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Self Organization Map
- 1. An introduction to Self Organization Map (SOM) By: zahra sadeghi
- 2. Cerebral cortex • different sensory inputs are mapped onto corresponding areas of the cerebral cortex in an orderly fashion. • Neurons, dealing with closely related pieces of information, are close together so that they can interact via short synaptic connections.
- 4. Cohonen model • invented by : Teuvo Kohonen • humans simply cannot visualize high dimensional data • a data visualization technique • represent multidimensional data in much lower dimensional spaces - one or two dimensions. • group similar data items together. – any topological relationships within the training set are maintained • they reduce dimensions and display similarities
- 5. SOM • Is an unsupervised learning algorithm • principle goal: – to transform an input into a one or two dimensional discrete map – to perform this transformation adaptively in a topologically ordered fashion.
- 6. Network Architecture • Feedforward structure • Two layers • The output layer consists of neurons arranged in 1)Rows and columns (two dimensional) 2)A single column or row (1dimensional)
- 7. Network Architecture • Each node has a specific topological position (an x, y coordinate in the lattice) • and contains a vector of weights of the same dimension as the input vectors. - if the training data consists of vectors, V, of n dimensions: V1, V2, V3...Vn - Then each node will contain a corresponding weight vector W, of n dimensions :W1, W2, W3...Wn
- 8. . •Each neuron in the lattice is fully connected to all the source nodes in the input layer. •There are no lateral connections between nodes within the lattice
- 10. SOM algorithm 1.Each node's weights are initialized. – random initialization – sample initialization 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. 4.The radius of the neighbourhood of the BMU is now calculated. Any nodes found within this radius are deemed to be inside the BMU's neighbourhood. 5.Each neighbouring node's weights are adjusted (The closer a node is to the BMU, the more its weights get altered.) 6.Repeat step 2 for N iterations.
- 11. Best Matching Unit: BMU • for a given training instance only a single neuron is activated called BMU – BMU is the neuron c whose weight vector has highest similarity with training instance x • d : Euclidean distance • for every training instance the BMU and additional neurons in the neighborhood of the BMU are adjusted by the Kohonen-Learning-Rule
- 12. Neighborhood • the neighbourhood is centered around the BMU • the area of the neighbourhood shrinks over time. • This is accomplished by making the radius of the neighbourhood shrink over time • initial radius of neighborhood may be equal to half the diameter of the SOM • Over time the neighbourhood will shrink to the size of just one node... the BMU
- 13. Adjusting the Weights • Every node within the BMU's neighbourhood (including the BMU) has its weight vector adjusted • L : learning rate, which decreases with time
- 14. Adjusting the Weights • the effect of learning should be proportional to the distance a node is from the BMU. • at the edges of the BMUs neighbourhood, the learning process should have barely any effect at all! • the amount of learning should fade over distance similar to the Gaussian decay