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Scalable sparse subspace clustering
- CVPR
"... In this paper, we address two problems in Sparse Sub-space Clustering algorithm (SSC), i.e., scalability issue and out-of-sample problem. SSC constructs a sparse similar-ity graph for spectral clustering by using 1-minimization based coefficients, has achieved state-of-the-art results for image clus ..."
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Cited by 6 (2 self)
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In this paper, we address two problems in Sparse Sub-space Clustering algorithm (SSC), i.e., scalability issue and out-of-sample problem. SSC constructs a sparse similar-ity graph for spectral clustering by using 1-minimization based coefficients, has achieved state-of-the-art results for image clustering and motion segmentation. However, the time complexity of SSC is proportion to the cubic of prob-lem size such that it is inefficient to apply SSC into large scale setting. Moreover, SSC does not handle with out-of-sample data that are not used to construct the similarity graph. For each new datum, SSC needs recalculating the cluster membership of the whole data set, which makes SSC is not competitive in fast online clustering. To address the problems, this paper proposes out-of-sample extension of SSC, named as Scalable Sparse Subspace Clustering (SSS-C), which makes SSC feasible to cluster large scale data sets. The solution of SSSC adopts a ”sampling, clustering, coding, and classifying ” strategy. Extensive experimental results on several popular data sets demonstrate the effec-tiveness and efficiency of our method comparing with the state-of-the-art algorithms. 1.
Clustering and Projected Clustering with Adaptive Neighbors
"... Many clustering methods partition the data groups based on the input data similarity matrix. Thus, the clustering results highly depend on the data similarity learning. Be-cause the similarity measurement and data clustering are often conducted in two separated steps, the learned data similarity may ..."
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Cited by 2 (1 self)
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Many clustering methods partition the data groups based on the input data similarity matrix. Thus, the clustering results highly depend on the data similarity learning. Be-cause the similarity measurement and data clustering are often conducted in two separated steps, the learned data similarity may not be the optimal one for data clustering and lead to the suboptimal results. In this paper, we pro-pose a novel clustering model to learn the data similarity matrix and clustering structure simultaneously. Our new model learns the data similarity matrix by assigning the adaptive and optimal neighbors for each data point based on the local distances. Meanwhile, the new rank constraint is imposed to the Laplacian matrix of the data similarity matrix, such that the connected components in the resulted similarity matrix are exactly equal to the cluster number. We derive an efficient algorithm to optimize the proposed challenging problem, and show the theoretical analysis on the connections between our method and the K-means clus-tering, and spectral clustering. We also further extend the new clustering model for the projected clustering to han-dle the high-dimensional data. Extensive empirical results on both synthetic data and real-world benchmark data sets show that our new clustering methods consistently outper-forms the related clustering approaches.
Efficient semidefinite spectral clustering via lagrange duality
- IEEE Trans. Image Processing
, 2014
"... Abstract—We propose an efficient approach to semidefinite spectral clustering (SSC), which addresses the Frobenius nor-malization with the positive semidefinite (p.s.d.) constraint for spectral clustering. Compared with the original Frobenius norm approximation based algorithm, the proposed algorith ..."
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Cited by 1 (0 self)
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Abstract—We propose an efficient approach to semidefinite spectral clustering (SSC), which addresses the Frobenius nor-malization with the positive semidefinite (p.s.d.) constraint for spectral clustering. Compared with the original Frobenius norm approximation based algorithm, the proposed algorithm can more accurately find the closest doubly stochastic approximation to the affinity matrix by considering the p.s.d. constraint. In this paper, SSC is formulated as a semidefinite programming (SDP) problem. In order to solve the high computational complexity of SDP, we present a dual algorithm based on the Lagrange dual formalization. Two versions of the proposed algorithm are proffered: one with less memory usage and the other with faster convergence rate. The proposed algorithm has much lower time complexity than that of the standard interior-point based SDP solvers. Experimental results on both UCI data sets and real-world image data sets demonstrate that 1) compared with the state-of-the-art spectral clustering methods, the proposed algorithm achieves better clustering performance; and 2) our algorithm is much more efficient and can solve larger-scale SSC problems than those standard interior-point SDP solvers. Index Terms—Spectral clustering, Doubly stochastic normal-ization, Semidefinite programming, Lagrange duality. I.
Contents lists available at ScienceDirect
"... Learning from normalized local and global discriminative information for semi-supervised regression and ..."
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Learning from normalized local and global discriminative information for semi-supervised regression and
An Out-of-sample Extension of Sparse Subspace Clustering and Low Rank Representation for Clustering Large Scale Data Sets
"... ar ..."
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Discriminative Embedded Clustering: A Framework for Grouping High Dimensional Data
"... In many real applications of machine learning and data mining, we are often confronted with high dimensional data. How to cluster high dimensional data is still a challenging problem due to the curse of dimensionality. In this paper, we try to address this problem using joint dimensionality reducti ..."
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In many real applications of machine learning and data mining, we are often confronted with high dimensional data. How to cluster high dimensional data is still a challenging problem due to the curse of dimensionality. In this paper, we try to address this problem using joint dimensionality reduction and clustering. Different from traditional approaches which conduct dimensionality reduction and clustering in sequence, we propose a novel framework referred to as Discriminative Embedded Clustering (DEC) which alternates them iteratively. Within this framework, we are able not only to view several traditional approaches and reveal their intrinsic relationships, but also to be stimulated to develop a new method. We also propose an effective approach for solving the formulated non-convex optimization problem. Comprehensive analyses, including convergence be-havior, parameter determination and computational complexity, together with the relationship to other related approaches, are also presented. Plenty of experimental results on benchmark data sets illustrate that the proposed method outperforms related state of the art clustering approaches and existing joint dimensionality reduction and clustering methods.
