filters function, 528gradients.jpg image, 532gray gradients, 525Laplacian and Sobel filters, 531results, 528source code, 530

face detection, 532gradient theory, 523OpenCV (see Open Source Computer

Vision (OpenCV))operations, 508representation of, 522

Indexing functionalitiesarithmetic and data

alignment, 118, 120dropping, 117–118reindexing, 114, 116

Integration, 47Interactive development environments

(IDEs)Eclipse (pyDev), 41–42Komodo, 45Liclipse, 43–46NinjaIDE, 44–45Spyder, 41Sublime, 42–43

Index

560

Interactive programming language, 20Interfaced programming language, 20Internet of Things (IoT), 353Interpreted programming language, 20Interpreter

characterization, 21Cython, 22Jython, 22PVM, 21PyPy, 22tokenization, 21

IPythonand IPython QtConsole, 233–234Jupyter project logo, 37Notebook, 39, 474

DataFrames, 420QtConsole, 38shell, 36tools of, 35

Iris flower datasetAnderson Iris Dataset, 316IPython QtConsole, 316Iris setosa features, 318–319length and width,

petal, 319–320matplotlib library, 318PCA decomposition, 320target attribute, 317types of analysis, 316variables, 319–320

JJavaScript D3 Library

bar chart, 454CSS definitions, 450–451data-driven documents, 449HTML importing library, 450

IPython Notebooks, 449Jinja2 library, 451–453pandas dataframe, 453render() function, 453require.config() method, 450web chart creation, 450

Jinja2 library, 451–453Jython, 22

KK-nearest neighbors classification

decision boundaries, 325–3262D scatterplot, sepals, 324predict() function, 323random.permutation(), 323training and testing set, 322

LLaTeX

accents, 540–547fonts, 539fractions, binomials, and stacked

numbers, 538–539with IPython Notebook

in Markdown Cell, 537in Python 2 Cell, 538

with matplotlib, 537radicals, 539subscripts and superscripts, 538symbols

arrow symbols, 540, 545–546big symbols, 542binary operation and relation

symbols, 542–543Delimiters, 540–541Hebrew, 541

Index

561

lowercase Greek, 540miscellaneous symbols, 540standard function names, 542uppercase Greek, 541

Learning phase, 378Liclipse, 43–46Linear regression, 12Line chart

annotate(), 274arrowprops kwarg, 274Cartesian axes, 273color codes, 270–271data points, 267different series, 269gca() function, 273Greek characters, 272LaTeX expression, 274line and color styles, 270mathematical expressions, 275mathematical function, 268pandas, 276plot() function, 268set_position() function, 273xticks() and yticks() functions, 271

Linux distribution, 90LOD cloud diagram, 16Logistic regression, 12

MMachine learning (ML), 5

algorithm development process, 313deep learning, 351diabetes dataset, 327–328features/attributes, 314Iris flower dataset, 316learning problem, 314linear/least square regression

coef_ attribute, 329fit() function, 329linear correlation, 330parameters, 328physiological factors and

progression of diabetes, 332–333single physiological factor, 330

schematization of, 352supervised learning, 314SVM (see Support vector machines

(SVMs))training and testing set, 315unsupervised learning, 314–315

Mappingadding values, 201–202inplace option, 204rename() function, 204renaming, axes, 202, 204replacing values, 199, 201

