The k means and forgy algorithms are iterative

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The k means and forgy algorithms are iterative procedures aiming to minimize the sum of squared error for a given number of classes. Both algorithms start from the initial cluster centers defined either by random selection among the available data or previously established by the user. Nearest neighbors classification is applied to reclassify all the patterns followed by update of the cluster centers by calculating the mean vector of the resulting classes. The above procedure is repeated until convergence. Up to this point, k means and forgy algorithms are identical. In addition to that, the forgy algorithm implements heuristic procedures for controlling the number of classes. 1. A new cluster is created if D av i D m i < T f D m i , where D av i is the average distance of pattern i to the existing cluster centers , D m i is the distance of pattern i to the nearest cluster center and T f is a user specified parameter in the range (0,1). 2. An existing cluster is omitted if it is sufficiently small and composing with less than N min patterns. This is the only way to decrease the number of clusters. Upon deleting small classes and establishing new ones, the k means iterations are repeated. The entire process is repeated until overall convergence. All the above algorithms are influenced by the initial cluster selection and require multiple runs for the selection of the optimum classification. Such instabilities might be avoided by the interactive coupling of maximum and minimum distance and forgy algorithm. 12 Demonstration of Unsupervised Pattern Recognition If prior knowledge about the data of Fig. 17 is not available, unsupervised pattern recognition techniques are used to demonstrate the classification sequence. For the demonstration, the pattern vector dimensions were restricted to six acoustic emission features: amplitude, acoustic energy, duration, absolute energy, frequency centroid and peak frequency. Feature selection was guided by experience and by close observation of two-dimensional and three-dimensional scatter and distribution plots. The resulting partitions from the application of the maximum/minimum distance algorithm using default parameters are presented in Fig. 19. The resulting partition shows that all the data from pencil breaks were grouped together in two classes for 100 percent recognition. Similarly, the electromagnetic interference data recorded from time durations greater than 50 s were all grouped together for 100 percent recognition. Finally, the acoustic emission test data because of friction, falling in a range between 37 and 47 s, were grouped in two different classes. The two acoustic emission hits from friction at time 22.5 s were successfully classified as friction. Overall, the classification process is correct and reflects the different phenomena of 165 Acoustic Emission Signal Processing
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interest properly. However, the three different sources were mapped to five classes during the unsupervised process, reflecting correlations unexpected in terms of acoustic emission testing.
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