Abstract-This paper revisits the integer programming (IP) problem, which plays a fundamental role in many computer vision and machine learning applications. The literature abounds with many seminal works that address this problem, some focusing on continuous approaches (e.g., linear program relaxation), while others on discrete ones (e.g., min-cut). However, since many of these methods are designed to solve specific IP forms, they cannot adequately satisfy the simultaneous requirements of accuracy, feasibility, and scalability. To this end, we propose a novel and versatile framework called p-box ADMM, which is based on two main ideas. (1) The discrete constraint is equivalently replaced by the intersection of a box and an p-norm sphere.(2) We infuse this equivalence into the ADMM (Alternating Direction Method of Multipliers) framework to handle the continuous constraints separately and to harness its attractive properties. More importantly, the ADMM update steps can lead to manageable sub-problems in the continuous domain. To demonstrate its efficacy, we apply it to an optimization form that occurs often in computer vision and machine learning, namely binary quadratic programming (BQP). In this case, the ADMM steps are simple, computationally efficient. Moreover, we present the theoretic analysis about the global convergence of the p-box ADMM through adding a perturbation with the sufficiently small factor to the original IP problem. Specifically, the globally converged solution generated by p-box ADMM for the perturbed IP problem will be close to the stationary and feasible point of the original IP problem within O( ). We demonstrate the applicability of p-box ADMM on three important applications: MRF energy minimization, graph matching, and clustering. Results clearly show that it significantly outperforms existing generic IP solvers both in runtime and objective. It also achieves very competitive performance to state-of-the-art methods designed specifically for these applications.
This work focuses on the problem of multi-label learning with missing labels (MLML), which aims to label each test instance with multiple class labels given training instances that have an incomplete/partial set of these labels (i.e. some of their labels are missing). The key point to handle missing labels is propagating the label information from the provided labels to missing labels, through a dependency graph that each label of each instance is treated as a node. We build this graph by utilizing different types of label dependencies. Specifically, the instance-level similarity is served as undirected edges to connect the label nodes across different instances and the semantic label hierarchy is used as directed edges to connect different classes. This base graph is referred to as the mixed dependency graph, as it includes both undirected and directed edges. Furthermore, we present another two types of label dependencies to connect the label nodes across different classes. One is the class co-occurrence, which is also encoded as undirected edges. Combining with the above base graph, we obtain a new mixed graph, called MG-CO (mixed graph with cooccurrence). The other is the sparse and low rank decom-position of the whole label matrix, to embed high-order dependencies over all labels. Combining with the base graph, the new mixed graph is called as MG-SL (mixed graph with sparse and low rank decomposition). Based on MG-CO and MG-SL, we further propose two convex transductive formulations of the MLML problem, denoted as MLMG-CO and MLMG-SL respectively. In both formulations, the instancelevel similarity is embedded through a quadratic smoothness term, while the semantic label hierarchy is used as a linear constraint. In MLMG-CO, the class co-occurrence is also formulated as a quadratic smoothness term, while the sparse and low rank decomposition is incorporated into MLMG-SL, through two additional matrices (one is assumed as sparse, and the other is assumed as low rank) and an equivalence constraint between the summation of this two matrices and the original label matrix. Interestingly, two important applications, including image annotation and tag based image retrieval, can be jointly handled using our proposed methods. Experimental results on several benchmark datasets show that our methods lead to significant improvements in performance and robustness to missing labels over the state-ofthe-art methods.
Face clustering and face tracking are two areas of active research in automatic facial video processing. They, however, have long been studied separately, despite the inherent link between them. In this paper, we propose to perform simultaneous face clustering and face tracking from real world videos. The motivation for the proposed research is that face clustering and face tracking can provide useful information and constraints to each other, thus can bootstrap and improve the performances of each other. To this end, we introduce a Coupled Hidden Markov Random Field (CHMRF) to simultaneously model face clustering, face tracking, and their interactions. We provide an effective algorithm based on constrained clustering and optimal tracking for the joint optimization of cluster labels and face tracking. We demonstrate significant improvements over state-of-the-art results in face clustering and tracking on several videos.
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