Mathematical expressions with LaTeX, see LaTeX

MATLAB, 17matplotlib, 48matplotlib library

architectureartist layer, 236–238backend layer, 236functions and tools, 235layers, 235pylab and pyplot, 238–239scripting layer (pyplot), 238

artist layergraphical representation, 237hierarchical structure, 236primitive and composite, 237

graphical representation, 231, 233LaTeX, 232NumPy, 246

Index

562

Matrix product, 60Merging operation

DataFrame, 183–184dataframe objects, 183index, 187join() function, 187–188JOIN operation, 182left_index/right_index

options, 187left join, right join and

outer join, 186left_on and right_on, 185, 187merge() function, 183, 184

Meteorological data, 409Adriatic Sea and Po Valley, 410

cities, 412Comacchio, 413image of, 411mountainous areas, 410reference standards, 412TheTimeNow website, 413

climate, 409data source

JSON file, 414Weather Map site, 414

IPython Notebookchart representation, 425, 429, 431CSV files, 421DataFrames, 422, 432humidity function, 433–435linear regression, 431matplotlib library, 423Milan, 423read_csv() function, 421result, 423shape() function, 422SVR method, 428–429temperature, 424, 426–427, 432

Jupyter Notebook, 415access internal data, 417command line, 415dataframe, 419–420extraction procedures, 418Ferrara, 416JSON file, 416json.load() function, 415parameters, 419prepare() function, 420

RoseWind (see RoseWind)wind speed, 441

Microsoft excel filesdataframe, 162data.xls, 160, 162internal module xlrd, 160read_excel() function, 161

MongoDB, 178–179Multi Layer Perceptron (MLP)

artificial networks, 360evaluation of, 404experimental data, 404hidden layers, 397IPython session, 387learning phase, 389model definition, 387test phase and accuracy

calculation, 395, 402Musical data, 553

NNatural Language Toolkit (NLTK)

bigrams and collocations, 498common_contexts() function, 493concordance() function, 493corpora, 488downloader tool, 489

Index

563

fileids() function, 491HTML pages, text, 501len() function, 491library, 489macbeth variable, 491Python library, 488request() function, 502selecting words, 497sentimental analysis, 502sents() function, 492similar() function, 494text, network, 500word frequency, 494

macbeth variable, 495most_common() function, 494nltk.download() function, 495nltk.FreqDist() function, 494stopwords, 495string() function, 496

word search, 493Ndarray, 47

array() function, 51–53data, types, 53–54dtype (data-type), 50, 54intrinsic creation, 55–57type() function, 51–52

NOSE MODULE, 91“Not a Number” data

filling, NaN occurrences, 133filtering out NaN

values, 132–133NaN value, 131–132

NumPy libraryarray manipulation (see Array

manipulation)basic operations

aggregate functions, 62arithmetic operators, 57–59

increment and decrement operators, 60–61

matrix product, 59–60ufunc, 61

broadcastingcompatibility, 77complex cases, 78–79operator/function, 76

BSD, 50conditions and Boolean arrays, 69copies/views of objects, 75data analysis, 49indexing, 63

bidimensional array, 64monodimensional ndarray, 63negative index value, 63

installation, 50iterating an array, 67–69ndarray (see Ndarray)Numarray, 49python language, 49reading and writing array data, 82shape manipulation, 70–71slicing, 65–66structured arrays, 79vectorization, 76

OObject-oriented programming language, 20OCR, see Optical Character Recognition

(OCR) softwareOpen data, 15–16Open data sources, 353

climatic data, 552demographics

IPython Notebook, 446matplotlib, 449

Index

564

pandas dataframes, 446–447pop2014_by_state dataframe, 448pop2014 dataframe, 447–448United States Census

Bureau, 445–446financial data, 552health data, 550miscellaneous and public

data sets, 551–552musical data, 553political and government

data, 549–550publications, newspapers,

and books, 553social data, 550–551sports data, 553

Open Source Computer Vision (OpenCV)deep learning, 509image processing and analysis, 509

add() function, 515blackish image, 518blending, 520destroyWindow() method, 512elementary operations, 514imread() method, 510imshow() method, 511load and display, 510merge() method, 513NumPy matrices, 519saving option, 514waitKey() method, 511working process, 512

installation, 509MATLAB packages, 508start programming, 510

Open-source programming language, 21

Optical Character Recognition (OCR) software, 473

order() function, 127

PPandas dataframes, 446, 453Pandas data structures

DataFrame, 102–105assigning values, 107–109deleting column, 110element selection, 105–107filtering, 110membership value, 109–110nested dict, 111transposition, 111

evaluating values, 98–99index objects, 112

duplicate labels, 112–113methods, 112

NaN values, 99, 101NumPy arrays and existing

series, 96–97operations, 120–122operations and mathematical

functions, 97–98series, 93

assigning values, 95declaration, 94dictionaries, 101filtering values, 97index, 93internal elements, selection, 95operations, 102

Pandas library, 87correlation and covariance, 129–131data structures (see Pandas data

structures)

Open data sources (cont.)

