Coupled Attribute Analysis on Numerical Data

The usual representation of quantitative data is to formalize it as an information table, which assumes the independence of attributes. In real-world data, attributes are more or less interacted and coupled via explicit or implicit relationships. Limited research has been conducted on analyzing such attribute interactions, which only describe a local picture of attribute couplings in an implicit way. This paper proposes a framework of the coupled attribute analysis to capture the global dependency of continuous attributes. Such global couplings integrate the intra-coupled interaction within an attribute (i.e. the correlations between attributes and their own powers) and inter-coupled interaction among different attributes (i.e. the correlations between attributes and the powers of others) to form a coupled representation for numerical objects by the Taylor-like expansion. This work makes one step forward towards explicitly addressing the global interactions of continuous attributes, verified by the applications in data structure analysis, data clustering, and data classification. Substantial experiments on 13 UCI data sets demonstrate that the coupled representation can effectively capture the global couplings of attributes and outperforms the traditional way, supported by statistical analysis.