1010 lines
44 KiB
Mathematica
1010 lines
44 KiB
Mathematica
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classdef NeuralNetwork < handle & ElasticNodes & NeuralNetworkConstants
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%NEURALNETWORK It encapsulate a common MLP (Multilayer Perceptron, aka
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%Feedforward network)
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% This object has the main attributes a Neural Network needs to
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% operate, along with its main functions/behaviors. Some extra
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% behaviors were built in order to achieve research goals.
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%
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% This class features elastic network width by ElasticNodes
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% inheritance. Network edith adaptation supports automatic generation
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% of new hidden nodes and prunning of inconsequential nodes. This
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% mechanism is controlled by the NS (Network Significance) method
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% which estimates the network generalization power in terms of bias
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% and variance.
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%% Standard Neural Network public properties
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properties (Access = public)
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layers %Layers of a standard neural network
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layerValue % Layer (Input and Hidden Layer) values
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outputLayerValue % Output layers values
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weight % Weights
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bias % Added bias
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momentum % Weight momentum
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biasMomentum
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outputWeight % Weights to output layer
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outputBias % Bias to output layer
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outputMomentum % Weight momentum from output layer
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outputBiasMomentum
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gradient % Gradients
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outputGradient % Gradients from output layers
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biasGradient;
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outputBiasGradient;
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activationFunction % Each real layer activation function
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outputActivationFunctionLossFunction % Each output activation function
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learningRate = 0.01; % Learning rate
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momentumRate = 0.95; % Momentum rate
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errorValue % Network error
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lossValue % Network Loss
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lambda = 0.001;
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end
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%% Standard Neural Network protected properties
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properties (Access = protected)
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nHiddenLayers % Number of hidden layers (i.e., not counting input and output layer
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inputSize % Size of input layer
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outputSize % Size of output layer
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end
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%% TODO define section name
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properties (Access = public)
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agmm
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end
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properties (Access = protected)
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isAgmmAble = false;
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end
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%% Metrics and performance public properties
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properties (Access = public)
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%test metrics
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sigma % Network's prediction
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misclassifications % Number of misclassifications after test
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classificationRate % Classification rate after test
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residualError % Residual error after test
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outputedClasses % Classed outputed during classes
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trueClasses % True target classes
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end
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%% Helpers protected properties
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properties (Access = protected)
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util = Util; % Caller for several util computations
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end
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%% Standard Neural Network public methods
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methods (Access = public)
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function self = NeuralNetwork(layers)
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%NeuralNetwork
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% layers (array)
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% This array describes a FeedForward Network structure by
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% the number of layers on it.
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% An FFNN with an input layer of 8 nodes, a hidden layer
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% of 10 nodes and an output layer of 3 nodes would be
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% described by [8 10 3].
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% An FFNN with an input layer of 784 nodes, a hidden
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% layer 1 of 800 nodes, a hidden layer 2 of 400 nodes and
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% an output layer of 10 nodes would be described as [784 800 400 10]
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self@ElasticNodes(numel(layers) - 1);
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self.inputSize = layers(1);
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self.outputSize = layers(end);
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self.layers = layers;
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self.nHiddenLayers = length(layers) - 2;
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for i = 1 : self.nHiddenLayers
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self.weight{i} = normrnd(0, sqrt(2 / self.layers(i) + 1), [self.layers(i + 1), self.layers(i)]);
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self.bias{i} = normrnd(0, sqrt(2 / self.layers(i) + 1), [1, self.layers(i + 1)]);
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self.momentum{i} = zeros(size(self.weight{i}));
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self.biasMomentum{i} = zeros(size(self.bias{i}));
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self.activationFunction(i) = self.ACTIVATION_FUNCTION_SIGMOID();
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end
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self.outputWeight = normrnd(0, sqrt(2 / self.layers(end) + 1), [self.layers(end), self.layers(end - 1)]);
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self.outputBias = normrnd(0, sqrt(2 / self.layers(end) + 1), [1, self.layers(end)]);
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self.outputMomentum = zeros(size(self.outputWeight));
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self.outputBiasMomentum = zeros(size(self.outputBias));
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self.outputActivationFunctionLossFunction = self.ACTIVATION_LOSS_FUNCTION_SOFTMAX_CROSS_ENTROPY();
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end
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function feedforward(self, X, y)
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% % feedforward
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% Perform the forwarding pass throughout the network and
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% calculate the network error
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% X (matrix)
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% Input matrix
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% y (matrix)
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% Target matrix
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self.forwardpass(X)
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self.calculateError(y)
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end
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function forwardpass(self, X)
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% forwardpass
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% Perform the forwarding pass throughout the network without
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% calculate the network error, that's why it doesn't need the
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% target class.
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% Because of this, we can use this class just to populate the
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% hidden layers from the source data
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% X (matrix)
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% Input matrix
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self.layerValue{1} = X;
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for i = 1 : self.nHiddenLayers
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previousLayerValueWithBias = [ones(size(self.layerValue{i}, 1), 1) self.layerValue{i}];
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switch self.activationFunction(i)
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case self.ACTIVATION_FUNCTION_SIGMOID()
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self.layerValue{i + 1} = sigmf(previousLayerValueWithBias * [self.bias{i}' self.weight{i}]', [1, 0]);
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case self.ACTIVATION_FUNCTION_TANH()
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error('Not implemented');
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case self.ACTIVATION_FUNCTION_RELU()
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error('Not implemented yet');
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case self.ACTIVATION_FUNCTION_LINEAR()
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error('Not implemented yet');
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case self.ACTIVATION_FUNCTION_SOFTMAX()
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error('Not implemented yet');
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end
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end
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previousLayerValueWithBias = [ones(size(self.layerValue{end}, 1), 1) self.layerValue{end}];
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switch self.outputActivationFunctionLossFunction
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case self.ACTIVATION_LOSS_FUNCTION_SIGMOID_MSE()
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self.outputLayerValue = sigmf(previousLayerValueWithBias * [self.outputBias' self.outputWeight]', [1, 0]);
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case self.ACTIVATION_LOSS_FUNCTION_TANH()
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error('Not implemented yet');
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case self.ACTIVATION_LOSS_FUNCTION_RELU()
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error('Not implemented yet');
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case self.ACTIVATION_LOSS_FUNCTION_SOFTMAX_CROSS_ENTROPY()
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self.outputLayerValue = previousLayerValueWithBias * [self.outputBias' self.outputWeight]';
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self.outputLayerValue = exp(self.outputLayerValue - max(self.outputLayerValue, [], 2));
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self.outputLayerValue = self.outputLayerValue./sum(self.outputLayerValue, 2);
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case self.ACTIVATION_LOSS_FUNCTION_LINEAR_CROSS_ENTROPY()
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error('Not implemented yet');
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end
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end
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function backpropagate(self)
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%backpropagate
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% Perform back-propagation thoughout the network.
