Feature transformation by function decomposition
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Abstract:
While not explicitly intended for feature transformation, some methods for switching circuit design implicitly deal with this problem. Given a tabulated Boolean function, these methods construct a circuit that implements that function. In 1950s and 1960s, Ashenhurst [1] and Curtis [2] proposed a function decomposition method that develops a switching circuit by constructing a nested hierarchy of tabulated Boolean functions. Both the hierarchy and the functions themselves are discovered by the decomposition method and are not given in advance. This is especially important from the viewpoint of feature construction, since the outputs of such functions can be regarded as new features not present in the original problem description. The basic principle of function decomposition is the following. Let a tabulated function y = F (X) use a set of input features X = x 1; : : : ; x n. The goal is to decompose this function into y = G(A; H(B)), where A and B are subsets of features in X such that A [ B = X. G and H are tabulated functions that are determined by the decomposition and are not predefined. Their
