Deep learning models have gained great success in many real-world applications. However, most existing networks are typically designed in heuristic manners, thus lack of rigorous mathematical principles and derivations. Several recent studies build deep structures by unrolling a particular optimization model that involves task information. Unfortunately, due to the dynamic nature of network parameters, their resultant deep propagation networks do not possess the nice convergence property as the original optimization scheme does. This paper provides a novel proximal unrolling framework to establish deep models by integrating experimentally verified network architectures and rich cues of the tasks. More importantly,we prove in theory that 1) the propagation generated by our unrolled deep model globally converges to a critical-point of a given variational energy, and 2) the proposed framework is still able to learn priors from training data to generate a convergent propagation even when task information is only partially available. Indeed, these theoretical results are the best we can ask for, unless stronger assumptions are enforced. Extensive experiments on various real-world applications verify the theoretical convergence and demonstrate the effectiveness of designed deep models.

Cascaded regression is prevailing in face alignment thanks to its accurate and robust localization of facial landmarks, but typically demands numerous annotated training examples of low discrepancy between shape-indexed features and shape updates. In this paper, we propose a self-reinforced strategy that iteratively expands the quantity and improves the quality of training examples, thus upgrading the performance of cascaded regression itself. The reinforced term evaluates the example quality upon the consistence on both local appearance and global geometry of human faces, and constitutes the example evolution by the philosophy of "survival of the fittest." We train a set of discriminative classifiers, each associated with one landmark label, to prune those examples with inconsistent local appearance, and further validate the geometric relationship among groups of labeled landmarks against the common global geometry derived from a projective invariant. We embed this generic strategy into two typical cascaded regressions, and the alignment results on several benchmark data sets demonstrate the effectiveness of training regressions with automatic example prediction and evolution starting from a small subset.

Locality preserving projection (LPP) is a well-known method for dimensionality reduction in which the neighborhood graph structure of data is preserved. Traditional LPP employ squared F-norm for distance measurement. This may exaggerate more distance errors, and result in a model being sensitive to outliers. In order to deal with this issue, we propose two novel F-norm-based models, termed as F-LPP and F-2DLPP, which are developed for vector-based and matrix-based data, respectively. In F-LPP and F-2DLPP, the distance of data projected to a low dimensional space is measured by F-norm. Thus it is anticipated that both methods can reduce the influence of outliers. To solve the F-norm-based models, we propose an iterative optimization algorithm, and give the convergence analysis of algorithm. The experimental results on three public databases have demonstrated the effectiveness of our proposed methods.

Considering the diversity of the views, assigning the multiviews with different weights is important to multi-view clustering. Several multi-view clustering algorithms have been proposed to assign different weights to the views. However, the existing weighting schemes do not simultaneously consider the characteristic of multi-view clustering and the characteristic of related single-view clustering. In this paper, based on the spectral perturbation theory of spectral clustering, we propose a weighted multi-view spectral clustering algorithm which employs the spectral perturbation to model the weights of the views. The proposed weighting scheme follows the two basic principles: 1) the clustering results on each view should be close to the consensus clustering result, and 2) views with similar clustering results should be assigned similar weights. According to spectral perturbation theory, the largest canonical angle is used to measure the difference between spectral clustering results. In this way, the weighting scheme can be formulated into a standard quadratic programming problem. Experimental results demonstrate the superiority of the proposed algorithm.

In recent years, skeleton based action recognition is becoming an increasingly attractive alternative to existing video-based approaches, beneficial from its robust and comprehensive 3D information. In this paper, we explore an unsupervised representation learning approach for the first time to capture the long-term global motion dynamics in skeleton sequences. We design a conditional skeleton inpainting architecture for learning a fixed-dimensional representation, guided by additional adversarial training strategies. We quantitatively evaluate the effectiveness of our learning approach on three well-established action recognition datasets. Experimental results show that our learned representation is discriminative for classifying actions and can substantially reduce the sequence inpainting errors.

