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‎Contents.m‎

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% Netlab Toolbox
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% Version 3.2.1 31-Oct-2001
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%
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% conffig - Display a confusion matrix.
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% confmat - Compute a confusion matrix.
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% conjgrad - Conjugate gradients optimization.
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% consist - Check that arguments are consistent.
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% datread - Read data from an ascii file.
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% datwrite - Write data to ascii file.
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% dem2ddat - Generates two dimensional data for demos.
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% demard - Automatic relevance determination using the MLP.
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% demev1 - Demonstrate Bayesian regression for the MLP.
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% demev2 - Demonstrate Bayesian classification for the MLP.
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% demev3 - Demonstrate Bayesian regression for the RBF.
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% demgauss - Demonstrate sampling from Gaussian distributions.
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% demglm1 - Demonstrate simple classification using a generalized linear model.
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% demglm2 - Demonstrate simple classification using a generalized linear model.
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% demgmm1 - Demonstrate density modelling with a Gaussian mixture model.
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% demgmm3 - Demonstrate density modelling with a Gaussian mixture model.
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% demgmm4 - Demonstrate density modelling with a Gaussian mixture model.
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% demgmm5 - Demonstrate density modelling with a PPCA mixture model.
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% demgp - Demonstrate simple regression using a Gaussian Process.
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% demgpard - Demonstrate ARD using a Gaussian Process.
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% demgpot - Computes the gradient of the negative log likelihood for a mixture model.
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% demgtm1 - Demonstrate EM for GTM.
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% demgtm2 - Demonstrate GTM for visualisation.
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% demhint - Demonstration of Hinton diagram for 2-layer feed-forward network.
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% demhmc1 - Demonstrate Hybrid Monte Carlo sampling on mixture of two Gaussians.
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% demhmc2 - Demonstrate Bayesian regression with Hybrid Monte Carlo sampling.
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% demhmc3 - Demonstrate Bayesian regression with Hybrid Monte Carlo sampling.
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% demkmean - Demonstrate simple clustering model trained with K-means.
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% demknn1 - Demonstrate nearest neighbour classifier.
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% demmdn1 - Demonstrate fitting a multi-valued function using a Mixture Density Network.
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% demmet1 - Demonstrate Markov Chain Monte Carlo sampling on a Gaussian.
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% demmlp1 - Demonstrate simple regression using a multi-layer perceptron
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% demmlp2 - Demonstrate simple classification using a multi-layer perceptron
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% demnlab - A front-end Graphical User Interface to the demos
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% demns1 - Demonstrate Neuroscale for visualisation.
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% demolgd1 - Demonstrate simple MLP optimisation with on-line gradient descent
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% demopt1 - Demonstrate different optimisers on Rosenbrock's function.
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% dempot - Computes the negative log likelihood for a mixture model.
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% demprgp - Demonstrate sampling from a Gaussian Process prior.
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% demprior - Demonstrate sampling from a multi-parameter Gaussian prior.
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% demrbf1 - Demonstrate simple regression using a radial basis function network.
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% demsom1 - Demonstrate SOM for visualisation.
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% demtrain - Demonstrate training of MLP network.
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% dist2 - Calculates squared distance between two sets of points.
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% eigdec - Sorted eigendecomposition
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% errbayes - Evaluate Bayesian error function for network.
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% evidence - Re-estimate hyperparameters using evidence approximation.
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% fevbayes - Evaluate Bayesian regularisation for network forward propagation.
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% gauss - Evaluate a Gaussian distribution.
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% gbayes - Evaluate gradient of Bayesian error function for network.
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% glm - Create a generalized linear model.
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% glmderiv - Evaluate derivatives of GLM outputs with respect to weights.
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% glmerr - Evaluate error function for generalized linear model.
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% glmevfwd - Forward propagation with evidence for GLM
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% glmfwd - Forward propagation through generalized linear model.
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% glmgrad - Evaluate gradient of error function for generalized linear model.
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% glmhess - Evaluate the Hessian matrix for a generalised linear model.
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% glminit - Initialise the weights in a generalized linear model.
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% glmpak - Combines weights and biases into one weights vector.
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% glmtrain - Specialised training of generalized linear model
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% glmunpak - Separates weights vector into weight and bias matrices.
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% gmm - Creates a Gaussian mixture model with specified architecture.
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% gmmactiv - Computes the activations of a Gaussian mixture model.
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% gmmem - EM algorithm for Gaussian mixture model.
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% gmminit - Initialises Gaussian mixture model from data
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% gmmpak - Combines all the parameters in a Gaussian mixture model into one vector.
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% gmmpost - Computes the class posterior probabilities of a Gaussian mixture model.
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% gmmprob - Computes the data probability for a Gaussian mixture model.
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% gmmsamp - Sample from a Gaussian mixture distribution.
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% gmmunpak - Separates a vector of Gaussian mixture model parameters into its components.
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% gp - Create a Gaussian Process.
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% gpcovar - Calculate the covariance for a Gaussian Process.
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% gpcovarf - Calculate the covariance function for a Gaussian Process.
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% gpcovarp - Calculate the prior covariance for a Gaussian Process.
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% gperr - Evaluate error function for Gaussian Process.
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% gpfwd - Forward propagation through Gaussian Process.
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% gpgrad - Evaluate error gradient for Gaussian Process.
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% gpinit - Initialise Gaussian Process model.
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% gppak - Combines GP hyperparameters into one vector.
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% gpunpak - Separates hyperparameter vector into components.
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% gradchek - Checks a user-defined gradient function using finite differences.
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% graddesc - Gradient descent optimization.
