Optimal Landmark Point Selection Using Clustering for Manifold Modeling and Data Classification

Abstract

As data volume and dimensions continue to grow, effective and efficient methods are needed to obtain the low dimensional features of the data that describe its true structure. Most nonlinear dimensionality reduction methods (NLDR) utilize the Euclidean distance between the data points to form a general idea of the data manifold structure. Isomap uses the geodesic distance between data points and then uses classical multidimensional scaling(cMDS) to obtain low dimensional features. As the data size increases Isomap becomes complex. To overcome this disadvantage, Landmark Isomap (L-Isomap) uses selected data points called landmark points and finds the geodesic distance from these points to all other non-landmark points. Traditionally, landmark points are randomly selected without considering any statistical property of the data manifold. We contend that the quality of the features extracted is dependent on the selection of the landmark points. In applications such as data classification, the net accuracy is dependent on the quality of the features selected, and hence landmark points selection might play a crucial role. In this paper, we propose a clustering approach to obtain the landmark points. These new points are now used to represent the data, and Fisher’s linear discriminants are used for classification. The proposed method is tested with different datasets to verify the efficacy of the approach.