Dimension Reduction Based on Centroids and Least Squares for Efficient Processing of Text Data

Abstract

Dimension reduction in today's vector space based information retrieval system is essential for improving computational efficiency in handling massive data. In our previous work we proposed a mathematical framework for lower dimensional representations of text data in vector space based information retrieval, and a couple of dimension reduction methods using minimization and matrix rank reduction formula. One of our proposed methods is CentroidQR method which utilizes orthogonal transformation on centroids, and the test results showed that its classification results were exactly the same as those of classification with full dimension when a certain classification algorithm is applied. In this paper we discuss in detail the CentroidQR method, and prove mathematically its classification properties with two different similarity measures of L2 and cosine.