Information Retrieval Using the Reduced Row Echelon Form of a Term-Document Matrix

Abstract

It is getting more difficult to retrieve relevant information regarding the user input query due to the large amount of information in the web. Unlike the conventional information retrieval (IR) algorithms, this study presents a new algorithm – reduced row echelon form IR method (rrefIR) – with higher average similarity precision to get more relevant and noise-free documents. For dimension reduction in the proposed algorithm, singular value decomposition (SVD) is applied on the reduced row echelon form – obtained by utilizing Gauss-Jordan method – of the covariance of term-document matrix (TDM). The rrefIR algorithm outperforms the LSI and COV algorithms with respect to Jaro-Winkler, Overlap, Tanimoto and Jaccard similarity measures in the means of average similarity precision. The physical reason for the better IR performance is the linear independent basis vectors set obtained by Gauss-Jordan operation. This basis set can be considered as the generating roots of the vector space spanned by TDM. Utilizing these vectors increases the latent semantic charateristics of the SVD phase of the proposed IR algorithm.