The technique of the electronic products classification into classes of the acceptable and potentially unacceptable instances using Kohonen Self-Organizing Maps (SOM) is given. The methodology was tested on two samples of special-purpose electronic components using application software. The analysis of the SOM is given. The classification accuracy is estimated and a comparison table, that includes the results of cluster analysis, is given. The recommendations for improving the classification quality are developed.
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This paper discusses the possibility of using Self-Organizing Maps (SOM) to classify electronic components into classes of reliable and potentially unreliable instances. Furthermore, the technique of using such network to classify samples of electronic components is presented.
The Kohonen networks are referred to as self-organizing neural networks, which allow to identify
groups of input data vectors with similar properties [
The Kohonen network is a single-layer network constructed from WTA neurons (Winner Takes All). Figure 1 shows the structure of such network.
Each neuron is associated with each component of the input data x1, x2,…,xm (the input data vector), which in this case is a set of informative parameters for each instance of the sample. Each neuron is presented as a linear combiner: = +
, =1 informative parameter; bj - is a threshold; wij – is a weight of the ith parameter of the jth neuron. whereSj – is an output result of the combiner; j – is a neuron number; i – is a number of the
From the output of each neuron the result goes to the competition function, which defines the neuron with the maximum result value at the output and assigns it a value of one. The remaining output signals are assigned a value of zero. For the neuron-winner, the following condition is fulfilled: ,
= min1 ≤ ≤ ( , ), whered(x, w) – is a distance between the vectors of the input data and the vector of the synaptic weights, j – is a number of the neuron-winner. It should be noted that the distance in the selected metric is an Euclidean distance.
The neuron-winner is a neuron, the vector of synaptic weights wi of which differs least from the vector of input data. In the case of determining the maximum result at the outputs of several neurons, the result equal to one is assigned to one of them, and the outputs of the remaining neurons are assigned a value of zero. Neuron-winner defines such a group, to which the vector of input data is closest .The scales are adjusted each training cycle: (1) (2) (3) closer vector of data is input. minimized.
The training of the Kohonen network consists in the selection of weight values when errors are ( +1) = ( ) + ƞ ( ) − ( ) of the jth neuron in the kth cycle. wherek – is a number of the training cycle; X – is an input vector; ƞi(k) – is a coefficient of learning rate
Thus, the neuron, whose synaptic weights vector was closer to the vector of the input data, is corrected and becomes even closer. Also, the weights of the nearest neurons are corrected to the neuron-winner. Thus, the probability of this neuron to become a neuron-winner is increased when a The developed classification technique based on Kohonen self-organizing maps is as follows: • • • determination of the vector of input data based on the results of the learning experiment; definition of network construction parameters; analysis of the results with an assessment of the accuracy of the classification.
Two samples of CMOS chips, obtained in [
Thus, the vector of input data is a set of informative parameters x1 and x2 of each sample.
The analytical platform "Deductor Academic 5.1" was chosen as a software tool for building Kohonen network. The following building parameters need to be defined: • size of the training and test set; • a network size (number of neurons); • a recognition criterion (the amount of recognition error); • rate and radius of learning; • number of clusters.
Because the samples size is small, the training set should be as large as possible and sufficient for the correct building of the network. In this case, the test set should be sufficient for testing the network with 100% recognition. Based on the set conditions, the size of the training set was 45 instances (90% of the sample), the test set size – 5 instances (10% of the sample).
The network size is chosen in such a way as to exclude the appearance of "dead" neurons (vector of synaptic weights is significantly removed from the vector of input data). Such neurons turn out to be inactive in network training, because they cannot win competition from the nearest neurons. This situation leads to the fact that the input data is interpreted by a smaller number of neurons than was originally set, which introduces distortions into the final result.
Networks with a dimension of 5×4 neurons (cells) were chosen for testing the presented samples. The type of cells is selected hexagonal: it more accurately displays the Cartesian distance between the cell centres. The remaining parameters of the Kohonen network building are presented in table 1.
From the whole set of variants of networks built according to the given parameters, the only option was chosen for each sample, at which the minimum average recognition error for the training set was achieved with 100% recognition of both the training set and the test set.
Because a fixed number of clusters equals two, according to the classification table it is not difficult to determine to which class of products the network relates each instance.
To estimate the accuracy of the classification, the technique given in [
Figure 2 shows the maps of the input data x1, x2 and the output data y for the network. The maps of such parameters are called component planes. Figure 3 shows the density hit matrix, the matrix of distances between the centres of neurons, and also a map of cell decomposition into two clusters.
Figure 2 shows that the maps of the neuron inputs (maps X1, X2) and the output map have a similar appearance: on the left there are cells that characterize neurons with smaller weights, and on the right there are cells characterizing neurons with large weights. Because the output map of neurons (map Y) is a projection of the maps of neuron inputs, its appearance will be similar.
Figure 3 shows that the map of cell decomposition is divided into 2 areas that characterize clusters. In this case, cluster 0 is a class of the reliable instances (class 1), cluster 1 is a class of the potentially unreliable instances (class 2). Table 2 provides the information on assigning each instance to a specific class, and Kfact means the actual belonging of the instance to a class, Krec. – is an assignment of the instance to a class based on recognition results using Kohonen maps.
Table 2 shows that for some instances, the actual class and the recognition class do not match.
Therefore, it is necessary to estimate the accuracy of this classification. For this the technique
presented in [
Figure 4 shows the maps of the input data x1, x2 and the output data y for the network. Figure 5 shows the density hit matrix, the matrix of distances between the centres of neurons, and also a map of cell decomposition into two clusters.
Figure 4 shows that the neuron input maps and the output map also have a similar appearance: on the left are cells that characterize neurons with smaller weights, and on the right are cells characterizing neurons with large weights.
Figure 5 shows that the map of cell decomposition is divided into 2 areas. Cluster 0 is a class of reliable instances (class 1), cluster 1 is a class of potentially unreliable instances (class 2). Table 4 provides information on assigning each instance to a specific class. Table 4 shows that for some instances, the actual class and the recognition class do not match. Therefore, it is necessary to estimate the accuracy of this classification.
Table 5 compares theaccuracy estimatesofthe classification with the best results obtained in [
The results are explained by the fact that small samples were used as input data, and, consequently, small training sets are used. The size of the networks was also limited, because with increasing network size the "dead" neurons appear, which should be avoided. One of the advantages of the developed technique is that the trained network is able to recognize any instance of the dot of products that is not part of the sample, which could not be done by cluster analysis algorithms. Thus, the developed technique can be recommended both as a method for verifying the results of the IF, and as the technique of the IF.
Criterion