Results 1 - 10
of
15
Flexible constrained spectral clustering
- in KDD, 2010
"... Constrained clustering has been well-studied for algorithms like K-means and hierarchical agglomerative clustering. However, how to encode constraints into spectral clustering remains a developing area. In this paper, we propose a flexible and generalized framework for constrained spectral clusterin ..."
Abstract
-
Cited by 38 (4 self)
- Add to MetaCart
(Show Context)
Constrained clustering has been well-studied for algorithms like K-means and hierarchical agglomerative clustering. However, how to encode constraints into spectral clustering remains a developing area. In this paper, we propose a flexible and generalized framework for constrained spectral clustering. In contrast to some previous efforts that implicitly encode Must-Link and Cannot-Link constraints by modifying the graph Laplacian or the resultant eigenspace, we present a more natural and principled formulation, which preserves the original graph Laplacian and explicitly encodes the constraints. Our method offers several practical advantages: it can encode the degree of belief (weight) in Must-Link and Cannot-Link constraints; it guarantees to lowerbound how well the given constraints are satisfied using a user-specified threshold; and it can be solved deterministically in polynomial time through generalized eigendecomposition. Furthermore, by inheriting the objective function from spectral clustering and explicitly encoding the constraints, much of the existing analysis of spectral clustering techniques is still valid. Consequently our work can be posed as a natural extension to unconstrained spectral clustering and be interpreted as finding the normalized min-cut of a labeled graph. We validate the effectiveness of our approach by empirical results on real-world data sets, with applications to constrained image segmentation and clustering benchmark data sets with both binary and degree-of-belief constraints.
Active co-analysis of a set of shapes
- ACM Trans. on Graph (SIGGRAPH Asia
, 2012
"... Figure 1: Overview of our active co-analysis: (a) We start with an initial unsupervised co-segmentation of the input set. (b) During active learning, the system automatically suggests constraints which would refine results and the user interactively adds constraints as appropriate. In this example, ..."
Abstract
-
Cited by 33 (9 self)
- Add to MetaCart
Figure 1: Overview of our active co-analysis: (a) We start with an initial unsupervised co-segmentation of the input set. (b) During active learning, the system automatically suggests constraints which would refine results and the user interactively adds constraints as appropriate. In this example, the user adds a cannot-link constraint (in red) and a must-link constraint (in blue) between segments. (c) The constraints are propagated to the set and the co-segmentation is refined. The process from (b) to (c) is repeated until the desired result is obtained. Unsupervised co-analysis of a set of shapes is a difficult problem since the geometry of the shapes alone cannot always fully describe the semantics of the shape parts. In this paper, we propose a semi-supervised learning method where the user actively assists in the co-analysis by iteratively providing inputs that progressively constrain the system. We introduce a novel constrained clustering method based on a spring system which embeds elements to better respect their inter-distances in feature space together with the usergiven set of constraints. We also present an active learning method that suggests to the user where his input is likely to be the most effective in refining the results. We show that each single pair of constraints affects many relations across the set. Thus, the method requires only a sparse set of constraints to quickly converge toward a consistent and error-free semantic labeling of the set.
Constrained 1-Spectral Clustering
"... An important form of prior information in clustering comes in form of cannot-link and must-link constraints. We present a generalization of the popular spectral clustering technique which integrates such constraints. Motivated by the recently proposed 1-spectral clustering for the unconstrained prob ..."
Abstract
-
Cited by 15 (2 self)
- Add to MetaCart
(Show Context)
An important form of prior information in clustering comes in form of cannot-link and must-link constraints. We present a generalization of the popular spectral clustering technique which integrates such constraints. Motivated by the recently proposed 1-spectral clustering for the unconstrained problem, our method is based on a tight relaxation of the constrained normalized cut into a continuous optimization problem. Opposite to all other methods which have been suggested for constrained spectral clustering, we can always guarantee to satisfy all constraints. Moreover, our soft formulation allows to optimize a trade-off between normalized cut and the number of violated constraints. An efficient implementation is provided which scales to large datasets. We outperform consistently all other proposed methods in the experiments. 1
Constrained Clustering by Spectral Kernel Learning
- in Proc. IEEE Int’l Conf. Computer Vision (ICCV
, 2009
"... Abstract ..."
(Show Context)
Clustering with Multi-Layer Graphs: A Spectral Perspective
, 2011
"... Observational data usually comes with a multimodal nature, which means that it can be naturally represented by a multi-layer graph whose layers share the same set of vertices (users) with different edges (pairwise relationships). In this paper, we address the problem of combining different layers of ..."
Abstract
-
Cited by 8 (1 self)
- Add to MetaCart
Observational data usually comes with a multimodal nature, which means that it can be naturally represented by a multi-layer graph whose layers share the same set of vertices (users) with different edges (pairwise relationships). In this paper, we address the problem of combining different layers of the multi-layer graph for improved clustering of the vertices compared to using layers independently. We propose two novel methods, which are based on joint matrix factorization and graph regularization framework respectively, to efficiently combine the spectrum of the multiple graph layers, namely the eigenvectors of the graph Laplacian matrices. In each case, the resulting combination, which we call a “joint spectrum ” of multiple graphs, is used for clustering the vertices. We evaluate our approaches by simulations with several real world social network datasets. Results demonstrate the superior or competitive performance of the proposed methods over state-of-the-art technique and common baseline methods, such as co-regularization [1] and summation of information from individual graphs.