Index

565

function application and mappingelement, 123row/column, 123, 125statistics, 125

getting started, 92hierarchical indexing and

leveling, 134–135, 137–138indexes (see Indexing functionalities)installation

Anaconda, 88–89development phases, 91Linux, 90module repository, Windows, 90PyPI, 89source, 90testing, 91

“Not a Number” data, 131–134python data analysis, 87–88sorting and ranking, 126–129

Permutationnew_order array, 211np.random.randint() function, 211numpy.random.permutation()

function, 210random sampling, 211

DataFrame, 211take() function, 211

Pickle—python object serializationcPickle, 168frame.pkl, 170pandas library, 169stream of bytes, 168

Political and government data, 549–550

pop2014_by_county dataframe, 465pop2014_by_state dataframe, 448–449pop2014 dataframe, 447–448Portable programming language, 20

PostgreSQL, 174Principal component analysis

(PCA), 320, 322Public data sets, 551–552PVM, see Python virtual machine (PVM)pyplot module

interactive chart, 239Line2D object, 240plotting window, 240

show() function, 240PyPy interpreter, 22Python, 17

data analysis library, 87–88deep learning, 354frameworks, 354module, 91OpenCV, 508

Python Package Index (PyPI), 39, 89Python’s world

code implementation, 28distributions, 24

Anaconda, 24Enthought Canopy, 26Python(x,y), 26

IDEs (see Interactive development environments (IDEs))

installation, 23–24interact, 28interpreter (see Interpreter)IPython (see IPython)programming language, 19–21PyPI, 39Python 2, 23Python 3, 23running, entire program code, 27SciPy

libraries, 46matplotlib, 48

Index

566

NumPy, 47pandas, 47

shell, 26source code

data structure, 30dictionaries and lists, 31functional programming, 33Hello World, 28index, 32libraries and functions, 30map() function, 33mathematical operations, 29print() function, 29

writing python code, indentation, 34–35

Python virtual machine (PVM), 21PyTorch, 355

QQualitative analysis, 14Quantitative analysis, 14

RR, 17Radial Basis Function (RBF), 340Radicals, LaTeX, 539Ranking, 128–129Reading and writing array

binary files, 82tabular data, 83–84

Reading and writing dataCSV and textual files

header option, 144index_col option, 145myCSV_01.csv, 143

myCSV_03.csv, 145names option, 145read_csv() function, 143, 145read_table() function, 143.txt extension, 142

databasescreate_engine() function, 171dataframe, 175pandas.io.sql module, 171pgAdmin III, 175–176PostgreSQL, 174read_sql() function, 172read_sql_query() function, 177read_sql_table() function, 177sqlalchemy, 171sqlite3, 171

DataFrame objects, 141functionalities, 141HDF5 library

data structures, 167HDFStore, 167hierarchical data format, 166mydata.h5, 167

HTML filesdata structures, 152read_html (), 155web_frames, 156web pages, 152web scraping, 152

I/O API Tools, 141–142JSON data

books.json, 164frame.json, 164json_normalize() function, 165JSONViewer, 162–163normalization, 164read_json() and to_json(), 162read_json() function, 164–165

Python’s world (cont.)

