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Open AccessArticle

Laplacian Eigenmaps Dimensionality Reduction Based on Clustering-Adjusted Similarity

by Honghu Zhou and Jun Wang *
College of Computer and Information Science, Southwest University, Chongqing 400715, China
*
Author to whom correspondence should be addressed.
Current address: College of Computer and Information Science, Southwest University, No.2 Tiansheng Road, Beibei District, Chongqing 400715, China
Algorithms 2019, 12(10), 210; https://doi.org/10.3390/a12100210
Received: 25 July 2019 / Revised: 12 September 2019 / Accepted: 30 September 2019 / Published: 4 October 2019
(This article belongs to the Special Issue Clustering Algorithms and Their Applications)
Euclidean distance between instances is widely used to capture the manifold structure of data and for graph-based dimensionality reduction. However, in some circumstances, the basic Euclidean distance cannot accurately capture the similarity between instances; some instances from different classes but close to the decision boundary may be close to each other, which may mislead the graph-based dimensionality reduction and compromise the performance. To mitigate this issue, in this paper, we proposed an approach called Laplacian Eigenmaps based on Clustering-Adjusted Similarity (LE-CAS). LE-CAS first performs clustering on all instances to explore the global structure and discrimination of instances, and quantifies the similarity between cluster centers. Then, it adjusts the similarity between pairwise instances by multiplying the similarity between centers of clusters, which these two instances respectively belong to. In this way, if two instances are from different clusters, the similarity between them is reduced; otherwise, it is unchanged. Finally, LE-CAS performs graph-based dimensionality reduction (via Laplacian Eigenmaps) based on the adjusted similarity. We conducted comprehensive empirical studies on UCI datasets and show that LE-CAS not only has a better performance than other relevant comparing methods, but also is more robust to input parameters.
Keywords: Laplacian Eigenmaps; dimensionality reduction; clustering-adjusted similarity Laplacian Eigenmaps; dimensionality reduction; clustering-adjusted similarity
MDPI and ACS Style

Zhou, H.; Wang, J. Laplacian Eigenmaps Dimensionality Reduction Based on Clustering-Adjusted Similarity. Algorithms 2019, 12, 210.

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