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% We assume that you already populate the hidden layers and the
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% network error by calling the feedforward method.
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dW = {zeros(1, self.nHiddenLayers + 1)};
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db = {zeros(1, self.nHiddenLayers + 1)};
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for i = self.nHiddenLayers : - 1 : 1
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if i == self.nHiddenLayers
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% THIS IS THE GRADIENT OF THE LOSS FUNCTION
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switch self.outputActivationFunctionLossFunction
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case self.ACTIVATION_LOSS_FUNCTION_SIGMOID_MSE()
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dW{i + 1} = - self.errorValue .* self.outputLayerValue .* (1 - self.outputLayerValue);
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db{i + 1} = - sum(self.errorValue, 1)/size(self.errorValue, 1);
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case self.ACTIVATION_LOSS_FUNCTION_TANH()
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error('Not implemented');
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case self.ACTIVATION_LOSS_FUNCTION_RELU()
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error('Not implemented');
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case self.ACTIVATION_LOSS_FUNCTION_SOFTMAX_CROSS_ENTROPY()
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dW{i + 1} = - self.errorValue;
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db{i + 1} = - sum(self.errorValue, 1)/size(self.errorValue, 1);
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case self.ACTIVATION_LOSS_FUNCTION_LINEAR_CROSS_ENTROPY()
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dW{i + 1} = - self.errorValue;
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db{i + 1} = - sum(self.errorValue, 1)/size(self.errorValue, 1);
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end
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end
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switch char(self.activationFunction(i))
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case self.ACTIVATION_FUNCTION_SIGMOID()
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dActivationFunction = self.layerValue{i + 1} .* (1 - self.layerValue{i + 1});
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case self.ACTIVATION_FUNCTION_TANH()
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error('Not implemented');
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case self.ACTIVATION_FUNCTION_RELU()
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error('Not implemented');
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case self.ACTIVATION_FUNCTION_LINEAR()
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dActivationFunction = 1;
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case self.ACTIVATION_FUNCTION_SOFTMAX()
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error('Not implemented');
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end
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if i == self.nHiddenLayers
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z = dW{i + 1} * self.outputWeight;
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dW{i} = z .* dActivationFunction;
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db{i} = sum(dW{i}, 1)/size(dW{i}, 1);
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else
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z = dW{i + 1} * self.weight{i + 1};
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dW{i} = z .* dActivationFunction;
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db{i} = sum(dW{i}, 1)/size(dW{i}, 1);
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end
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end
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self.outputGradient = dW{end}' * self.layerValue{end};
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self.outputBiasGradient = db{end};
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for i = 1 : self.nHiddenLayers
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self.gradient{i} = dW{i}' * self.layerValue{i};
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self.biasGradient{i} = db{i};
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end
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end
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function test(self, X, y)
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%test
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% Test the neural network, getting its output by an ensemble
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% composed of a selected numbers of outputLayers.
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% It also has the ability to update the importance weight of
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% each output layer, if necessary.
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% X (matrix)
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% Input matrix
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% y (matrix)
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% Target matrix
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self.feedforward(X, y);
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m = size(y, 1);
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[~, self.trueClasses] = max(y, [], 2);
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self.sigma = self.outputLayerValue;
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[rawOutput, outputtedClasses] = max(self.sigma, [], 2);
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self.misclassifications = find(outputtedClasses ~= self.trueClasses);
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self.classificationRate = 1 - numel(self.misclassifications) / m;
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self.residualError = 1 - rawOutput;
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self.outputedClasses = outputtedClasses;
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end
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function train(self, X, y, weightNo)
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%train
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% Train the neural network performing 3 complete stages:
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% - Feed-forward
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% - Back-propagation
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% - Weight updates
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% X (matrix)
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% Input matrix
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% y (matrix)
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% Target matrix
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% weightNo (integer) [optional]
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% You has the ability to define which weight and bias you
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% want to update using backpropagation. This method will
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% update only that weight and bias, even if there is
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% weights and biases on layers before and after that.
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% The number of the weight and bias you want to update.
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% Remember that 1 indicates the weight and bias that get
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% out of the input layer.
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self.feedforward(X,y);
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self.backpropagate();
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switch nargin
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case 4
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self.trainWeight(weightNo);
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case 3
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for i = self.nHiddenLayers + 1 : -1 : 1
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self.trainWeight(i);
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end
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end
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end
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function trainWeight(self,weightNo)
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%trainWeight
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% This methods will only update a set of weights and biases.
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% Normally you will not call this method directly, but will
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% the method train as a middle man.
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% weightNo (integer)
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% The number of the weight and bias you want to update.
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% Remember that 1 indicates the weight and bias that get
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% out of the input layer.