Index

567

Microsoft excel files, 159NoSQL database

insert() function, 179MongoDB, 178–180

pickle—python object serialization, 168RegExp

metacharacters, 146read_table(), 146skiprows, 148

TXT files, 147–148nrows and skiprows options, 149portion by portion, 149

writing (see Writing data)XML (see XML)

Regression models, 4, 12Reindexing, 114–116RoseWind

DataFrame, 436–437hist array, 438–439polar chart, 438, 440–441scatter plot representation, 438showRoseWind() function, 439, 441

SScikit-learn library, 473

data analysis, 474k-nearest neighbors classification, 322PCA, 320Python module, 313sklearn.svm.SVC, 475supervised learning, 315svm module, 475

SciPylibraries, 46matplotlib, 48NumPy, 47pandas, 47

Sentimental analysis, 502document_features()

function, 504documents, 503list() function, 504movie_reviews, 503negative/positive opinion, 505opinion mining, 502

Shape manipulationreshape() function, 70shape attribute, 70transpose() function, 71

Single layer perceptron (SLP), 371accuracy, 359activation function, 358, 359architecture, 357cost optimization, 382data analysis, 372evaluation phase, 359learning phase, 359, 378model definition, 374

explicitly, 376implicitly, 376learning phase, 375placeholders, 376tf.add() function, 377tf.nn.softmax() function, 377

modules, 372representation, 358testing set, 385test phase and accuracy

calculation, 383training sets, 359

Social data, 550sort_index() function, 126–128, 138Sports data, 553SQLite3, 171stack() function, 136

Index

568

String manipulationbuilt-in methods

count() function, 214error message, 214index() and find(), 213join() function, 213replace() function, 214split() function, 212strip() function, 212

regular expressionsfindall() function, 215–216match() function, 216re.compile() function, 215regex, 214re.split() function, 215split() function, 215

Structured arraysdtype option, 79, 81structs/records, 79

Subjective interpretations, 14Subscripts and superscripts,

LaTeX, 538Supervised learning

machine learning, 314scikit-learn, 315

Support vector classification (SVC), 475decision area, 336effect, decision boundary, 338–339nonlinear, 339–341number of points, C parameter, 337–338predict() function, 336–337regularization, 337support_vectors array, 337training set, decision space, 334–336

Support vector machines (SVMs)decisional space, 334decision boundary, 334Iris Dataset

decision boundaries, 342linear decision boundaries, 342–343polynomial decision boundaries, 344polynomial kernel, 343–344RBF kernel, 344training set, 342

SVC (see Support vector classification (SVC))

SVR (see Support vector regression (SVR))

Support vector regression (SVR)curves, 347diabetes dataset, 345linear predictive model, 345test set, data, 345

swaplevel() function, 137

TTensorFlow, 349, 354, 362, 480

data flow graph, 362Google’s framework, 362installation, 363IPython QtConsole, 364MLP (see Multi Layer Perceptron

(MLP))model and sessions, 364SLP (see Single layer perceptron (SLP))tensors

operation, 370parameters, 366print() function, 368representations of, 367tf.convert_to_tensor() function, 368tf.ones() method, 369tf.random_normal() function, 369tf.random_uniform() function, 369tf.zeros() method, 368

Index

569

Text analysis techniquesdefinition, 487NLTK (see Natural Language Toolkit

(NLTK))techniques, 488

Theano, 355trigrams() function, 499

U, VUnited States Census Bureau, 445–446Universal functions (ufunc), 61Unsupervised learning, 314

WWeb Scraping, 4, 10Wind speed

polar chart representation, 442RoseWind_Speed() function, 441ShowRoseWind() function, 442

ShowRoseWind_Speed() function, 442to_csv () function, 443

Writing dataHTML files

myFrame.html, 155to_html() function, 153–154

na_rep option, 151to_csv() function, 150–151

X, Y, ZXML

books.xml, 157–158getchildren(), 158getroot() function, 158lxml.etree tree structure, 159lxml library, 157objectify, 158parse() function, 158tag attribute, 158text attribute, 159

Index

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