Lower Dimensional Representation of Text Data Based on Centroids and Least Squares

Abstract

Dimension reduction in today’s vector space based informat ion retrieval system is essential for improving computational efficiency in handling massive amounts of dat a. A mathematical framework for lower dimensional representation of text data in vector space based inf ormation retrieval is proposed using minimization and a matrix rank reduction formula. We illustrate how the commonly used Latent Semantic Indexing based on the Singular Value Decomposition (LSI/SVD) can be derived as a method for dimension reduction from our mathematical framework. Then two new methods for dimension reduction based on the centroids of data clusters are proposed and shown to be more efficient and e ffective than LSI/SVD when we have a priori information on the cluster structure of the data. Several ad vantages of the new methods in terms of computational efficiency and data representation in the reduced s pace, as well as their mathematical properties are discussed. Experimental results are presented to illustrate the effec tiveness of our methods on certain classification problems in a reduced dimensional space. The results indicate that for a successful lower dimensional representation of the data, it is important to incorporate a priori knowledge in the dimension reduction algorithms.