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The Separating Capacity of a Multithreshold Threshold Element
January 1985 (vol. 7 no. 1)
pp. 112-116
Ryuzo Takiyama, Department of Visual Communication Design, Kyushu Institute of Design, Minami-ku, Fukuoka 815, Japan.
In answer to what represents the intrinsic information-processing capability of the pattern classification system, Cover [1] has defined the separating capacity, and has derived it for the linear machine and the so-called ¿ machine. In this paper, the separating capacity of a multithreshold classification element is obtained. It is shown that the capacity of a multithreshold threshold element with k thresholds-k-threshold element-in n-dimensional space is 2(n + k). A linear machine is a special case in the k-threshold element with k = 1; therefore, its capacity becomes 2(n + 1) from the above result. Further, although it is intuitively apparent that the larger the number of thresholds, the more powerful the information-processing capability of the k-threshold element, using the capacity as a measure of this capability, we may now state that the separating power of the k-threshold element increases linearly with respect to k.
Ryuzo Takiyama, "The Separating Capacity of a Multithreshold Threshold Element," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 7, no. 1, pp. 112-116, Jan. 1985, doi:10.1109/TPAMI.1985.4767626
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