Authors:
Xili Sun
and
Yonggang Lu
Affiliation:
Lanzhou University, China
Keyword(s):
Dimension Reduction, Locally Linear Embedding, Rank-order Distance, Pattern Recognition.
Related
Ontology
Subjects/Areas/Topics:
Embedding and Manifold Learning
;
Pattern Recognition
;
Theory and Methods
Abstract:
Dimension reduction has become an important tool for dealing with high dimensional data. Locally linear embedding (LLE) is a nonlinear dimension reduction method which can preserve local configurations of nearest neighbors. However, finding the nearest neighbors requires the definition of a distance measure, which is a critical step in LLE. In this paper, the Rank-order distance measure is used to substitute the traditional Euclidean distance measure in order to find better nearest neighbor candidates for preserving local configurations of the manifolds. The Rank-order distance between the data points is calculated using their neighbors’ ranking orders, and is shown to be able to improve the clustering of high dimensional data. The proposed method is called Rank-order based LLE (RLLE). The RLLE method is evaluated by comparing with the original LLE, ISO-LLE and IED-LLE on two handwritten datasets. It is shown that the effectiveness of a distance measure in the LLE method is closely r
elated to whether it can be used to find good nearest neighbors. The experimental results show that the proposed RLLE method can improve the process of dimension reduction effectively, and C-index is another good candidate for evaluating the dimension reduction results.
(More)