Journal
IEEE TRANSACTIONS ON IMAGE PROCESSING
Volume 28, Issue 8, Pages 3973-3985Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIP.2019.2903294
Keywords
Subspace clustering; triplet relationship; estimating the number of clusters; hyper-graph clustering
Funding
- NSFC [61876094, 61620106008, 61572264]
- Natural Science Foundation of Tianjin, China [18JCYBJC15400, 18ZXZNGX00110]
- Open Project Program of the National Laboratory of Pattern Recognition (NLPR)
- Fundamental Research Funds for the Central Universities
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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, state-of-the-art subspace clustering approaches often optimize a self-representation 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 the 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.
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