Reducing Dimensionality in Text Mining using Conjugate Gradients and Hybrid Cholesky Decomposition

Abstract

Abstract-Generally, data mining in larger datasets consists of certain limitations in identifying the relevant datasets for the given queries. The limitations include: lack of interaction in the required objective space, inability to handle the data sets or discrete variables in datasets, especially in the presence of missing variables and inability to classify the records as per the given query, and finally poor generation of explicit knowledge for a query increases the dimensionality of the data. Hence, this paper aims at resolving the problems with increasing data dimensionality in datasets using modified non-integer matrix factorization (NMF). Further, the increased dimensionality arising due to non-orthogonally of NMF is resolved with Cholesky decomposition (cdNMF). Initially, the structuring of datasets is carried out to form a well-defined geometric structure. Further, the complex conjugate values are extracted and conjugate gradient algorithm is applied to reduce the sparse matrix from the data vector. The cdNMF is used to extract the feature vector from the dataset and the data vector is linearly mapped from upper triangular matrix obtained from the Cholesky decomposition. The experiment is validated against accuracy and normalized mutual information (NMI) metrics over three text databases of varied patterns. Further, the results prove that the proposed technique fits well with larger instances in finding the documents as per the query, than NMF, neighborhood preserving: nonnegative matrix factorization (NPNMF), multiple manifolds non-negative matrix factorization (MMNMF), robust non-negative matrix factorization (RNMF), graph regularized non-negative matrix factorization (GNMF), hierarchical non-negative matrix factorization (HNMF) and cdNMF.