Generalization Error Bounds for Threshold Decision Lists
The Journal of Machine Learning Research
ICANN'06 Proceedings of the 16th international conference on Artificial Neural Networks - Volume Part I
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We introduce the concept of multilinear partition of a point set V⊂Rn and the concept of multilinear separability of a function f:V→K={0,...,k-1}. Based on well-known relationships between linear partitions and minimal pairs, we derive formulae for the number of multilinear partitions of a point set in general position and of the set K2. The (n,k,s)-perceptrons partition the input space V into s+1 regions with s parallel hyperplanes. We obtain results on the capacity of a single (n,k,s)-perceptron, respectively, for V⊂Rn in general position and for V=K2. Finally, we describe a fast polynomial-time algorithm for counting the multilinear partitions of K2.