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Bidirectional Clustering of Weights for Finding Succinct Multivariate Polynomials


Yusuke Tanahashi, Ryohei Nakano


Vol. 8  No. 5  pp. 85-94


We present a weight sharing method called BCW and evaluate its effectiveness by applying it to find succinct multivariate polyno-mials. In our framework, polynomials are obtained by learning a three-layer perceptron for data having only numerical variables. If data have both numerical and nominal variables, we consider a set of nominally conditioned multivariate polynomials. To obtain succinct polynomials, we focus on weight sharing. Weight sharing constrains the freedom of weight values such that weights are allowed to have one of common weights. The BCW employs merge and split operations based on 2nd-order optimal criteria, and can escape local optima through bidirectional clustering. Moreover, the BCW selects the optimal model based on the Bayesian Information Criterion (BIC). Our experiments showed that connectionist polynomial regressions with the proposed BCW can restore succinct polynomials almost equivalent to the original for artificial data sets, and obtained readable results and satisfactory generalization performance better than other methods for many real data sets.


polynomial regression, multi-layer perceptron, weight sharing, bidirectional clustering