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Diffrac: a discriminative and flexible framework for clustering
 In Advances in Neural Information Processing Systems 20
, 2007
"... We present a novel linear clustering framework (DIFFRAC) which relies on a linear discriminative cost function and a convex relaxation of a combinatorial optimization problem. The large convex optimization problem is solved through a sequence of lower dimensional singular value decompositions. Thi ..."
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Cited by 54 (11 self)
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We present a novel linear clustering framework (DIFFRAC) which relies on a linear discriminative cost function and a convex relaxation of a combinatorial optimization problem. The large convex optimization problem is solved through a sequence of lower dimensional singular value decompositions. This framework has several attractive properties: (1) although apparently similar to Kmeans, it exhibits superior clustering performance than Kmeans, in particular in terms of robustness to noise. (2) It can be readily extended to non linear clustering if the discriminative cost function is based on positive definite kernels, and can then be seen as an alternative to spectral clustering. (3) Prior information on the partition is easily incorporated, leading to stateoftheart performance for semisupervised learning, for clustering or classification. We present empirical evaluations of our algorithms on synthetic and real mediumscale datasets. 1
A fast semidefinite approach to solving binary quadratic problems
 In CVPR ’13
, 2013
"... Many computer vision problems can be formulated as binary quadratic programs (BQPs). Two classic relaxation methods are widely used for solving BQPs, namely, spectral methods and semidefinite programming (SDP), each with their own advantages and disadvantages. Spectral relaxation is simple and easy ..."
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Cited by 3 (1 self)
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Many computer vision problems can be formulated as binary quadratic programs (BQPs). Two classic relaxation methods are widely used for solving BQPs, namely, spectral methods and semidefinite programming (SDP), each with their own advantages and disadvantages. Spectral relaxation is simple and easy to implement, but its bound is loose. Semidefinite relaxation has a tighter bound, but its computational complexity is high for large scale problems. We present a new SDP formulation for BQPs, with two desirable properties. First, it has a similar relaxation bound to conventional SDP formulations. Second, compared with conventional SDP methods, the new SDP formulation leads to a significantly more efficient and scalable dual optimization approach, which has the same degree of complexity as spectral methods. Extensive experiments on various applications including clustering, image segmentation, cosegmentation and registration demonstrate the usefulness of our SDP formulation for solving largescale BQPs. 1.
Weakly supervised learning of image partitioning using decision trees with structured split criteria∗
"... We propose a scheme that allows to partition an image into a previously unknown number of segments, using only minimal supervision in terms of a few mustlink and cannotlink annotations. We make no use of regional data terms, learning instead what constitutes a likely boundary between segments. Si ..."
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We propose a scheme that allows to partition an image into a previously unknown number of segments, using only minimal supervision in terms of a few mustlink and cannotlink annotations. We make no use of regional data terms, learning instead what constitutes a likely boundary between segments. Since boundaries are only implicitly specified through cannotlink constraints, this is a hard and nonconvex latent variable problem. We address this problem in a greedy fashion using a randomized decision tree on features associated with interpixel edges. We use a structured purity criterion during tree construction and also show how a backtracking strategy can be used to prevent the greedy search from ending up in poor local optima. The proposed strategy is compared with prior art on natural images. 1
Targeted image segmentation using graph methods
, 2012
"... Traditional image segmentation is the process of subdividing an image into smaller regions based on some notion of homogeneity or cohesiveness among groups of pixels. Several prominent traditional segmentation algorithms have been based on graph theoretic methods [1, 2, 3, 4, 5, 6]. However, these m ..."
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Traditional image segmentation is the process of subdividing an image into smaller regions based on some notion of homogeneity or cohesiveness among groups of pixels. Several prominent traditional segmentation algorithms have been based on graph theoretic methods [1, 2, 3, 4, 5, 6]. However, these methods have been notoriously difficult to quantitatively evaluate since there is no formal definition of the segmentation problem (see [7, 8] for some approaches to evaluating traditional segmentation algorithms). In contrast to the traditional image segmentation scenario, many realworld applications of image segmentation instead focus on identifying those pixels belonging to a specific object or objects (which we will call targeted segmentation) for which there are some known characteristics. In this chapter, we focus only on the extraction of a single object (i.e., labeling each pixel as object or background). The segmentation of a specific object from the background is not just a special case of the traditional image segmentation problem which is restricted to two labels. Instead, a targeted image segmentation algorithm must input the additional information that determines which object is being segmented. This additional information, which we will call target specification, can take many forms: user interaction, appearance models, pairwise pixel affinity models, contrast polarity, shape models, topology specification, relational information and/or feature2 Image Processing and Analysing Graphs: Theory and Practice inclusion. The ideal targeted image segmentation algorithm could input any or all of the target specification
MANUSCRIPT 1 Largescale Binary Quadratic Optimization Using Semidefinite Relaxation and Applications
"... In computer vision, many problems such as image segmentation, pixel labelling, and scene parsing can be formulated as binary quadratic programs (BQPs). For submodular problems, cuts based methods can be employed to efficiently solve largescale problems. However, general nonsubmodular problems are s ..."
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In computer vision, many problems such as image segmentation, pixel labelling, and scene parsing can be formulated as binary quadratic programs (BQPs). For submodular problems, cuts based methods can be employed to efficiently solve largescale problems. However, general nonsubmodular problems are significantly more challenging to solve. Finding a solution when the problem is of large size to be of practical interest, however, typically requires relaxation. Two standard relaxation methods are widely used for solving general BQPs—spectral methods and semidefinite programming (SDP), each with their own advantages and disadvantages. Spectral relaxation is simple and easy to implement, but its bound is loose. Semidefinite relaxation has a tighter bound, but its computational complexity is high, especially for large scale problems. In this work, we present a new SDP formulation for BQPs, with two desirable properties. First, it has a similar relaxation bound to conventional SDP formulations. Second, compared with conventional SDP methods, the new SDP formulation leads to a significantly more efficient and scalable dual optimization approach, which has the same degree of complexity as spectral methods. We then propose two solvers, namely, quasiNewton and smoothing Newton methods, for the dual problem. Both of them are significantly more efficiently than standard interiorpoint methods. In practice, the smoothing Newton solver is faster than the quasiNewton solver for dense or mediumsized problems, while the quasiNewton solver is preferable for large sparse/structured problems. Our experiments on a few computer vision applications including clustering, image segmentation, cosegmentation and registration show the potential of our SDP formulation for solving largescale BQPs. I.