Simultaneous Clustering and Model Selection for Tensor Affinities

Li, Zhuwen; Yang, Shuoguang; Cheong, Loong-Fah; Toh, Kim-Chuan

doi:10.1109/cvpr.2016.577

Cited by 7 publications

(15 citation statements)

References 35 publications

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“…Some transform the hyper-correlation into a simpler pairwise graph [21], [66], followed by a standard graph clustering method, e.g., normalized cut [11], to calculate the assignments. Besides, other methods [39], [13] explore a generalized way of extending the pairwise graph to the hyper-graph or hyperdimensional tensor analysis. For instance, Li et al propose a tensor affinity variant of SCAMS, i.e., SCAMSTA [13], which exploits the higher order mathematical structures by providing multiple groups of nodes in the binary matrix derived from an outer product operation on multiple indicator vectors.…”

Section: Hyper-graph Clusteringmentioning

confidence: 99%

“…2) Comparative Methods: We make comparisons with the following methods: SCAMS [13], [29], a density peak based method (DP) [19], a singular value decomposition based method (SVD) [58] and DP-space [12]. Besides, we utilize the following subspace representation methods to generate different coefficient matrices C: LRR [39], CASS [52], LSR [46], SMR [32] and ORGEN [33].…”

Section: A Experimental Setupmentioning

confidence: 99%

“…We conduct experiments on the extended Yale B and COIL-20 datasets with different numbers of subjects, and compare four methods with the proposed autoSC and autoSC-N on the metrics of NC e and NMI. For SCAMS [13], [29], DP [19], SVD [58] and our autoSC, the optimization module in SMR [32] is employed to generate the similarity matrix C. The DP-space method simultaneously estimates K and finds the subspaces without the requirement of a similarity matrix. All parameters of the contrasted methods are tuned to provide the best performance.…”

Section: B Comparisons Among Automatic Clusteringmentioning

confidence: 99%

“…Table VI reports the comparison against four automatic clustering methods. For SCAMS [13], [29], DP [19] and SVD [58], the SMR [32] is firstly conducted to calculate the similarity matrix. As shown in the table, the proposed autoSC achieves best performance on both metrics, indicating that the autoSC is effective at both estimating the number of motions (about 0.18 error rate) and segmenting the feature points (obtains NMI of more than 0.98).…”

Section: E Real Application: Motion Segmentationmentioning

confidence: 99%

“…Nevertheless, it is challenging to estimate the number of clusters in a unified optimization framework, since the definition of clusters is subjective, especially in the high-dimensional ambient space [13]. Also, for samples which are of different clusters but near the intersection of two subspaces, they may be even closer than samples from same cluster.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Simultaneous Subspace Clustering and Cluster Number Estimating Based on Triplet Relationship

Liang

Yang

Cheng

et al. 2019

IEEE Trans. on Image Process.

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In this paper we propose a unified framework to simultaneously discover the number of clusters and group the data points into them using subspace clustering. 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. Three samples in each triplet are encouraged to be highly correlated and are considered as a meta-element during clustering, which show more robustness than pairwise relationships when segmenting two densely distributed subspaces. 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 oversegmentation. Extensive experimental results on both synthetic and real-world datasets validate the effectiveness and robustness of the proposed method.

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Section: Hyper-graph Clusteringmentioning

confidence: 99%