Locally Linear Embedding based on Rank-order Distance

Xili Sun, Yonggang Lu


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 related 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.


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Paper Citation

in Harvard Style

Sun X. and Lu Y. (2016). Locally Linear Embedding based on Rank-order Distance . In Proceedings of the 5th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM, ISBN 978-989-758-173-1, pages 162-169. DOI: 10.5220/0005658601620169

in Bibtex Style

author={Xili Sun and Yonggang Lu},
title={Locally Linear Embedding based on Rank-order Distance},
booktitle={Proceedings of the 5th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,},

in EndNote Style

JO - Proceedings of the 5th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,
TI - Locally Linear Embedding based on Rank-order Distance
SN - 978-989-758-173-1
AU - Sun X.
AU - Lu Y.
PY - 2016
SP - 162
EP - 169
DO - 10.5220/0005658601620169