learning vector quantization lvq
TRANSCRIPT
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Machine Learning&
Neural Networks
Eric Postma
IKAT
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Contenido
Perceptron y perceptrón multicapa
Learning Vector Quantisation
Kohonen Self-Organising Feature Map
Multidimensional Scaling (optional)
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Perceptrón
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Deducción de la regla delta de aprendizaje
Target output
Actual output
h = i
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Perceptrón Multicapa
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Función sigmoidal
Puede ser también tanh (<-1,+1> ipv <0,1>) Obteniendo f’(x) = f(x) [1 – f(x)]
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Deducción de la regla delta generalizada
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Función de error (LMS)
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Ajuste del vector de pesos (capa oculta – salida)
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Ajuste del vector de pesos (capa de entrada – capa oculta)
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Propagación hacia adelante y retropropagación
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El problema de muestras dispersas
Los puntos (muestras) dispersos tienen la mayor contribución en el error total
outlier
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Solución al problema de los puntos dispersos
Error Minkowsky (R < 2)
Para R = 1 es el mínimo de la función de error de mediana de los datos
( Número de puntos < mediana = Número de puntos > mediana )
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El problema de inversión
x
t
x
t
Functional mappingNon-functional inverse mapping
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Ejemplo: análisis espectral
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Alternativa: modelos mixtos
Entrada de la red: vector de parámetros Una combinación lineal de funciones
kernel parametrizadas (p.e. Funciones Gaussianas) dada como salida
El vector de parámetros determina la forma de las funciones kernel
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Solución m.b.v. Modelo mixto
x
t
Non-functional inverse mapping
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Weight decay
Conjunción del valor absoluto de los pesos Resulta en un modelo simple El parametro Lambda determina el peso relativo
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Regla delta generalizada con Weight Decay
Deducción de la regla delta generalizada para una red con
LMS error + weight decay
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Regla de aprendizaje con weight decay
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Cushings Dataset
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Algunos resultados… Perceptrón multicapa (2-2-3) 1 capa oculta Conexión directa entrada-salida Salida Soft-max Total 21 pesos
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2 hidden (perfect fit)
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2 hidden (perfect fit)
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2 hidden, lambda = 0.001(smoother)
= Lokaal minimum
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2 hidden, lambda = 0.01
= Lokaal minimum
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5 hidden, lambda = 0.01
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20 hidden, lambda = 0.01
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Learning Vector Quantisation(LVQ)
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Self-organizing Feature Maps
Teuvo Kohonen
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Inspiración biológica Imágenes
topográficas en la corteza
Corteza visual Corteza
somatosensorial Corteza motora Corteza
inferotemporal
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La diferencia más importante con LVQ
La vecindad
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SOM toegepast op tijdreeksen
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Matlab SOM toolbox
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Los datos (3D)
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Unified Distance Matrix
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Sammon mapping
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Hit histogram 1 (numeric)
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Hit histogram 2 (size)