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Simultaneous subspace clustering and cluster number estimating based on triplet relationship

Liang, Jie, Yang, Jufeng, Cheng, Ming-Ming, Rosin, Paul L. ORCID: and Wang, Liang 2019. Simultaneous subspace clustering and cluster number estimating based on triplet relationship. IEEE Transactions on Image Processing 28 (8) , pp. 3973-3985. 10.1109/TIP.2019.2903294

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In this paper we propose a unified framework to discover the number of clusters and group the data points into different clusters using subspace clustering simultaneously. Real data distributed in a high-dimensional space can be disentangled into a union of low-dimensional subspaces, which can benefit various applications. To explore such intrinsic structure, stateof- the-art subspace clustering approaches often optimize a selfrepresentation problem among all samples, to construct a pairwise affinity graph for spectral clustering. However, a graph with pairwise similarities lacks robustness for segmentation, especially for samples which lie on the intersection of two subspaces. To address this problem, we design a hyper-correlation based data structure termed as the triplet relationship, which reveals high relevance and local compactness among three samples. The triplet relationship can be derived from the self-representation matrix, and be utilized to iteratively assign the data points to clusters. Based on the triplet relationship, we propose a unified optimizing scheme to automatically calculate clustering assignments. Specifically, we optimize a model selection reward and a fusion reward by simultaneously maximizing the similarity of triplets from different clusters while minimizing the correlation of triplets from same cluster. The proposed algorithm also automatically reveals the number of clusters and fuses groups to avoid over-segmentation. Extensive experimental results on both synthetic and real-world datasets validate the effectiveness and robustness of the proposed method.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Computer Science & Informatics
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
ISSN: 1057-7149
Date of First Compliant Deposit: 5 June 2019
Date of Acceptance: 19 February 2019
Last Modified: 08 Nov 2023 05:54

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