SOM study notes 1

Som's study notes are intended to write two articles, from the early stage of the work to be resolved in the pre-warning product quality on multiple ate on the issue of Low. The first chapter introduces SOM's network model and learning algorithm from a theoretical point of view, and the second one shows the actual application from the perspective of application in the form of demo. What is 1.SOM?

Som English is self-organizing maps, the Chinese general Translation self-organization Map Network, it is a neural network, by Kohonen, belongs to unsupervised learning, it imitates the human brain neurons to the information processing way, through their own training, automatic input mode clustering. 2.SOM Network Model

The SOM network has two layers, namely Inputlayer and Outputlayer. Inputlayer and Outputlayer are connected by weights, Inputlayer is the input layer, and its input is generally high dimensional vector. Outputlayer neurons are typically placed in a two-dimensional grid, and neurons in the output layer's neighbors are also connected by weight values.

3. Inner Star Learning rules

Som is based on the rules of internal learning, it is necessary to learn the following rules: Assuming that the input information is an n-dimensional vector, the vector is connected with the weight vector, output to the output neuron y, y using the hard limit amplitude function as the transfer function, the output is limited to 1 and 0 The target of the training of the star model makes Neuron Y only excited about certain input vectors, that is, the output of the neurons in Y is 1.

Through the learning rate η to adjust the weight, when the y=1, the weight of the adjustment, when the y=0, the weights do not adjust, the resulting network weights tend to approximate the average of the input vectors

The

4.SOM Learning Algorithm Set Variable: x=[x1,x2,x3,..., XM] is an input sample and each sample is an m-dimensional vector. Ωi (k) =[ωi1 (k), Ωi2 (k),..., Ωin (k)] initializes the weight vector between the I input node and the output neuron: the weights are initialized with a smaller random value, and the input vectors and weights are normalized
X ' = x/| | x| |
Ω ' I (k) =ωi (k)/| | Ωi (k) | |
| | x| | and | | Ωi (k) | | The Euclidean norm of the input vector and the weight vector is the sample input network: The sample and the weight vector do the inner product, the output neuron with the maximal value of the inner product wins the competition, which is recorded as the winning neuron renewing weights: the neurons in the neighborhood of the winning neuron topology are updated with the internal star rule
Ω (k+1) =ω (k) X-ω (k)) updates the learning rate η and topological neighborhood, and determines whether or not the weighted value after learning is normalized. If the center changes very small or reaches a predetermined number of iterations, the end algorithm 5.SOM advantages and disadvantages of advantages
The results are very easy to understand, this will be seen in the second demo to achieve a relatively simple disadvantage
computational complexity is high, Very sensitive to the measurement of similarity cannot apply a dataset with missing values