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self.updateWeight(weightNo);
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end
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end
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%% Standard Neural Network private methods
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methods (Access = private)
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function updateWeight(self, weightNo)
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%updateWeights
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% Perform weight and bias update into a single weight and bias
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% weightNo (integer)
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% Number/Position of the weight/bias you want to update
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w = weightNo; %readability
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if w > self.nHiddenLayers
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dW = self.learningRate .* self.outputGradient;
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db = self.learningRate' .* self.outputBiasGradient;
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if self.momentumRate > 0
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self.outputMomentum = self.momentumRate * self.outputMomentum + dW;
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self.outputBiasMomentum = self.momentumRate * self.outputBiasMomentum + db;
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dW = self.outputMomentum;
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db = self.outputBiasMomentum;
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end
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if true == false
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self.outputWeight = (1 - self.learningRate * self.lambda) * self.outputWeight - dW;
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self.outputBias = (1 - self.learningRate * self.lambda) * self.outputBias - db;
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self.outputWeight = (1 - self.learningRate * self.lambda) * self.outputWeight - dW;
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self.outputBias = (1 - self.learningRate * self.lambda) * self.outputBias - db;
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else
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self.outputWeight = self.outputWeight - dW;
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self.outputBias = self.outputBias - db;
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end
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else
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dW = self.learningRate .* self.gradient{w};
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db = self.learningRate' .* self.biasGradient{w};
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if self.momentumRate > 0
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self.momentum{w} = self.momentumRate * self.momentum{w} + dW;
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self.biasMomentum{w} = self.momentumRate * self.biasMomentum{w} + db;
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dW = self.momentum{w};
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db = self.biasMomentum{w};
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end
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if true == false
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self.weight{w} = (1 - self.learningRate * self.lambda) * self.weight{w} - dW;
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self.bias{w} = (1 - self.learningRate * self.lambda) * self.bias{w} - db;
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else
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self.weight{w} = self.weight{w} - dW;
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self.bias{w} = self.bias{w} - db;
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end
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end
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||
|
|
end
|
||
|
|
|
||
|
|
function calculateError(self, y)
|
||
|
|
%calculateError
|
||
|
|
% Calculates the error.
|
||
|
|
% This method probably will be called by the feedforward
|
||
|
|
% method and seldom will be used standalone.
|
||
|
|
m = size(y,1);
|
||
|
|
|
||
|
|
%TODO: Add the possibility to input which error function we
|
||
|
|
%want to use
|
||
|
|
switch self.outputActivationFunctionLossFunction
|
||
|
|
case self.ACTIVATION_LOSS_FUNCTION_SIGMOID_MSE()
|
||
|
|
self.errorValue = y - self.outputLayerValue;
|
||
|
|
self.lossValue = 1 / 2 * sum(sum(self.errorValue .^ 2)) / m;
|
||
|
|
|
||
|
|
case self.ACTIVATION_LOSS_FUNCTION_TANH()
|
||
|
|
error('Not implemented');
|
||
|
|
|
||
|
|
case self.ACTIVATION_LOSS_FUNCTION_RELU()
|
||
|
|
error('Not implemented');
|
||
|
|
|
||
|
|
case self.ACTIVATION_LOSS_FUNCTION_SOFTMAX_CROSS_ENTROPY()
|
||
|
|
self.errorValue = y - self.outputLayerValue;
|
||
|
|
self.lossValue = - sum(sum(y .* log(self.outputLayerValue))) / m;
|
||
|
|
|
||
|
|
case self.ACTIVATION_LOSS_FUNCTION_LINEAR_CROSS_ENTROPY()
|
||
|
|
error('Not implemented yet');
|
||
|
|
end
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
%% Standard Neural Network statistical metrics public methods
|
||
|
|
methods (Access = public)
|
||
|
|
function bias2 = computeNetworkBiasSquare(self, y)
|
||
|
|
%computeNetworkBias
|
||
|
|
% Compute the Network Squared Bias in relation to a target
|
||
|
|
%
|
||
|
|
% y (vector)
|
||
|
|
% A single target
|
||
|
|
% agmm (object)
|
||
|
|
% AGMM object
|
||
|
|
%
|
||
|
|
% Returns
|
||
|
|
% The squared bias of the network related to this target
|
||
|
|
dataMean = self.dataMean;
|
||
|
|
dataStd = self.dataStd;
|
||
|
|
dataVar = self.dataVar;
|
||
|
|
self.nSamplesFeed = self.nSamplesFeed + 1;
|
||
|
|
[~, ~, Ez, ~] = self.computeExpectedValues(self.nHiddenLayers + 1);
|
||
|
|
bias2 = self.computeBIAS2(Ez, y);
|
||
|
|
self.nSamplesFeed = self.nSamplesFeed - 1;
|
||
|
|
self.dataMean = dataMean;
|
||
|
|
self.dataStd = dataStd;
|
||
|
|
self.dataVar = dataVar;
|
||
|
|
end
|
||
|
|
|
||
|
|
function var = computeNetworkVariance(self)
|
||
|
|
%computeNetworkVariance
|
||
|
|
% Compute the Network Variance in relation to a target
|
||
|
|
%
|
||
|
|
% agmm (object)
|
||
|
|
% AGMM object
|
||
|
|
%
|
||
|
|
% Returns
|
||
|
|
% The squared bias of the network related to this target
|
||
|
|
dataMean = self.dataMean;
|
||
|
|
dataStd = self.dataStd;
|
||
|
|
dataVar = self.dataVar;
|
||
|
|
self.nSamplesFeed = self.nSamplesFeed + 1;
|
||
|
|
[~, ~, Ez, Ez2] = self.computeExpectedValues(self.nHiddenLayers + 1);
|
||
|
|
var = self.computeVAR(Ez, Ez2);
|
||
|
|
self.nSamplesFeed = self.nSamplesFeed - 1;
|
||
|
|
self.dataMean = dataMean;
|
||
|
|
self.dataStd = dataStd;
|
||
|
|
self.dataVar = dataVar;
|
||
|
|
end
|
||
|
|
end
|
||
|
|
%% Standard Neural Networks extra public methods
|
||
|
|
methods (Access = public)
|
||
|
|
function loss = updateWeightsByKullbackLeibler(self, Xs, ys, Xt, yt, GAMMA)
|
||
|
|
%updateWeightsByKullbackLeibler
|
||
|
|
% This method is used on Transfer Learning procedures. The
|
||
|
|
% idea is to approximate the source and target distributions.
