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Face recognition remains a hot topic in computer vision, and it is challenging to tackle the problem that both the training and testing images are corrupted. In this paper, we propose a novel semi-supervised method based on the theory of the low-rank matrix recovery for face recognition, which can simultaneously learn discriminative low-rank and sparse representations for both training and testing images. To this end, a correlation penalty term is introduced into the formulation of our proposed method to learn an incoherent dictionary. Experimental results on several face image databases demonstrate the effectiveness of our method, i.e., the proposed method is robust to the illumination, expression and pose variations, as well as images with noises such as block occlusion or uniform noises., Comment: 27 pages, 7 figures

This paper studies a coordinate alignment problem for cooperative mobile sensor network localization with range-based measurements. The network consists of target nodes, each of which has only access position information in a local fixed coordinate frame, and anchor nodes with GPS position information. To localize target nodes, we aim to align their coordinate frames, which leads to a non-convex optimization problem over a rotation group $\text{SO}(3)$. Then, we reformulate it as an optimization problem with a convex objective function over spherical surfaces. We explicitly design both iterative and recursive algorithms for localizing a target node with an anchor node, and extend to the case with multiple target nodes. Finally, the advantages of our algorithms against the literature are validated via simulations.

This paper studies problems on locally stopping distributed consensus algorithms over networks where each node updates its state by interacting with its neighbors and decides by itself whether certain level of agreement has been achieved among nodes. Since an individual node is unable to access the states of those beyond its neighbors, this problem becomes challenging. In this work, we first define the stopping problem for generic distributed algorithms. Then, a distributed algorithm is explicitly provided for each node to stop consensus updating by exploring the relationship between the so-called local and global consensus. Finally, we show both in theory and simulation that its effectiveness depends both on the network size and the structure.

This paper is concerned with a constrained optimization problem over a directed graph (digraph) of nodes, in which the cost function is a sum of local objectives, and each node only knows its local objective and constraints. To collaboratively solve the optimization, most of the existing works require the interaction graph to be balanced or "doubly-stochastic", which is quite restrictive and not necessary as shown in this paper. We focus on an epigraph form of the original optimization to resolve the "unbalanced" problem, and design a novel two-step recursive algorithm with a simple structure. Under strongly connected digraphs, we prove that each node asymptotically converges to some common optimal solution. Finally, simulations are performed to illustrate the effectiveness of the proposed algorithms., Comment: arXiv admin note: substantial text overlap with arXiv:1612.09029

This paper considers a distributed convex optimization problem with inequality constraints over time-varying unbalanced digraphs, where the cost function is a sum of local objectives, and each node of the graph only knows its local objective and inequality constraints. Although there is a vast literature on distributed optimization, most of them require the graph to be balanced, which is quite restrictive and not necessary. Very recently, the unbalanced problem has been resolved only for either time-invariant graphs or unconstrained optimization. This work addresses the unbalancedness by focusing on an epigraph form of the constrained optimization. A striking feature is that this novel idea can be easily used to study time-varying unbalanced digraphs. Under local communications, a simple iterative algorithm is then designed for each node. We prove that if the graph is uniformly jointly strongly connected, each node asymptotically converges to some common optimal solution.

This paper proposes distributed algorithms to solve robust convex optimization (RCO) when the constraints are affected by nonlinear uncertainty. We adopt a scenario approach by randomly sampling the uncertainty set. To facilitate the computational task, instead of using a single centralized processor to obtain a "global solution" of the scenario problem (SP), we resort to {\it multiple interconnected processors} that are distributed among different nodes of a network to simultaneously solve the SP. Then, we propose a primal-dual sub-gradient algorithm and a random projection algorithm to distributedly solve the SP over undirected and directed graphs, respectively. Both algorithms are given in an explicit recursive form with simple iterations, which are especially suited for processors with limited computational capability. We show that, if the underlying graph is strongly connected, each node asymptotically computes a common optimal solution to the SP with a convergence rate $O(1/(\sum_{t=1}^k\zeta^t))$ where $\{\zeta^t\}$ is a sequence of appropriately decreasing stepsizes. That is, the RCO is effectively solved in a distributed way. The relations with the existing literature on robust convex programs are thoroughly discussed and an example of robust system identification is included to validate the effectiveness of our distributed algorithms., Comment: 15 pages, 4 figures

We revisit the study of a wrist-mounted camera system (referred to as HandCam) for recognizing activities of hands. HandCam has two unique properties as compared to egocentric systems (referred to as HeadCam): (1) it avoids the need to detect hands; (2) it more consistently observes the activities of hands. By taking advantage of these properties, we propose a deep-learning-based method to recognize hand states (free v.s. active hands, hand gestures, object categories), and discover object categories. Moreover, we propose a novel two-streams deep network to further take advantage of both HandCam and HeadCam. We have collected a new synchronized HandCam and HeadCam dataset with 20 videos captured in three scenes for hand states recognition. Experiments show that our HandCam system consistently outperforms a deep-learning-based HeadCam method (with estimated manipulation regions) and a dense-trajectory-based HeadCam method in all tasks. We also show that HandCam videos captured by different users can be easily aligned to improve free v.s. active recognition accuracy (3.3% improvement) in across-scenes use case. Moreover, we observe that finetuning Convolutional Neural Network consistently improves accuracy. Finally, our novel two-streams deep network combining HandCam and HeadCam features achieves the best performance in four out of five tasks. With more data, we believe a joint HandCam and HeadCam system can robustly log hand states in daily life.