Point-wise mutual information-based video segmentation with high temporal consistency

In this paper, we tackle the problem of temporally consistent boundary detection and hierarchical segmentation in videos. While finding the best high-level reasoning of region assignments in videos is the focus of much recent research, temporal consistency in boundary detection has so far only rarely been tackled. We argue that temporally consistent boundaries are a key component to temporally consistent region assignment. The proposed method is based on the point-wise mutual information (PMI) of spatio-temporal voxels. Temporal consistency is established by an evaluation of PMI-based point affinities in the spectral domain over space and time. Thus, the proposed method is independent of any optical flow computation or previously learned motion models. The proposed low-level video segmentation method outperforms the learning-based state of the art in terms of standard region metrics

Efficient Semidefinite Spectral Clustering via Lagrange Duality

We propose an efficient approach to semidefinite spectral clustering (SSC), which addresses the Frobenius normalization 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.Comment: 13 page

Clustering and Community Detection in Directed Networks: A Survey

Networks (or graphs) appear as dominant structures in diverse domains, including sociology, biology, neuroscience and computer science. In most of the aforementioned cases graphs are directed - in the sense that there is directionality on the edges, making the semantics of the edges non symmetric. An interesting feature that real networks present is the clustering or community structure property, under which the graph topology is organized into modules commonly called communities or clusters. The essence here is that nodes of the same community are highly similar while on the contrary, nodes across communities present low similarity. Revealing the underlying community structure of directed complex networks has become a crucial and interdisciplinary topic with a plethora of applications. Therefore, naturally there is a recent wealth of research production in the area of mining directed graphs - with clustering being the primary method and tool for community detection and evaluation. The goal of this paper is to offer an in-depth review of the methods presented so far for clustering directed networks along with the relevant necessary methodological background and also related applications. The survey commences by offering a concise review of the fundamental concepts and methodological base on which graph clustering algorithms capitalize on. Then we present the relevant work along two orthogonal classifications. The first one is mostly concerned with the methodological principles of the clustering algorithms, while the second one approaches the methods from the viewpoint regarding the properties of a good cluster in a directed network. Further, we present methods and metrics for evaluating graph clustering results, demonstrate interesting application domains and provide promising future research directions.Comment: 86 pages, 17 figures. Physics Reports Journal (To Appear

Large-scale 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 large-scale 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, quasi-Newton and smoothing Newton methods, for the dual problem. Both of them are significantly more efficiently than standard interior-point methods. In practice, the smoothing Newton solver is faster than the quasi-Newton solver for dense or medium-sized problems, while the quasi-Newton solver is preferable for large sparse/structured problems. Our experiments on a few computer vision applications including clustering, image segmentation, co-segmentation and registration show the potential of our SDP formulation for solving large-scale BQPs.Comment: Fixed some typos. 18 pages. Accepted to IEEE Transactions on Pattern Analysis and Machine Intelligenc