The Concave-Convex Procedure

Yuille, Alan; Rangarajan, Anand

doi:10.1162/08997660360581958

Cited by 1,140 publications

(912 citation statements)

References 26 publications

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“…The presence of hidden variables h in (12) make the overall optimization problem non-convex. The problem in (12) can be expressed as a difference of two convex terms f (w) and g(w), and thus can be solved using the CCCP algorithm [26]. Our learning iterates two steps: (i) Given w, eachŷ (l) , h (l) , and h * (l) can be efficiently estimated using our bottom-up/top-down inference explained in Sec.…”

Section: Max-margin Learningmentioning

confidence: 99%

HiRF: Hierarchical Random Field for Collective Activity Recognition in Videos

Amer

Peng

Todorovic

2014

Lecture Notes in Computer Science

107

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Abstract. This paper addresses the problem of recognizing and localizing coherent activities of a group of people, called collective activities, in video. Related work has argued the benefits of capturing long-range and higher-order dependencies among video features for robust recognition. To this end, we formulate a new deep model, called Hierarchical Random Field (HiRF). HiRF models only hierarchical dependencies between model variables. This effectively amounts to modeling higher-order temporal dependencies of video features. We specify an efficient inference of HiRF that iterates in each step linear programming for estimating latent variables. Learning of HiRF parameters is specified within the max-margin framework. Our evaluation on the benchmark New Collective Activity and Collective Activity datasets, demonstrates that HiRF yields superior recognition and localization as compared to the state of the art.

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Section: Max-margin Learningmentioning

confidence: 99%

HiRF: Hierarchical Random Field for Collective Activity Recognition in Videos

Amer

Peng

Todorovic

2014

Lecture Notes in Computer Science

107

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“…In that case, (7) implies (9). If on the other hand (7) is false, all y ∈ N H ℓ (x) are not labeled ℓ + 1.…”

Section: Sub-and Supermodularity Of the General Priormentioning

confidence: 99%

“…We will show that this problem can be approximated efficiently using the submodular-supermodular procedure [8]. This technique was inspired by the concave-convex procedure for continuous functions [9]. Our algorithm changes the underlying graph in a way different from earlier submodular-supermodular techniques [10,11].…”

Section: Introductionmentioning

confidence: 99%

Hausdorff Distance Constraint for Multi-surface Segmentation

Schmidt

Boykov

2012

Computer Vision – ECCV 2012

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Abstract. It is well known that multi-surface segmentation can be cast as a multi-labeling problem. Different segments may belong to the same semantic object which may impose various inter-segment constraints [1]. In medical applications, there are a lot of scenarios where upper bounds on the Hausdorff distances between subsequent surfaces are known. We show that incorporating these priors into multi-surface segmentation is potentially NP-hard. To cope with this problem we develop a submodularsupermodular procedure that converges to a locally optimal solution well-approximating the problem. While we cannot guarantee global optimality, only feasible solutions are considered during the optimization process. Empirically, we get useful solutions for many challenging medical applications including MRI and ultrasound images.

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“…A recent local search approach for the linear case is given by Wang et al [146,156]. It is based on applying the so-called constrained concave-convex procedure [133,152], which is an iterative optimization strategy yielding a local optimum for a non-convex optimization problem [134,152]. Wang et al [146] apply this iterative scheme by deriving appropriate quadratic programming problems (with many constraints) to be solved per iteration.…”

Section: Unsupervised Support Vector Machinesmentioning

confidence: 99%

From Supervised to Unsupervised Support Vector Machines and Applications in Astronomy

Gieseke

2013

Künstl Intell

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A common task in the field of machine learning is the classification of objects. The basis for such a task is usually a training set consisting of patterns and associated class labels. A typical example is, for instance, the automatic classification of stars and galaxies in the field of astronomy. Here, the training set could consist of images and associated labels, which indicate whether a particular image shows a star or a galaxy. For such a learning scenario, one aims at generating models that can automatically classify new, unseen images. In the field of machine learning, various classification schemes have been proposed. One of the most popular ones is the concept of support vector machines, which often yields excellent classification results given sufficient labeled data.However, for a variety of real-world tasks, the acquisition of sufficient labeled data can be quite time-consuming. In contrast to labeled training data, unlabeled one can often be obtained easily in huge quantities. Semi-and unsupervised techniques aim at taking these unlabeled patterns into account to generate appropriate models. In the literature, various ways of extending support vector machines to these scenarios have been proposed. One of these ways leads to combinatorial optimization tasks that are difficult to address.In this thesis, several optimization strategies will be developed for these tasks that (1) aim at solving them exactly or (2) aim at obtaining (possibly suboptimal) candidate solutions in an efficient kind of way. More specifically, we will derive a polynomial-time approach that can compute exact solutions for special cases of both tasks. This approach is among the first ones that provide upper runtime bounds for the tasks at hand and, thus, yield theoretical insights into their computational complexity. In addition to this exact scheme, two heuristics tackling both problems will be provided. The first one is based on least-squares variants of the original tasks whereas the second one relies on differentiable surrogates for the corresponding objective functions. While direct implementations of both heuristics are still computationally expensive, we will show how to make use of matrix operations to speed up their execution. This will result in two optimization schemes that exhibit an excellent classification and runtime performance.Despite these theoretical derivations, we will also depict possible application domains of machine learning methods in astronomy. Here, the massive amount of data given for today's and future projects renders a manual analysis impossible and necessitates the use of sophisticated techniques. In this context, we will derive an efficient way to preprocess spectroscopic data, which is based on an adaptation of support vector machines, and the benefits of semi-supervised learning schemes for appropriate learning tasks will be sketched. As a further contribution to this field, we will propose the use of so-called resilient algorithms for the automatic data analysis taking place aboard toda...

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The Concave-Convex Procedure

Cited by 1,140 publications

References 26 publications

HiRF: Hierarchical Random Field for Collective Activity Recognition in Videos

HiRF: Hierarchical Random Field for Collective Activity Recognition in Videos

Hausdorff Distance Constraint for Multi-surface Segmentation

From Supervised to Unsupervised Support Vector Machines and Applications in Astronomy

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