Big Feature Data Analytics: Split and Combine Linear Discriminant Analysis (SC-LDA) for Integration Towards Decision Making Analytics

Abstract

This paper introduces a novel big feature data analytics scheme for integration toward data analytics with decision making. In this scheme, a split and combine approach for a linear discriminant analysis (LDA) algorithm termed SC-LDA is proposed. The SC-LDA replaces the full eigenvector decomposition of LDA with much cheaper eigenvector decompositions on smaller sub-matrices, and then recombines the intermediate results to obtain the exact reconstruction as for the original algorithm. The splitting or decomposition can be further applied recursively to obtain a multi-stage SC-LDA algorithm. The smaller sub-matrices can then be computed in parallel to reduce the time complexity for big data applications. The approach is discussed for an LDA algorithm variation (LDA/QR), which is suitable for the analytics of Big Feature data sets. The projected data vectors into the LDA subspace can then be integrated toward the decision-making process involving classification. Experiments are conducted on real-world data sets to confirm that our approach allows the LDA problem to be divided into the size-reduced sub-problems and can be solved in parallel while giving an exact reconstruction as for the original LDA/QR.