Adverse drug-drug interactions (DDIs) remain a leading cause of morbidity and mortality around the world. Identifying potential DDIs during the drug design process is critical in guiding targeted clinical drug safety testing. Although detection of adverse DDIs is conducted during Phase IV clinical trials, there are still a large number of new DDIs founded by accidents after the drugs were put on market. With the arrival of big data era, more and more pharmaceutical research and development data are becoming available, which provides an invaluable resource for digging insights that can potentially be leveraged in early prediction of DDIs. Many computational approaches have been proposed in recent years for DDI prediction. However, most of them focused on binary prediction (with or without DDI), despite the fact that each DDI is associated with a different type. Predicting the actual DDI type will help us better understand the DDI mechanism and identify proper ways to prevent it. In this paper, we formulate the DDI type prediction problem as a multitask dyadic regression problem, where the prediction of each specific DDI type is treated as a task. Compared with conventional matrix completion approaches which can only impute the missing entries in the DDI matrix, our approach can directly regress those dyadic relationships (DDIs) and thus can be extend to new drugs more easily. We developed an effective proximal gradient method to solve the problem. Evaluation on real world datasets is presented to demonstrate the effectiveness of the proposed approach.

The explosion of streaming data poses challenges to feature learning methods including linear discriminant analysis (LDA). Many existing LDA algorithms are not efficient enough to incrementally update with samples that sequentially arrive in various manners. First, we propose a new fast batch LDA (FLDA/QR) learning algorithm that uses the cluster centers to solve a lower triangular system that is optimized by the Cholesky-factorization. To take advantage of the intrinsically incremental mechanism of the matrix, we further develop an exact incremental algorithm (IFLDA/QR). The Gram-Schmidt process with reorthogonalization in IFLDA/QR significantly saves the space and time expenses compared with the rank-one QR-updating of most existing methods. IFLDA/QR is able to handle streaming data containing 1) new labeled samples in the existing classes, 2) samples of an entirely new (novel) class, and more significantly, 3) a chunk of examples mixed with those in 1) and 2). Both theoretical analysis and numerical experiments have demonstrated much lower space and time costs (2~10 times faster) than the state of the art, with comparable classification accuracy.

Being one of the most effective methods, Alternating Direction Method (ADM) has been extensively studied in numerical analysis for solving linearly constrained convex program. However, there are few studies focusing on the convergence property of ADM under nonconvex framework though it has already achieved well-performance on applying to various nonconvex tasks. In this paper, a linearized algorithm with penalization is proposed on the basis of ADM for solving nonconvex and nonsmooth optimization. We start from analyzing the convergence property for the classical constrained problem with two variables and then establish a similar result for multi-block case. To demonstrate the effectiveness of our proposed algorithm, experiments with synthetic and real-world data have been conducted on specific applications in signal and image processing.

It is a challenging problem to cluster multi- and high-dimensional data with complex intrinsic properties and non-linear manifold structure. The recently proposed subspace clustering method, Low Rank Representation (LRR), shows attractive performance on data clustering, but it generally does with data in Euclidean spaces. In this paper, we intend to cluster complex high dimensional data with multiple varying factors. We propose a novel representation, namely Product Grassmann Manifold (PGM), to represent these data. Additionally, we discuss the geometry metric of the manifold and expand the conventional LRR model in Euclidean space onto PGM and thus construct a new LRR model. Several clustering experimental results show that the proposed method obtains superior accuracy compared with the clustering methods on manifolds or conventional Euclidean spaces.

Multi-task clustering and multi-view clustering have severally found wide applications and received much attention in recent years. Nevertheless, there are many clustering problems that involve both multi-task clustering and multi-view clustering, i.e., the tasks are closely related and each task can be analyzed from multiple views. In this paper, for non-negative data (e.g., documents), we introduce a multi-task multi-view clustering (MTMVC) framework which integrates within-view-task clustering, multi-view relationship learning and multi-task relationship learning. We then propose a specific algorithm to optimize the MTMVC framework. Experimental results show the superiority of the proposed algorithm over either multi-task clustering algorithms or multi-view clustering algorithms for multi-task clustering of multi-view data.