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% gsamp - Sample from a Gaussian distribution.
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% gtm - Create a Generative Topographic Map.
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% gtmem - EM algorithm for Generative Topographic Mapping.
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% gtmfwd - Forward propagation through GTM.
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% gtminit - Initialise the weights and latent sample in a GTM.
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% gtmlmean - Mean responsibility for data in a GTM.
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% gtmlmode - Mode responsibility for data in a GTM.
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% gtmmag - Magnification factors for a GTM
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% gtmpost - Latent space responsibility for data in a GTM.
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% gtmprob - Probability for data under a GTM.
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% hbayes - Evaluate Hessian of Bayesian error function for network.
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% hesschek - Use central differences to confirm correct evaluation of Hessian matrix.
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% hintmat - Evaluates the coordinates of the patches for a Hinton diagram.
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% hinton - Plot Hinton diagram for a weight matrix.
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% histp - Histogram estimate of 1-dimensional probability distribution.
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% hmc - Hybrid Monte Carlo sampling.
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% kmeans - Trains a k means cluster model.
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% knn - Creates a K-nearest-neighbour classifier.
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% knnfwd - Forward propagation through a K-nearest-neighbour classifier.
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% linef - Calculate function value along a line.
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% linemin - One dimensional minimization.
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% mdn - Creates a Mixture Density Network with specified architecture.
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% mdn2gmm - Converts an MDN mixture data structure to array of GMMs.
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% mdndist2 - Calculates squared distance between centres of Gaussian kernels and data
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% mdnerr - Evaluate error function for Mixture Density Network.
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% mdnfwd - Forward propagation through Mixture Density Network.
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% mdngrad - Evaluate gradient of error function for Mixture Density Network.
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% mdninit - Initialise the weights in a Mixture Density Network.
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% mdnpak - Combines weights and biases into one weights vector.
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% mdnpost - Computes the posterior probability for each MDN mixture component.
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% mdnprob - Computes the data probability likelihood for an MDN mixture structure.
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% mdnunpak - Separates weights vector into weight and bias matrices.
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% metrop - Markov Chain Monte Carlo sampling with Metropolis algorithm.
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% minbrack - Bracket a minimum of a function of one variable.
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% mlp - Create a 2-layer feedforward network.
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% mlpbkp - Backpropagate gradient of error function for 2-layer network.
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% mlpderiv - Evaluate derivatives of network outputs with respect to weights.
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% mlperr - Evaluate error function for 2-layer network.
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% mlpevfwd - Forward propagation with evidence for MLP
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% mlpfwd - Forward propagation through 2-layer network.
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% mlpgrad - Evaluate gradient of error function for 2-layer network.
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% mlphdotv - Evaluate the product of the data Hessian with a vector.
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% mlphess - Evaluate the Hessian matrix for a multi-layer perceptron network.
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% mlphint - Plot Hinton diagram for 2-layer feed-forward network.
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% mlpinit - Initialise the weights in a 2-layer feedforward network.
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% mlppak - Combines weights and biases into one weights vector.
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% mlpprior - Create Gaussian prior for mlp.
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% mlptrain - Utility to train an MLP network for demtrain
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% mlpunpak - Separates weights vector into weight and bias matrices.
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% netderiv - Evaluate derivatives of network outputs by weights generically.
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% neterr - Evaluate network error function for generic optimizers
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% netevfwd - Generic forward propagation with evidence for network
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% netgrad - Evaluate network error gradient for generic optimizers
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% nethess - Evaluate network Hessian
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% netinit - Initialise the weights in a network.
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% netopt - Optimize the weights in a network model.
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% netpak - Combines weights and biases into one weights vector.
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% netunpak - Separates weights vector into weight and bias matrices.
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% olgd - On-line gradient descent optimization.
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% pca - Principal Components Analysis
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% plotmat - Display a matrix.
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% ppca - Probabilistic Principal Components Analysis
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% quasinew - Quasi-Newton optimization.
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% rbf - Creates an RBF network with specified architecture
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% rbfbkp - Backpropagate gradient of error function for RBF network.
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% rbfderiv - Evaluate derivatives of RBF network outputs with respect to weights.
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% rbferr - Evaluate error function for RBF network.
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% rbfevfwd - Forward propagation with evidence for RBF
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% rbffwd - Forward propagation through RBF network with linear outputs.
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% rbfgrad - Evaluate gradient of error function for RBF network.
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% rbfhess - Evaluate the Hessian matrix for RBF network.
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% rbfjacob - Evaluate derivatives of RBF network outputs with respect to inputs.
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% rbfpak - Combines all the parameters in an RBF network into one weights vector.
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% rbfprior - Create Gaussian prior and output layer mask for RBF.
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% rbfsetbf - Set basis functions of RBF from data.
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% rbfsetfw - Set basis function widths of RBF.
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% rbftrain - Two stage training of RBF network.
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% rbfunpak - Separates a vector of RBF weights into its components.
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% rosegrad - Calculate gradient of Rosenbrock's function.
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% rosen - Calculate Rosenbrock's function.
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% scg - Scaled conjugate gradient optimization.
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% som - Creates a Self-Organising Map.
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% somfwd - Forward propagation through a Self-Organising Map.
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% sompak - Combines node weights into one weights matrix.
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% somtrain - Kohonen training algorithm for SOM.
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% somunpak - Replaces node weights in SOM.
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%
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% Copyright (c) Ian T Nabney (1996-2001)
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%

