The Separating Capacity of a Multithreshold Threshold Element

  • Authors:

  • Ryuzo Takiyama

  • Affiliations:

  • Department of Visual Communication Design, Kyushu Institute of Design, Minami-ku, Fukuoka 815, Japan.

  • Venue:
  • IEEE Transactions on Pattern Analysis and Machine Intelligence
  • Year:
  • 1985

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Abstract

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 驴 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.