|
||
|
|
% If you don't have access to the target domain classes, call
|
||
|
|
% this method from a generative model (AutoEncoder or
|
||
|
|
% DenoisingAutoEncoder)
|
||
|
|
% Xs (matrix)
|
||
|
|
% Source input
|
||
|
|
% ys (matrix)
|
||
|
|
% Source target
|
||
|
|
% Xt (matrix)
|
||
|
|
% Target input
|
||
|
|
% yt (matrix)
|
||
|
|
% Target target
|
||
|
|
% GAMMA (float)
|
||
|
|
% Regularizer coeficient
|
||
|
|
if nargin == 5
|
||
|
|
GAMMA = 0.0001;
|
||
|
|
end
|
||
|
|
|
||
|
|
nHL = self.nHiddenLayers + 1; %readability
|
||
|
|
|
||
|
|
self.forwardpass(Xs);
|
||
|
|
sourceLayerValue = self.layerValue;
|
||
|
|
sourceOutputLayerValue = self.outputLayerValue;
|
||
|
|
|
||
|
|
self.forwardpass(Xt);
|
||
|
|
targetLayerValue = self.layerValue;
|
||
|
|
targetOutputLayerValue = self.outputLayerValue;
|
||
|
|
|
||
|
|
klLoss = 0;
|
||
|
|
for i = nHL : -1 : 2
|
||
|
|
klLoss = klLoss + self.util.KLDiv(sum(sourceLayerValue{i}), sum(targetLayerValue{i}))...
|
||
|
|
+ self.util.KLDiv(sum(targetLayerValue{i}), sum(sourceLayerValue{i}));
|
||
|
|
end
|
||
|
|
if ~isfinite(klLoss)
|
||
|
|
loss = 1000;
|
||
|
|
else
|
||
|
|
loss = klLoss;
|
||
|
|
end
|
||
|
|
|
||
|
|
|
||
|
|
dSource{nHL} = (sourceOutputLayerValue - ys) .* sourceOutputLayerValue .* (1 - sourceOutputLayerValue);
|
||
|
|
dTarget{nHL} = (targetOutputLayerValue - yt) .* targetOutputLayerValue .* (1 - targetOutputLayerValue);
|
||
|
|
for i = 1 : self.nHiddenLayers
|
||
|
|
dSource{i} = sourceLayerValue{i + 1} .* (1 - sourceLayerValue{i + 1});
|
||
|
|
dTarget{i} = targetLayerValue{i + 1} .* (1 - targetLayerValue{i + 1});
|
||
|
|
end
|
||
|
|
|
||
|
|
for i = nHL : -1 : 1
|
||
|
|
if (i == nHL)
|
||
|
|
inboundSourceLayerValue = sourceLayerValue{end};
|
||
|
|
inboundTargetLayerValue = targetLayerValue{end};
|
||
|
|
else
|
||
|
|
if (i == self.nHiddenLayers)
|
||
|
|
outboundWeight = self.outputWeight;
|
||
|
|
else
|
||
|
|
outboundWeight = self.weight{i + 1};
|
||
|
|
end
|
||
|
|
inboundSourceLayerValue = sourceLayerValue{i};
|
||
|
|
inboundTargetLayerValue = targetLayerValue{i};
|
||
|
|
end
|
||
|
|
|
||
|
|
if (i == nHL)
|
||
|
|
dW{i} = (2 * dSource{i}' * inboundSourceLayerValue)...
|
||
|
|
+ (2 * dTarget{i}' * inboundTargetLayerValue);
|
||
|
|
|
||
|
|
b = sum((2 * dSource{i}) + (2 * dTarget{i}), 1);
|
||
|
|
db{i} = sum(b, 1) / size(b, 1);
|
||
|
|
else
|
||
|
|
dW{i} = ((2 * dSource{i + 1} * outboundWeight) .* dSource{i})' * inboundSourceLayerValue...
|
||
|
|
+ ((2 * dTarget{i + 1} * outboundWeight) .* dTarget{i})' * inboundTargetLayerValue;
|
||
|
|
|
||
|
|
b = ((2 * dSource{i + 1} * outboundWeight) .* dSource{i})...
|
||
|
|
+ ((2 * dTarget{i + 1} * outboundWeight) .* dTarget{i});
|
||
|
|
|
||
|
|
db{i} = sum(b, 1) / size(b, 1);
|
||
|
|
end
|
||
|
|
end
|
||
|
|
for i = nHL : -1 : 1
|
||
|
|
if (i == nHL)
|
||
|
|
self.outputWeight = self.outputWeight - self.learningRate * dW{i};
|
||
|
|
self.outputBias = self.outputBias - self.learningRate * db{i};
|
||
|
|
else
|
||
|
|
self.weight{i} = self.weight{i} - self.learningRate * dW{i};
|
||
|
|
self.bias{i} = self.bias{i} - self.learningRate * db{i};
|
||
|
|
end
|
||
|
|
end
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
%% Elastic/Evolving Neural Network public methods
|
||
|
|
methods (Access = public)
|
||
|
|
function widthAdaptationStepwise(self, layerNo, y)
|
||
|
|
%widthAdaptationStepwise
|
||
|
|
% Performs network width adaptation in a specific layer,
|
||
|
|
% stepwise (it means that it execute one row at a time).
|
||
|
|
% Also, this method assume that you already passe the input
|
||
|
|
% data through the model via forwardpass procedure.
|
||
|
|
% layerNo (integer)
|
||
|
|
% Number of the layer you want to perform width
|
||
|
|
% adaptation. This is normally a hidden layer.
