Abstract: . . .  ij = 1.0 - || x - m ij || / d max Winner: maximal y responding unit: i, j = argmax n ij Neighborhood: nearby nodes with similar weight vectors: N c Weights updated: ? µ ij = a ( t ) [ x - µ ij ] for ( i,j ) ? N c ( t ) © Mat hew W. Crocker Computational Psycholinguistics - Winter 2006 24 Summary Associate multiple stimulus-response patterns in a single network Networks can be represented as a weight matrix Weights are sensitive to similarity The more similar, the higher the netinput; . . .
. . .  x - m ij || / d max Winner: maximal y responding unit: i, j = argmax n ij Neighborhood: nearby nodes with similar weight vectors: N c Weights updated: ? µ ij = a ( t ) [ x - µ ij ] for ( i,j ) ? N c ( t ) © Mat hew W. Crocker Computational Psycholinguistics - Winter 2006 24 Summary Associate multiple stimulus-response patterns in a single network Networks can be represented as a weight matrix Weights are sensitive to similarity The more similar, the higher the netinput; the dot . . .
. . .  psycholinguistics Page 1 1 Computational Psycholinguistics Lecture 11: Pattern Associators and Competitive Networks Marshall R. Mayberry Computerlinguistik Universität des Saarlandes © Mat hew W. Crocker Computational Psycholinguistics - Winter 2006 2 Overview Learning: The delta rule The perceptron . . .
. . .  psycholinguistics Page 1 1 Computational Psycholinguistics Lecture 11: Pattern Associators and Competitive Networks Marshall R. Mayberry Computerlinguistik Universität des Saarlandes © Mat hew W. Crocker Computational Psycholinguistics - Winter 2006 2 Overview Learning: The delta rule The perceptron convergence . . .
. . .  Neighborhood: nearby nodes with similar weight vectors: N c Weights updated: ? µ ij = a ( t ) [ x - µ ij ] for ( i,j ) ? N c ( t ) © Mat hew W. Crocker Computational Psycholinguistics - Winter 2006 24 Summary Associate multiple stimulus-response patterns in a single network Networks can be represented as a weight matrix Weights are sensitive to similarity The more similar, the higher the netinput; the dot product of P and W Important properties Generalisation: robust to noisy input Fault . . .
. . .  teacher is required Remove redundancy: set of inputs associated with a single output Sparsification: convert pat ern stimuli to a localist representation Outputs are less correlated (possibly orthogonal) than inputs: Useful as input to pat ern associators (easier to learn less correlated pat erns) © Mat hew W. Crocker Computational Psycholinguistics - Winter 2006 21 An example: Pattern classification We can use an unsupervised network to classify patterns of letters Input is a 7 x14 . . .
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