‎conffig.m‎

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function fh=conffig(y, t)
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%CONFFIG Display a confusion matrix.
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%
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% Description
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% CONFFIG(Y, T) displays the confusion matrix and classification
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% performance for the predictions mat{y} compared with the targets T.
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% The data is assumed to be in a 1-of-N encoding, unless there is just
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% one column, when it is assumed to be a 2 class problem with a 0-1
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% encoding. Each row of Y and T corresponds to a single example.
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%
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% In the confusion matrix, the rows represent the true classes and the
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% columns the predicted classes.
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%
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% FH = CONFFIG(Y, T) also returns the figure handle FH which can be
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% used, for instance, to delete the figure when it is no longer needed.
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%
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% See also
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% CONFMAT, DEMTRAIN
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%
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% Copyright (c) Ian T Nabney (1996-2001)
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[C, rate] = confmat(y, t);
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fh = figure('Name', 'Confusion matrix', ...
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'NumberTitle', 'off');
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plotmat(C, 'k', 'k', 14);
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title(['Classification rate: ' num2str(rate(1)) '%'], 'FontSize', 14);

‎confmat.m‎

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function [C,rate]=confmat(Y,T)
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%CONFMAT Compute a confusion matrix.
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%
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% Description
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% [C, RATE] = CONFMAT(Y, T) computes the confusion matrix C and
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% classification performance RATE for the predictions mat{y} compared
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% with the targets T. The data is assumed to be in a 1-of-N encoding,
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% unless there is just one column, when it is assumed to be a 2 class
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% problem with a 0-1 encoding. Each row of Y and T corresponds to a
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% single example.
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%
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% In the confusion matrix, the rows represent the true classes and the
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% columns the predicted classes. The vector RATE has two entries: the
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% percentage of correct classifications and the total number of correct
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% classifications.
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%
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% See also
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% CONFFIG, DEMTRAIN
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%
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% Copyright (c) Ian T Nabney (1996-2001)
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[n c]=size(Y);
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[n2 c2]=size(T);
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if n~=n2 | c~=c2
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error('Outputs and targets are different sizes')
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end
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if c > 1
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% Find the winning class assuming 1-of-N encoding
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[maximum Yclass] = max(Y', [], 1);
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TL=[1:c]*T';
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else
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% Assume two classes with 0-1 encoding
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c = 2;
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class2 = find(T > 0.5);
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TL = ones(n, 1);
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TL(class2) = 2;
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class2 = find(Y > 0.5);
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Yclass = ones(n, 1);
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Yclass(class2) = 2;
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end
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% Compute
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correct = (Yclass==TL);
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total=sum(sum(correct));
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rate=[total*100/n total];
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C=zeros(c,c);
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for i=1:c
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for j=1:c
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C(i,j) = sum((Yclass==j).*(TL==i));
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end
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end

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