Spectral Clustering Approach with K-Nearest Neighbor and Weighted Mahalanobis Distance for Data Mining

Abstract

This paper proposes a spectral clustering method using k-means and weighted Mahalanobis distance (Referred to as MDLSC) to enhance the degree of correlation between data points and improve the clustering accuracy of Laplacian matrix eigenvectors. First, we used the correlation coefficient as the weight of the Mahalanobis distance to calculate the weighted Mahalanobis distance between any two data points and constructed the weighted Mahalanobis distance matrix of the data set; then, based on the weighted Mahalanobis distance matrix, we used the K-nearest neighborhood (KNN) algorithm construct similarity matrix. Secondly, the regularized Laplacian matrix was calculated according to the similarity matrix, normalized and decomposed, and the feature space for clustering was obtained. This method fully considered the degree of linear correlation between data and special spatial structure and achieved accurate clustering. Finally, various spectral clustering algorithms were used to conduct multi-angle comparative experiments on artificial and UCI data sets. The experimental results show that MDLSC has certain advantages in each clustering index and the clustering quality is better. The distribution results of the eigenvectors also show that the similarity matrix calculated by MDLSC is more reasonable, and the calculation of the eigenvectors of the Laplacian matrix maximizes the retention of the distribution characteristics of the original data, thereby improving the accuracy of the clustering algorithm.