Variants of Self-Organizing Maps Essay

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IEEE TRANSACTIONS ON N E U R A L NETWORKS. VOL. I , NO. I . MARCH 1990 93 Variants of Self-organizing Maps Abstmct-The self-organizing maps have a bearing on traditional vector quantization. A characteristic that makes them more resemble certain biological brain maps, however, is the spatial order of their responses, which is formed in the learning process. This paper discusses the basic algorithms and two innovations: dynamic weighting of the input signals at each input of each cell, which improves the ordering when very different input signals are used, and definition of neighborhoods in the learning algorithm by the minimal spanning tree, which provides a far better and faster approximation of prominently structured density functions. Finally, it is cautioned that if the maps are used for pattern recognition and decision processes, it is necessary to fine tune the reference vectors so that they directly define the decision borders. I . BASICALGORITHMS THE “MAPS” FOR OMPETITIVE learning is an adaptive process, in which the cells of, say, a neural network are tuned to specific features of input. The responses from the network then tend to become localized [1]-[3]. The basic principle underlying competitive learning stems from early studies of certain problems in mathematical statistics, namely, cluster analysis. The original idea behind it was roughly the following. Assume a sequence of statistical samples of a vectorial observable x = x ( t ) E R“ where t is the time coordinate, and a set of variable reference (or “codebook”) vectors { m i ( t ) ;m iE R“, i = 1 , 2 , , k } . Assume that the m i ( 0 )have been initialized in some proper way; random selection will often do. Competitive learning then means that if the input x ( t ) can somehow be compared in parallel with all the mi ( t )at each successive time instant, taken here to be an integer t = 1,

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