A Fast Harmonic Mean Linear Discriminant Analysis for Dimensionality Reduction
International journal of intelligent engineering and systems · 2022
Dimensionality reduction is the most prominent process in artificial intelligence and data science because of using a massive amount of high-dimensional information.In recent days, many dimensionality reduction algorithms focused on the harmonic mean-based linear discriminant analysis (HLDA) which was the enhanced version of classical LDA.In particular, two different variants such as HLDA and HLDA pairwise (HLDAp) have been applied to reduce the high-dimensional data by using the harmonic mean between-class distance.However, its computation time complexity was high during the initialization phase since it comprises the matrix Eigen decomposition/inverse.Hence this article proposes the Fast HLDA (FHLDA) and FHLDA pairwise (FHLDAp) algorithms for reducing the high-dimensional data during classification.In this algorithm, a joint diagonalization scheme is introduced instead of Eigen decomposition depending on Taylor expansion for lessening the number of iterations in the initialization step to produce the discriminant.It does not a choice to a sweeping task so that every element of the Eigenvector matrix at every iteration is calculated to minimize the computation time burden.As well, a first-order approximation of the inverse Eigenvector matrix and the complete matrix of Eigenvectors are updated at every iteration.On the contrary, the overlap among the samples of dissimilar classes tends to miscategorization.So, the optimal discriminant vector is discovered to solve this issue by extending the between-class scatter matrices.Finally, the experimental outcomes show that the FHLDA and FHLDAp algorithms achieve 10 % higher average accuracy than LDA, ALDA, WLDA, G2DLDA, HLDA, and HLDAp algorithms.