Instance Selection Based on Hypertuples

Abstract

Instance selection aims to search for a representative portion of data that serves the same purpose as the whole data. In this chapter we propose a novel procedure for instance selection based on hypertuples, a generalization of traditional database tuples. This procedure has two tasks: building a model and selecting instances based on the model. For the first task, we propose to merge data tuples while ensuring some criteria are satisfied. This merge operation results in a set of hypertuples which, under certain conditions, serves as a model of the original data. We identify two types of criteria for the task of instance selection: preserving classification structures and maximizing density of hypertuples. For the first criterion we propose a formalism that leads to a unique solution — the least E-set. We then propose algorithms for finding this unique solution and for finding a compromised solution efficiently. For the second criterion we propose a new measure of density, which is normalized and quantized, and which applies to both numerical and categorical data. Using this measure of density, we then propose a hill-climbing algorithm that can efficiently find a quasi-optimal set of hypertuples, which is “quasi-densest”.

Having a model of data, we can generate a set of representative instances — the second task of the procedure. We propose to calculate the centers of the hypertuples in the model and take these centers as the representative instances of the original data. To use the selected instances for classification, we propose to use a nearest neighbor (NN) approach.

Experiments using real world public data show that, when used with the proposed NN classifier, the selected instances are not only representative but even outperform C5 in some cases.