|
||
|
|
% y (double or vector)
|
||
|
|
% Double, if you are performing regression
|
||
|
|
% Vector if you are performing classification
|
||
|
|
% The targer data to be used as validation
|
||
|
|
nhl = layerNo; % readability
|
||
|
|
|
||
|
|
self.nSamplesFeed = self.nSamplesFeed + 1;
|
||
|
|
self.nSamplesLayer(nhl) = self.nSamplesLayer(nhl) + 1;
|
||
|
|
|
||
|
|
[Ex, ~, Ey, Ey2] = computeExpectedValues(self, nhl);
|
||
|
|
|
||
|
|
bias2 = self.computeBIAS2(Ey, y);
|
||
|
|
var = self.computeVAR(Ey, Ey2);
|
||
|
|
|
||
|
|
[self.meanBIAS(nhl), self.varBIAS(nhl), self.stdBIAS(nhl)] ...
|
||
|
|
= self.util.recursiveMeanStd(bias2, self.meanBIAS(nhl), self.varBIAS(nhl), self.nSamplesFeed);
|
||
|
|
|
||
|
|
[self.meanVAR(nhl), self.varVAR(nhl), self.stdVAR(nhl)] ...
|
||
|
|
= self.util.recursiveMeanStd(var, self.meanVAR(nhl), self.varVAR(nhl), self.nSamplesFeed);
|
||
|
|
|
||
|
|
if self.nSamplesLayer(nhl) <= 1 || self.growable(nhl) == true
|
||
|
|
self.minMeanBIAS(nhl) = self.meanBIAS(nhl);
|
||
|
|
self.minStdBIAS(nhl) = self.stdBIAS(nhl);
|
||
|
|
else
|
||
|
|
self.minMeanBIAS(nhl) = min(self.minMeanBIAS(nhl), self.meanBIAS(nhl));
|
||
|
|
self.minStdBIAS(nhl) = min(self.minStdBIAS(nhl), self.stdBIAS(nhl));
|
||
|
|
end
|
||
|
|
|
||
|
|
if self.nSamplesLayer(nhl) <= self.inputSize + 1 || self.prunable{nhl}(1) ~= 0
|
||
|
|
self.minMeanVAR(nhl) = self.meanVAR(nhl);
|
||
|
|
self.minStdVAR(nhl) = self.stdVAR(nhl);
|
||
|
|
else
|
||
|
|
self.minMeanVAR(nhl) = min(self.minMeanVAR(nhl), self.meanVAR(nhl));
|
||
|
|
self.minStdVAR(nhl) = min(self.minStdVAR(nhl), self.stdVAR(nhl));
|
||
|
|
end
|
||
|
|
|
||
|
|
self.BIAS2{nhl} = [self.BIAS2{nhl} self.meanBIAS(nhl)];
|
||
|
|
self.VAR{nhl} = [self.VAR{nhl} self.meanVAR(nhl)];
|
||
|
|
|
||
|
|
self.growable(nhl) = self.isGrowable(nhl, bias2);
|
||
|
|
if nargin == 3
|
||
|
|
self.prunable{nhl} = self.isPrunable(nhl, var, Ex, self.PRUNE_SINGLE_LEAST_CONTRIBUTION_NODES());
|
||
|
|
elseif nargin == 4
|
||
|
|
self.prunable{nhl} = self.isPrunable(nhl, var, Ex, self.PRUNE_MULTIPLE_NODES_WITH_CONTRIBUTION_BELOW_EXPECTED());
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
function grow(self, layerNo)
|
||
|
|
%grow
|
||
|
|
% Add 1 new node to a hidden layer. Because of this, it will
|
||
|
|
% add 1 extra weight and bias at the outbound row and 1 extra
|
||
|
|
% weight at the inbound row.
|
||
|
|
% layerNo (integer)
|
||
|
|
% Number of the layer you want to add a node.
|
||
|
|
self.layers(layerNo) = self.layers(layerNo) + 1;
|
||
|
|
if layerNo > 1
|
||
|
|
self.growWeightRow(layerNo - 1)
|
||
|
|
self.growBias(layerNo - 1);
|
||
|
|
end
|
||
|
|
if layerNo < numel(self.layers)
|
||
|
|
self.growWeightColumn(layerNo)
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
function prune(self, layerNo, nodeNo)
|
||
|
|
%prune
|
||
|
|
% Remove 1 node from the hidden layer. Because of this, it
|
||
|
|
% will remove 1 weight and bias at the outbound row and 1
|
||
|
|
% weight from the inbound row.
|
||
|
|
% layerNo (integer)
|
||
|
|
% Number of the layer you want to add a node.
|
||
|
|
% nodeNo (integer)
|
||
|
|
% Position of the node to be removed
|
||
|
|
self.layers(layerNo) = self.layers(layerNo) - 1;
|
||
|
|
if layerNo > 1
|
||
|
|
self.pruneWeightRow(layerNo - 1, nodeNo);
|
||
|
|
self.pruneBias(layerNo - 1, nodeNo);
|
||
|
|
end
|
||
|
|
if layerNo < numel(self.layers)
|
||
|
|
self.pruneWeightColumn(layerNo, nodeNo);
|
||
|
|
end
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
%% Elastic/Evolving Neural Network protected methods
|
||
|
|
methods (Access = protected)
|
||
|
|
function isGrowable = isGrowable(self, layerNo, BIAS2)
|
||
|
|
%isGrowable
|
||
|
|
% Evaluate if a specific layer need a node added to have its
|
||
|
|
% network significance parameters stable
|
||
|
|
% layerNo (integer)
|
||
|
|
% Layer which the evaluation will be performed. Usually
|
||
|
|
% it is a hidden layer.
|
||
|
|
% BIAS2 (double)
|
||
|
|
% The squished BIAS2 of that layer at that time
|
||
|
|
%
|
||
|
|
% returns a boolean indicating if that layer is ready to
|
||
|
|
% receive a new node or not.
|
||
|
|
nhl = layerNo; %readability
|
||
|
|
isGrowable = false;
|
||
|
|
ALPHA_1 = 1.25;
|
||
|
|
ALPHA_2 = 0.75;
|
||
|
|
|
||
|
|
current = (self.meanBIAS(nhl) + self.stdBIAS(nhl));
|
||
|
|
biased_min = (self.minMeanBIAS(nhl)...
|
||
|
|
+ (ALPHA_1 * exp(-BIAS2) + ALPHA_2)...
