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Self Organizing Maps

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This presentation is based on: http://www.ai-junkie.com/ann/som/som1.html SOM’s are invented by Teuvo Kohonen. They represent multidimensional data in much lower dimensional spaces - usually two dimensions. Common example is the mapping of colors from their three dimensional components - red, green and blue, into two dimensions. 8 colors on the right have been presented as 3D vectors and the system has learnt to represent them in the 2D space. In addition to clustering the colors into distinct regions, regions of similar properties are usually found adjacent to each other.

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Network Architecture Data consists of vectors, V, of n dimensions: V1, V2, V3…Vn Each node will contain a corresponding weight vector W, of n dimensions: W1, W2, W3...Wn.

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Network Example Each node in the 40-by-40 lattice has three weights, one for each element of the input vector: red, green and blue. Each node is represented by a rectangular cell when drawn to display.

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Overview of the Algorithm Idea: Any new, previously unseen input vector presented to the network will stimulate nodes in the zone with similar weight vectors. 1.Each node's weights are initialized. 2.A vector is chosen at random from the set of training data and presented to the lattice. 3.Every node is examined to calculate which one's weights are most like the input vector. The winning node is commonly known as the Best Matching Unit (BMU). 4.The radius of the neighborhood of the BMU is now calculated. This is a value that starts large, typically set to the 'radius' of the lattice, but diminishes each time-step. Any nodes found within this radius are deemed to be inside the BMU's neighborhood. 5.Each neighboring node's (the nodes found in step 4) weights are adjusted to make them more like the input vector. The closer a node is to the BMU, the more its weights get altered. 6.Repeat step 2 for N iterations.

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Details Initializing the Weights Set to small standardized random values 0 < w < 1 Calculating the Best Matching Unit Use some distance Determining the Best Matching Unit's Local Neighborhood Area of the neighborhood shrinks over time by shrinking the radius of the neighborhood over time For this use the exponential decay function: 0 is the width of the lattice at time t 0 is a constant t is the iteration number

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Details Over time the neighborhood will shrink to the size of just one node... the BMU

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Details Adjusting the Weights Every node within the BMU's neighborhood (including the BMU) has its weight vector adjusted according to the following equation: where t represents the time-step and L is a small variable called the learning rate, which decreases with time. The decay of the learning rate is calculated each iteration using the following equation:

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Details Also, the effect of learning should be proportional to the distance a node is from the BMU.

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Applications SOM’s are commonly used as visualization aids. –They can make it easy to see relationships between vast amounts of data.

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