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Pattern Association

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Introduction Pattern association involves associating a new pattern with a stored pattern. Is a “simplified” model of human memory. Types of associative memory: Heteroassociative memory Autoassociative memory Hopfield Net Bidirectional Associative Memory (BAM)

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**Introduction These are usually single-layer networks.**

The neural network is firstly trained to store a set of patterns in the form s : t s represents the input vector and t the corresponding output vector. The neural network is then tested on a set of data to test its “memory” by using it to identify patterns containing incorrect or missing information.

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**Introduction Associative memory can be feedforward or recurrent.**

Autoassociative memory cannot hold an infinite number of patterns. Factors that affect this: Complexity of each pattern Similarity of input patterns

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**Heteroassociative Memory Architecture**

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**Heteroassociative Memory**

The inputs and output vectors s and t are different. The Hebb rule is used as a learning algorithm or calculate the weight matrix by summing the outer products of each input-output pair. The heteroassociative application algorithm is used to test the algorithm.

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The Hebb Algorithm Initialize weights to zero, wij =0, where i = 1, …, n and j = 1, …, m. For each training case s:t repeat: xi = si , where i=1,...,n yi = tj, where j = 1, .., m Adjust weights wij(new) = wij(old) + xiyj, where i = 1, .., n and j = 1, .., m

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Exercise Train a heteroassociative neural network to store the following input and output vectors: Test the neural network using all input data and the following input vector:

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**Autoassociative Memory**

The inputs and output vectors s and t are the same. The Hebb rule is used as a learning algorithm or calculate the weight matrix by summing the outer products of each input-output pair. The autoassociative application algorithm is used to test the algorithm.

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**Autoassociative Memory Architecture**

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Exercise Store the pattern in an autoassociative neural network. Test the neural network on the following input:

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**The Hopfield Neural Network**

Is a recurrent associative memory neural network. Application algorithm Exercise: Store the pattern [ ] using a Hopfield neural network. Test the neural network to see whether it is able to correctly identify an input vector with two mistakes in it: [ ]. Note θi=0, for i=1,..,4

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**Bidirectional Associative Memory (BAM)**

Consists of two layers, x and y. Signals are sent back and forth between both layers until an equilibrium is reached. An equilibrium is reached if the x and y vectors no longer change. Given an x vector the BAM is able to produce the y vector and vice versa. Application algorithm

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BAM Exercise Store the vectors representing the following patterns using a BAM: [ ] with the output vector [1 -1] [ ] with the output vector [-1 1] θi=0, θj=0 for i = 1,..3 and j=1..2

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