|
||
|
|
* self.minStdBIAS(nhl));
|
||
|
|
|
||
|
|
if self.nSamplesLayer(nhl) > 1 && current >= biased_min
|
||
|
|
isGrowable = true;
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
function prunableNodes = isPrunable(self, layerNo, VAR, expectedY, option)
|
||
|
|
%isPrunable
|
||
|
|
% Evaluate if a specific layer need a node pruned to have its
|
||
|
|
% network significance parameters stable
|
||
|
|
% layerNo (integer)
|
||
|
|
% Layer which the evaluation will be performed. Usually
|
||
|
|
% it is a hidden layer.
|
||
|
|
% VAR (double)
|
||
|
|
% The squished VAR of that layer at that time
|
||
|
|
% expectedY (vector)
|
||
|
|
% See self.getExpectedValues
|
||
|
|
% This value is used to determine the node with minimum
|
||
|
|
% contribution to the network.
|
||
|
|
% option (string)
|
||
|
|
% 'least_contribution': In case the pruning rule get
|
||
|
|
% approved, it will return the position for the least
|
||
|
|
% contributing node.
|
||
|
|
% 'below_contribution': In case the pruning rule get
|
||
|
|
% approved, it will return an array with the position for
|
||
|
|
% all nodes that have the contribution below a certain
|
||
|
|
% quantity
|
||
|
|
%
|
||
|
|
% returns a integer indicating the position of which node
|
||
|
|
% should be removed from that layer. If no node should be
|
||
|
|
% removed, returns zero instead.
|
||
|
|
nhl = layerNo; %readability
|
||
|
|
prunableNodes = 0;
|
||
|
|
ALPHA_1 = 2.5;
|
||
|
|
ALPHA_2 = 1.5;
|
||
|
|
|
||
|
|
current = (self.meanVAR(nhl) + self.stdVAR(nhl));
|
||
|
|
biased_min = (self.minMeanVAR(nhl)...
|
||
|
|
+ (ALPHA_1 * exp(-VAR) + ALPHA_2)...
|
||
|
|
* self.minStdVAR(nhl));
|
||
|
|
|
||
|
|
if self.growable(nhl) == false ...
|
||
|
|
&& self.layers(nhl) > 1 ...
|
||
|
|
&& self.nSamplesLayer(nhl) > self.inputSize + 1 ...
|
||
|
|
&& current >= biased_min
|
||
|
|
|
||
|
|
switch option
|
||
|
|
case self.PRUNE_SINGLE_LEAST_CONTRIBUTION_NODES()
|
||
|
|
[~, prunableNodes] = min(expectedY);
|
||
|
|
case self.PRUNE_MULTIPLE_NODES_WITH_CONTRIBUTION_BELOW_EXPECTED()
|
||
|
|
nodesToPrune = expectedY <= abs(mean(expectedY) - var(expectedY));
|
||
|
|
if sum(nodesToPrune)
|
||
|
|
prunableNodes = find(expectedY <= abs(mean(expectedY) - var(expectedY)));
|
||
|
|
else
|
||
|
|
[~, prunableNodes] = min(expectedY);
|
||
|
|
end
|
||
|
|
end
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
function growWeightRow(self, weightArrayNo)
|
||
|
|
%growWeightRow
|
||
|
|
% Add 1 extra weight at the inbound row.
|
||
|
|
% weightArrayNo (integer)
|
||
|
|
% Weight position
|
||
|
|
w = weightArrayNo; % readability
|
||
|
|
if w > numel(self.weight)
|
||
|
|
[n_in, n_out] = size(self.outputWeight);
|
||
|
|
n_in = n_in + 1;
|
||
|
|
self.outputWeight = [self.outputWeight; normrnd(0, sqrt(2 / (n_in)), [1, n_out])];
|
||
|
|
self.outputMomentum = [self.outputMomentum; zeros(1, n_out)];
|
||
|
|
else
|
||
|
|
[n_in, n_out] = size(self.weight{w});
|
||
|
|
n_in = n_in + 1;
|
||
|
|
self.weight{w} = [self.weight{w}; normrnd(0, sqrt(2 / (n_in)), [1, n_out])];
|
||
|
|
self.momentum{w} = [self.momentum{w}; zeros(1, n_out)];
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
function growWeightColumn(self, weightArrayNo)
|
||
|
|
%growWeightColumn
|
||
|
|
% Add 1 extra weight at the outbound column.
|
||
|
|
% weightArrayNo (integer)
|
||
|
|
% Weight position
|
||
|
|
w = weightArrayNo; % readability
|
||
|
|
if w > numel(self.weight)
|
||
|
|
[n_out, n_in] = size(self.outputWeight);
|
||
|
|
n_in = n_in + 1;
|
||
|
|
self.outputWeight = [self.outputWeight normrnd(0, sqrt(2 / (n_in)), [n_out, 1])];
|
||
|
|
self.outputMomentum = [self.outputMomentum zeros(n_out, 1)];
|
||
|
|
else
|
||
|
|
[n_out, n_in] = size(self.weight{w});
|
||
|
|
n_in = n_in + 1;
|
||
|
|
self.weight{w} = [self.weight{w} normrnd(0, sqrt(2 / (n_in)), [n_out, 1])];
|
||
|
|
self.momentum{w} = [self.momentum{w} zeros(n_out, 1)];
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
function pruneWeightRow(self, weightNo, nodeNo)
|
||
|
|
%pruneWeightRow
|
||
|
|
% Remove 1 weight from the inbound row.
