A new polynomial-time algorithm for linear programming
Combinatorica
Complexity of finite precision neural network classifier
Advances in neural information processing systems 2
The Perceptron algorithm is fast for non-malicious distributions
Advances in neural information processing systems 2
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We investigate the convergence rate of the perceptron algorithm when the patterns are given with high precision. In particular, using the result of A. Dembo (Quart. Appl. Math.47 (1989), 185-195), we show that when the n pattern vectors are independent and uniformly distributed over {+1, -1}^n^l^o^g^n, as n - ~, with high probability, the patterns can be classified into all 2^n possible ways using perceptron algorithm with O(n log n) iteration. Further, the storage of parameters requires only O(n log^2n) bits. We also indicate some interesting mathematical connections with the theory of random matrices.