On The Number of Multilinear Partitions and The Computing Capacity of Multiple-Valued Multiple-Threshold Perceptrons  

Oleh:

Ngom, A. ; Stojmenovic, I. ; Zunic, J.

Jenis: Article from Journal - ilmiah internasional
Dalam koleksi: IEEE Transactions on Neural Networks vol. 14 no. 3 (May 2003), page 469-477.
Topik: Multilinear; multilinear partitions; computing capacity; multiple - valued; multiple - threshold; perceptrons

Ketersediaan

Perpustakaan Pusat (Semanggi) Nomor Panggil: II36.7 Non-tandon: 1 (dapat dipinjam: 0) Tandon: tidak ada

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Isi artikel

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.

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