Abstract

Abstract Dimension reduction in today's vector space based information retrieval system is essential for improvingcomputational efficiency in handling massive amounts of data. A mathematical framework for lower dimensional representation of text data in vector space based information retrieval is proposed using minimizationand 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 fromour 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 effective than LSI/SVD when we have a prioriinformation on the cluster structure of the data. Several advantages of the new methods in terms of computational efficiency and data representation in the reduced space, as well as their mathematical properties arediscussed. Experimental results are presented to illustrate the effectiveness of our methods on certain classificationproblems 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 reductionalgorithms.

Citations