|
||
|
|
% weightNo (integer)
|
||
|
|
% Weight position
|
||
|
|
% nodeNo (integer)
|
||
|
|
% Position of the node to be removed
|
||
|
|
w = weightNo; % readability
|
||
|
|
n = nodeNo; %readability
|
||
|
|
if w > numel(self.weight)
|
||
|
|
self.outputWeight(n, :) = [];
|
||
|
|
self.outputMomentum(n, :) = [];
|
||
|
|
else
|
||
|
|
self.weight{w}(n, :) = [];
|
||
|
|
self.momentum{w}(n, :) = [];
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
function pruneWeightColumn(self, weightNo, nodeNo)
|
||
|
|
%pruneWeightColumn
|
||
|
|
% Remove 1 weight from the outbound column
|
||
|
|
% weightArrayNo (integer)
|
||
|
|
% Weight position
|
||
|
|
% nodeNo (integer)
|
||
|
|
% Position of the node to be removed
|
||
|
|
w = weightNo; % readability
|
||
|
|
n = nodeNo; %readability
|
||
|
|
if w > numel(self.weight)
|
||
|
|
self.outputWeight(:, n) = [];
|
||
|
|
self.outputMomentum(:, n) = [];
|
||
|
|
else
|
||
|
|
self.weight{w}(:, n) = [];
|
||
|
|
self.momentum{w}(:, n) = [];
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
function growBias(self, biasArrayNo)
|
||
|
|
%growBias
|
||
|
|
% Add 1 extra bias at the inbound row.
|
||
|
|
% biasArrayNo (integer)
|
||
|
|
% Bias position
|
||
|
|
b = biasArrayNo; %readability
|
||
|
|
if b > numel(self.weight)
|
||
|
|
self.outputBias = [self.outputBias normrnd(0, sqrt(2 / (self.layers(end) + 1)))];
|
||
|
|
self.outputBiasMomentum = [self.outputBiasMomentum 0];
|
||
|
|
else
|
||
|
|
self.bias{b} = [self.bias{b} normrnd(0, sqrt(2 / (self.layers(b) + 1)))];
|
||
|
|
self.biasMomentum{b} = [self.biasMomentum{b} 0];
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
function pruneBias(self, biasArrayNo, nodeNo)
|
||
|
|
%pruneBias
|
||
|
|
% Remove 1 bias from the inbound row.
|
||
|
|
% biasArrayNo (integer)
|
||
|
|
% Bias position
|
||
|
|
% nodeNo (integer)
|
||
|
|
% Position of the node to be removed
|
||
|
|
b = biasArrayNo; % readability
|
||
|
|
n = nodeNo; %readability
|
||
|
|
if b > numel(self.weight)
|
||
|
|
self.outputBias(n) = [];
|
||
|
|
self.outputBiasMomentum(n) = [];
|
||
|
|
else
|
||
|
|
self.bias{b}(n) = [];
|
||
|
|
self.biasMomentum{b}(n) = [];
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
function [Ex, Ex2, Ez, Ez2] = computeExpectedValues(self, nHiddenLayer)
|
||
|
|
%computeExpectedValues
|
||
|
|
% Compute statisticals expectations values for a specific
|
||
|
|
% hidden layer
|
||
|
|
%
|
||
|
|
% Returns Ex = Expected value of that layer
|
||
|
|
% Ex2 = Expected squared value of that layer
|
||
|
|
% Ez = Expected outbound value of that layer
|
||
|
|
% Ez2 = Expected outbound squared value of that layer
|
||
|
|
nhl = nHiddenLayer; %readability
|
||
|
|
x = self.layerValue{1};
|
||
|
|
[self.dataMean, self.dataVar, self.dataStd]...
|
||
|
|
= self.util.recursiveMeanStd(x, self.dataMean, self.dataVar, self.nSamplesFeed);
|
||
|
|
|
||
|
|
if self.isAgmmAble
|
||
|
|
Ex = 0;
|
||
|
|
Ex2 = 0;
|
||
|
|
for m = 1 : self.agmm.M()
|
||
|
|
gmm = self.agmm.gmmArray(m);
|
||
|
|
[tempEx, tempEx2] = computeInboundExpectedValues(self, nhl, gmm);
|
||
|
|
Ex = Ex + tempEx;
|
||
|
|
Ex2 = Ex2 + tempEx2;
|
||
|
|
end
|
||
|
|
else
|
||
|
|
[Ex, Ex2] = computeInboundExpectedValues(self, nhl);
|
||
|
|
end
|
||
|
|
|
||
|
|
[Ez, Ez2] = computeOutboundExpectedValues(self, Ex, Ex2);
|
||
|
|
end
|
||
|
|
|
||
|
|
function [Ex, Ex2] = computeInboundExpectedValues(self, layerNo, gmm)
|
||
|
|
%computeInboundExpectedValues
|
||
|
|
% Compute statisticals expectations values for a specific
|
||
|
|
% hidden layer
|
||
|
|
% nHiddenLayer (integer)
|
||
|
|
% layer to be evaluated
|
||
|
|
%
|
||
|
|
% Returns Ex = Expected value of that layer
|
||
|
|
% Ex2 = Expected squared value of that layer
|
||
|
|
nhl = layerNo - 1; %readability
|
||
|
|
if nhl == 1
|
||
|
|
inference = 1;
|
||
|
|
center = self.dataMean;
|
||
|
|
std = self.dataStd;
|
||
|
|
|
||
|
|
if nargin == 3
|
||
|
|
inference = gmm.weight;
|
||
|
|
center = gmm.center;
|
||
|
|
std = sqrt(gmm.var);
|
||
|
|
end
|
||
|
|
|
||
|
|
py = self.util.probit(center, std);
|
||
|
|
Ex = inference * sigmf(self.weight{1} * py' + self.bias{1}', [1, 0]);
|
||
|
|
else
|
||
|
|
[Ex, ~] = self.computeInboundExpectedValues(nhl);
|
||
|
|
weight_ = self.outputWeight;
|
||
|
|
bias_ = self.outputBias;
|
||
|
|
|
||
|
|
if nhl < self.nHiddenLayers + 1
|
||
|
|
weight_ = self.weight{nhl};
|
||
|
|
bias_ = self.bias{nhl};
|
||
|
|
end
|
||
|
|
|
||
|
|
