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In answer to what represents the intrinsic information-processing capability of the pattern classification system, Cover  has defined the separating capacity, and has derived it for the linear machine and the so-called Â¿ 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.
Pattern Analysis and Machine Intelligence, IEEE Transactions on (Volume:PAMI-7 , Issue: 1 )
Date of Publication: Jan. 1985