Combining the Perceptron Algorithm with Logarithmic Simulated Annealing

Abstract

We present results of computational experiments with an extension of the Perceptron algorithm by a special type of simulated annealing. The simulated annealing procedure employs a logarithmic cooling schedule c(k)eΓ/ln(k+2), where Γ is a parameter that depends on the underlying configuration space. For sample sets S of n-dimensional vectors generated by randomly chosen polynomials w1·x1a1+···+wn·xnangt, we try to approximate the positive and negative examples by linear threshold functions. The approximations are computed by both the classical Perceptron algorithm and our extension with logarithmic cooling schedules. For ne256,…, 1024 and aie3,…, 7, the extension outperforms the classical Perceptron algorithm by about 15% when the sample size is sufficiently large. The parameter Γ was chosen according to estimations of the maximum escape depth from local minima of the associated energy landscape.