Ex = sigmf(weight_ * Ex + bias_', [1, 0]);
|
||
|
|
end
|
||
|
|
Ex2 = Ex .^ 2;
|
||
|
|
end
|
||
|
|
|
||
|
|
function [Ez, Ez2] = computeOutboundExpectedValues(self, Ex, Ex2)
|
||
|
|
%computeOutboundExpectedValues
|
||
|
|
% Compute statisticals expectations values for a specific
|
||
|
|
% hidden layer
|
||
|
|
% Ey (double, vector or matrix)
|
||
|
|
% Expected value
|
||
|
|
% Ey2 (double, vector or matrix)
|
||
|
|
% Expected squared value
|
||
|
|
%
|
||
|
|
% Returns Ez = Expected outbound value of that layer
|
||
|
|
% Ez2 = Expected outbound squared value of that layer
|
||
|
|
Ez = self.outputWeight * Ex + self.outputBias';
|
||
|
|
Ez = exp(Ez - max(Ez));
|
||
|
|
Ez = Ez ./ sum(Ez);
|
||
|
|
|
||
|
|
Ez2 = self.outputWeight * Ex2 + self.outputBias';
|
||
|
|
Ez2 = exp(Ez2 - max(Ez2));
|
||
|
|
Ez2 = Ez2 ./ sum(Ez2);
|
||
|
|
end
|
||
|
|
|
||
|
|
function NS = computeNetworkSignificance(self, Ez, Ez2, y)
|
||
|
|
%computeNetworkSignificance
|
||
|
|
% Compute the current Network Significance of the model in
|
||
|
|
% respect to a target
|
||
|
|
% Ez (double, vector or matrix)
|
||
|
|
% Expected outbound value of that layer
|
||
|
|
% Ez2 (double, vector or matrix)
|
||
|
|
% Expected outbound squared value of that layer
|
||
|
|
% y (double, vector or matrix)
|
||
|
|
% A target class
|
||
|
|
%
|
||
|
|
% return NS = The network significance
|
||
|
|
NS = self.computeBIAS2(Ez, z) + self.computeVAR(Ez, Ez2);
|
||
|
|
end
|
||
|
|
|
||
|
|
function BIAS2 = computeBIAS2(~, Ez, y)
|
||
|
|
%computeBIAS2
|
||
|
|
% Compute the current BIAS2 of the model wrt a target
|
||
|
|
% Ez (double, vector or matrix)
|
||
|
|
% Expected outbound value of that layer
|
||
|
|
% y (double, vector or matrix)
|
||
|
|
% A target class
|
||
|
|
%
|
||
|
|
% return BIAS2 = The network squared BIAS
|
||
|
|
BIAS2 = norm((Ez - y') .^2 , 'fro');
|
||
|
|
end
|
||
|
|
|
||
|
|
function VAR = computeVAR(~, Ez, Ez2)
|
||
|
|
%computeVAR
|
||
|
|
% Compute the current VAR of the model
|
||
|
|
% Ez (double, vector or matrix)
|
||
|
|
% Expected outbound value of that layer
|
||
|
|
% Ez2 (double, vector or matrix)
|
||
|
|
% Expected outbound squared value of that layer
|
||
|
|
%
|
||
|
|
% return VAR = The network VAR (variance)
|
||
|
|
VAR = norm(Ez2 - Ez .^ 2, 'fro');
|
||
|
|
end
|
||
|
|
end
|
||
|
|
%% GIVE A NAME TO THIS SECTION
|
||
|
|
methods (Access = public)
|
||
|
|
function agmm = runAgmm(self, x, y)
|
||
|
|
|
||
|
|
bias2 = self.computeNetworkBiasSquare(y);
|
||
|
|
|
||
|
|
self.agmm.run(x, bias2);
|
||
|
|
|
||
|
|
agmm = self.agmm;
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
%% Getters and Setters
|
||
|
|
methods (Access = public)
|
||
|
|
function setAgmm(self, agmm)
|
||
|
|
%setAgmm
|
||
|
|
% You can use this method to set your own AGMM to this
|
||
|
|
% network
|
||
|
|
% agmm (AGMM)
|
||
|
|
% The AGMM you want to set to this network.
|
||
|
|
self.isAgmmAble = true;
|
||
|
|
self.agmm = agmm;
|
||
|
|
end
|
||
|
|
|
||
|
|
function agmm = getAgmm(self)
|
||
|
|
%getAgmm
|
||
|
|
% Gets the agmm that the network is using. If the network has
|
||
|
|
% an empty agmm or is not using a agmm, it will enable AGMM
|
||
|
|
% and return to you a new AGMM
|
||
|
|
if isempty(self.agmm) || self.isAgmmAble == false
|
||
|
|
self.enableAgmm();
|
||
|
|
end
|
||
|
|
agmm = self.agmm;
|
||
|
|
end
|
||
|
|
|
||
|
|
function enableAgmm(self)
|
||
|
|
%enableAgmm
|
||
|
|
% Tell the network that it will use AGMM from now on
|
||
|
|
% It also creates a random AGMM. If you want to use your own
|
||
|
|
% AGMM, make sure to use setAgmm method afterwards
|
||
|
|
self.isAgmmAble = true;
|
||
|
|
self.agmm = AGMM();
|
||
|
|
end
|
||
|
|
|
||
|
|
function disableAgmm(self)
|
||
|
|
%disableAgmm
|
||
|
|
% Tell the network that it will NOT use AGMM frmo now on.
|
||
|
|
% It deletes the agmm that was attached to this model. If you
|
||
|
|
% want to keep track of that agmm, make sure to load it into
|
||
|
|
% some variable using the getAgmm method.
|
||
|
|
self.isAgmmAble = false;
|
||
|
|
self.agmm = [];
|
||
|
|
end
|
||
|
|
|
||
|
|
function nHiddenLayers = getNumberHiddenLayers(self)
|
||
|
|
%getNumberHiddenLayers
|
||
|
|
% Return the number of hidden layers in the network
|
||
|
|
%
|
||
|
|
% Returns
|
||
|
|
% nHiddenLayers (integer): Number of hidden layers
|
||
|
|
nHiddenLayers = self.nHiddenLayers;
|
||
|
|
end
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|