Discriminant laplacian eigenmaps by the approximation of discriminant analysis using similarity

Abstract

The dimension of data influences the clustering method used for pattern recognition. Dimension reduction method, therefore, has a significant impact on clustering performance. This study compares discriminant analysis (DA) and Laplacian eigenmaps (LE), two supervised and unsupervised dimension reduction methods, from the standpoint of the degree of separation. This comparison revealed that LE suffers from a loss of accuracy due to the lack of an averaging operation. Therefore, we propose a new dimensionality reduction method, discriminant LE (DLE), which eliminates the shortcomings of LE. DLE is a straightforward approximation of DA using the similarity. We also propose recursive similarity processing method to reduce pseudoclusters. Finally, we also conclude that DLE is more useful than LE for clustering and that recursive similarity processing improves the performance of DLE.