ImageClassification_RadialBasisFunctions_SelfOrganizingMaps

Image classification on MNIST Hand-written Digits Dataset and function aproximation (regression) via full custom Radial Basis Functions (Exact Interpolation + Fixed Centers Selected at Random Method + Regularization) and Self Organizing Maps implementation.

For usage instructions please check Usage README

For full documentation - system design, experiments & findings please read ImageClassification_RadialBasisFunctions_SelfOrganizingMapsDoc Report

GutHub Pages Format

Introduction

Few experiments are undertaken:

Q1. Function Approximation with RBFN

๐‘ฆ = 1.2sin(๐œ‹๐‘ฅ)โˆ’cos(2.4๐œ‹๐‘ฅ), ๐‘“๐‘œ๐‘Ÿ ๐‘ฅ โˆˆ [โˆ’1.6,1.6]

(a) Exact interpolation method (Gaussian, standard deviation of 0.1).

(b) Fixed Centers Selected at Random

(c) Regularization study

Q2. Handwritten Digits Classification using RBFN

(a) Exact Interpolation Method + regularization (Gaussian function, standard deviation of 100)

(b) Gaussian function with standard deviation of 100 + varying width

(c) Xlassical โ€œK-Mean Clusteringโ€ with 2 centers.

Q3. Self-Organizing Map (SOM)

(a) Map a 1-dimensional output layer of 40 neurons to a โ€œhatโ€ (sinc function) + visualisation.

(b) Maps a 2-dimensional output layer of 64 (i.e. 8ร—8) neurons to a โ€œcircleโ€ + visualisation.

(c) Cluster and classifiy handwritten digits.

+ Visualisation of conceptual/semantic map of the trained SOM and the trained weights of each output neuron on a 10ร—10 map.

Figures:

Radial Basis Functions

Radial Basis Function SIN Aproximation Radial Basis Function SIN Aproximation

Radial Basis Function SIN Aproximation Radial Basis Function Architecture

Self Organizing Maps

Self Organizing Maps SIN Aproximation Self Organizing Maps SIN Aproximation Self Organizing Maps SIN Aproximation Self Organizing Maps SIN Aproximation Self Organizing Maps SIN Aproximation Self Organizing Maps SIN Aproximation Self Organizing Maps SIN Aproximation Self Organizing Maps SIN Aproximation

Self Organizing Maps CIRCLE Aproximation Self Organizing Maps CIRCLE Aproximation Self Organizing Maps CIRCLE Aproximation Self Organizing Maps CIRCLE Aproximation Self Organizing Maps CIRCLE Aproximation Self Organizing Maps CIRCLE Aproximation Self Organizing Maps CIRCLE Aproximation Self Organizing Maps CIRCLE Aproximation

Self Organizing Maps MNIST Classification Self Organizing Maps MNIST Classification

Self Organizing Maps MNIST Classification Self Organizing Maps MNIST Classification