KNOWLEDGE DISCOVERY FROM NUMERICAL DATA

摘要

Since many real data consist of numerical data, the discovery of understandable propositions from numerical data is important, and can be regarded as inductive learning with continuous classes. One of the authors previously presented an al-gorithm for discovering understandable propositions from numerical data. The algorithm consists of normalization, multiple regression analysis and the approx-imation of multilinear functions by continuous Boolean functions. Continuous Boolean functions are included in the space of multilinear functions. The space of multilinear functions can be corresponded to the space of probability distributions using the principle of indifference. The distance between two probability distri-butions is described by Kullback-Leibler (KL) information. Thus, the distance between multilinear functions and continuous Boolean functions is described using KL information. Therefore multilinear functions can be approximated to continu-ous Boolean functions. However, since the approximation algorithm is exponential in computational complexity, it can hardly be applied to real databases. This pa-per presents a polynomial approximation algorithm and applies the algorithm to bodyfat data to discover understandable propositions.