Fast Graph Laplacian Regularized Kernel Learning via Semidefinite–Quadratic–Linear Programming
"... Kernel learning is a powerful framework for nonlinear data modeling. Using the kernel trick, a number of problems have been formulated as semidefinite programs (SDPs). These include Maximum Variance Unfolding (MVU) (Weinberger et al., 2004) in nonlinear dimensionality reduction, and Pairwise Constra ..."
Abstract
-
Cited by 8 (1 self)
- Add to MetaCart
(Show Context)
Kernel learning is a powerful framework for nonlinear data modeling. Using the kernel trick, a number of problems have been formulated as semidefinite programs (SDPs). These include Maximum Variance Unfolding (MVU) (Weinberger et al., 2004) in nonlinear dimensionality reduction, and Pairwise Constraint Propagation (PCP) (Li et al., 2008) in constrained clustering. Although in theory SDPs can be efficiently solved, the high computational complexity incurred in numerically processing the huge linear matrix inequality constraints has rendered the SDP approach unscalable. In this paper, we show that a large class of kernel learning problems can be reformulated as semidefinite-quadratic-linear programs (SQLPs), which only contain a simple positive semidefinite constraint, a second-order cone constraint and a number of linear constraints. These constraints are much easier to process numerically, and the gain in speedup over previous approaches is at least of the order m 2.5, where m is the matrix dimension. Experimental results are also presented to show the superb computational efficiency of our approach. 1
Learning must-link constraints for video segmentation based on spectral clustering
- In GCPR
, 2014
"... Abstract. In recent years it has been shown that clustering and seg-mentation methods can greatly benefit from the integration of prior in-formation in terms of must-link constraints. Very recently the use of such constraints has been integrated in a rigorous manner also in graph-based methods such ..."
Abstract
-
Cited by 2 (1 self)
- Add to MetaCart
(Show Context)
Abstract. In recent years it has been shown that clustering and seg-mentation methods can greatly benefit from the integration of prior in-formation in terms of must-link constraints. Very recently the use of such constraints has been integrated in a rigorous manner also in graph-based methods such as normalized cut. On the other hand spectral cluster-ing as relaxation of the normalized cut has been shown to be among the best methods for video segmentation. In this paper we merge these two developments and propose to learn must-link constraints for video segmentation with spectral clustering. We show that the integration of learned must-link constraints not only improves the segmentation result but also significantly reduces the required runtime, making the use of costly spectral methods possible for today’s high quality video. 1
Constraints as Features
"... In this paper, we introduce a new approach to constrained clustering which treats the constraints as features. Our method augments the original feature space with additional dimensions, each of which derived from a given Cannot-link constraints. The specified Cannot-link pair gets extreme coordinate ..."
Abstract
-
Cited by 1 (0 self)
- Add to MetaCart
(Show Context)
In this paper, we introduce a new approach to constrained clustering which treats the constraints as features. Our method augments the original feature space with additional dimensions, each of which derived from a given Cannot-link constraints. The specified Cannot-link pair gets extreme coordinates values, and the rest of the points get coordinate values that express their spatial influence from the specified constrained pair. After augmenting all the new features, a standard unconstrained clustering algorithm can be performed, like k-means or spectral clustering. We demonstrate the efficacy of our method for active semi-supervised learning applied to image segmentation and compare it to alternative methods. We also evaluate the performance of our method on the four most commonly evaluated datasets from the UCI machine learning repository. 1.
Scalable Constrained Clustering: A Generalized Spectral Method
"... We present a principled spectral approach to the well-studied constrained clustering problem. It reduces clustering to a generalized eigenvalue problem on Laplacians. The method works in nearly-linear time and provides concrete guaran-tees for the quality of the clusters, at least for the case of 2- ..."
Abstract
-
Cited by 1 (1 self)
- Add to MetaCart
We present a principled spectral approach to the well-studied constrained clustering problem. It reduces clustering to a generalized eigenvalue problem on Laplacians. The method works in nearly-linear time and provides concrete guaran-tees for the quality of the clusters, at least for the case of 2-way partitioning. In practice this translates to a very fast implementation that consistently outperforms existing spec-tral approaches. We support this claim with experiments on various data sets: our approach recovers correct clusters in examples where previous methods fail, and handles data sets with millions of data points- two orders of magnitude larger than before. 1.
Activity Understanding and Unusual Event Detection in Surveillance Videos
, 2010
"... Computer scientists have made ceaseless efforts to replicate cognitive video understanding abilities of human brains onto autonomous vision systems. As video surveillance cameras become ubiquitous, there is a surge in studies on automated activity understanding and unusual event detection in surveil ..."
Abstract
-
Cited by 1 (0 self)
- Add to MetaCart
Computer scientists have made ceaseless efforts to replicate cognitive video understanding abilities of human brains onto autonomous vision systems. As video surveillance cameras become ubiquitous, there is a surge in studies on automated activity understanding and unusual event detection in surveillance videos. Nevertheless, video content analysis in public scenes remained a formidable challenge due to intrinsic difficulties such as severe inter-object occlusion in crowded scene and poor quality of recorded surveillance footage. Moreover, it is nontrivial to achieve robust detection of unusual events, which are rare, ambiguous, and easily confused with noise. This thesis proposes solutions for resolving ambiguous visual observations and overcoming unreliability of conventional activity analysis methods by exploiting multi-camera visual context and human feedback. The thesis first demonstrates the importance of learning visual context for establishing reliable reasoning on observed activity in a camera network. In the proposed approach, a new Cross Canonical Correlation Analysis (xCCA) is formulated to discover and quantify time delayed pairwise correlations of regional activities observed within and across multiple camera views. This
