Finding nominally conditioned multivariate polynomials using a four-layer perceptron having shared weights

Authors:
Yusuke Tanahashi;Kazumi Saito;Daisuke Kitakoshi;Ryohei Nakano
Affiliations:
Nagoya Institute of Technology, Nagoya, Japan;NTT Communication Science Laboratories, NTT Corporation, Soraku, Kyoto, Japan;Nagoya Institute of Technology, Nagoya, Japan;Nagoya Institute of Technology, Nagoya, Japan
Venue:
KES'06 Proceedings of the 10th international conference on Knowledge-Based Intelligent Information and Engineering Systems - Volume Part II
Year:
2006

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Abstract

We present a method for discovering nominally conditioned polynomials to fit multivariate data containing numeric and nominal variables using a four-layer perceptron having shared weights. A polynomial is accompanied with the nominal condition stating a subspace where the polynomial is applied. To get a succinct neural network, we focus on weight sharing, where a weight is allowed to have one of common weights. A near-zero common weight can be eliminated. Our method iteratively merges and splits common weights based on 2nd-order criteria, escaping from local optima. Moreover, our method selects the optimal number of hidden units based on cross-validation. The experiments showed that our method can restore the original sharing structure for an artificial data set, and discovers rather succinct rules for a real data set.