Linearized Alternating Direction Method with Parallel Splitting and Adaptive Penalty for Separable Convex Programs in Machine Learning

Many problems in machine learning and other fields can be (re)for-mulated as linearly constrained separable convex programs. In most of the cases, there are multiple blocks of variables. However, the traditional alternating direction method (ADM) and its linearized version (LADM, obtained by linearizing the quadratic penalty term) are for the two-block case and cannot be naively generalized to solve the multi-block case. So there is great demand on extending the ADM based methods for the multi-block case. In this paper, we propose LADM with parallel splitting and adaptive penalty (LADMPSAP) to solve multi-block separable convex programs efficiently. When all the component objective functions have bounded subgradients, we obtain convergence results that are stronger than those of ADM and LADM, e.g., allowing the penalty parameter to be unbounded and proving the sufficient and necessary conditions} for global convergence. We further propose a simple optimality measure and reveal the convergence rate of LADMPSAP in an ergodic sense. For programs with extra convex set constraints, with refined parameter estimation we devise a practical version of LADMPSAP for faster convergence. Finally, we generalize LADMPSAP to handle programs with more difficult objective functions by linearizing part of the objective function as well. LADMPSAP is particularly suitable for sparse representation and low-rank recovery problems because its subproblems have closed form solutions and the sparsity and low-rankness of the iterates can be preserved during the iteration. It is also highly parallelizable and hence fits for parallel or distributed computing. Numerical experiments testify to the advantages of LADMPSAP in speed and numerical accuracy.Comment: Preliminary version published on Asian Conference on Machine Learning 201

Linearized Alternating Direction Method with Adaptive Penalty for Low-Rank Representation

Low-rank representation (LRR) is an effective method for subspace clustering and has found wide applications in computer vision and machine learning. The existing LRR solver is based on the alternating direction method (ADM). It suffers from $O(n^3)$ computation complexity due to the matrix-matrix multiplications and matrix inversions, even if partial SVD is used. Moreover, introducing auxiliary variables also slows down the convergence. Such a heavy computation load prevents LRR from large scale applications. In this paper, we generalize ADM by linearizing the quadratic penalty term and allowing the penalty to change adaptively. We also propose a novel rule to update the penalty such that the convergence is fast. With our linearized ADM with adaptive penalty (LADMAP) method, it is unnecessary to introduce auxiliary variables and invert matrices. The matrix-matrix multiplications are further alleviated by using the skinny SVD representation technique. As a result, we arrive at an algorithm for LRR with complexity $O(rn^2)$, where $r$ is the rank of the representation matrix. Numerical experiments verify that for LRR our LADMAP method is much faster than state-of-the-art algorithms. Although we only present the results on LRR, LADMAP actually can be applied to solving more general convex programs.Comment: Manuscript accepted by NIPS 201

Learning Optimization-inspired Image Propagation with Control Mechanisms and Architecture Augmentations for Low-level Vision

In recent years, building deep learning models from optimization perspectives has becoming a promising direction for solving low-level vision problems. The main idea of most existing approaches is to straightforwardly combine numerical iterations with manually designed network architectures to generate image propagations for specific kinds of optimization models. However, these heuristic learning models often lack mechanisms to control the propagation and rely on architecture engineering heavily. To mitigate the above issues, this paper proposes a unified optimization-inspired deep image propagation framework to aggregate Generative, Discriminative and Corrective (GDC for short) principles for a variety of low-level vision tasks. Specifically, we first formulate low-level vision tasks using a generic optimization objective and construct our fundamental propagative modules from three different viewpoints, i.e., the solution could be obtained/learned 1) in generative manner; 2) based on discriminative metric, and 3) with domain knowledge correction. By designing control mechanisms to guide image propagations, we then obtain convergence guarantees of GDC for both fully- and partially-defined optimization formulations. Furthermore, we introduce two architecture augmentation strategies (i.e., normalization and automatic search) to respectively enhance the propagation stability and task/data-adaption ability. Extensive experiments on different low-level vision applications demonstrate the effectiveness and flexibility of GDC.Comment: 15 page

CoCoNet: Coupled Contrastive Learning Network with Multi-level Feature Ensemble for Multi-modality Image Fusion

Infrared and visible image fusion targets to provide an informative image by combining complementary information from different sensors. Existing learning-based fusion approaches attempt to construct various loss functions to preserve complementary features from both modalities, while neglecting to discover the inter-relationship between the two modalities, leading to redundant or even invalid information on the fusion results. To alleviate these issues, we propose a coupled contrastive learning network, dubbed CoCoNet, to realize infrared and visible image fusion in an end-to-end manner. Concretely, to simultaneously retain typical features from both modalities and remove unwanted information emerging on the fused result, we develop a coupled contrastive constraint in our loss function.In a fused imge, its foreground target/background detail part is pulled close to the infrared/visible source and pushed far away from the visible/infrared source in the representation space. We further exploit image characteristics to provide data-sensitive weights, which allows our loss function to build a more reliable relationship with source images. Furthermore, to learn rich hierarchical feature representation and comprehensively transfer features in the fusion process, a multi-level attention module is established. In addition, we also apply the proposed CoCoNet on medical image fusion of different types, e.g., magnetic resonance image and positron emission tomography image, magnetic resonance image and single photon emission computed tomography image. Extensive experiments demonstrate that our method achieves the state-of-the-art (SOTA) performance under both subjective and objective evaluation, especially in preserving prominent targets and recovering vital textural details.Comment: 25 pages, 16 figure

Key technologies for extraction and identification of gas target area for pressure relief in inclined thick coal seam

In order to study the dip angle effect on the evolution law of the target area for pressure relief gas drainage in inclined thick coal seams, the physical similarity simulation test and theoretical analysis were combined to study the fracture evolution in the target area under different coal seam dip angles. The evolution law of broken fracture’s width, the area proportion of bed-separated fracture, and the fractal dimension of fracture with the change of coal seam dip angle in the target area were obtained, and then the coal seam dip angle effect model of the targeted area evolution was established. The results showed that the broken fracture’s width presented the distribution characteristics that the boundary area on both sides of the goaf was greater than that in the middle, and the low horizon was greater than that in the higher horizon. What’s more, the broken fracture’s width was strongly affected by the hinged beam. With the increase of the coal seam dip angle (0° < 15° < 30°), the broken fracture’s width in the upper region of the first layer of hinged beam is significantly reduced compared with that in the lower region, which is only 52.8%, 64.3%, and 71.1%, respectively. The area proportion of bed-separated fracture in the dominant gas migration channel zone was the largest at the bottom, followed by the top, and the smallest in the middle. The fractal dimension of overlying fractures decreased first and then increased as a whole. The fracture evolution laws were obviously different on both sides of the layer where the hinged beam of the first layer and the minimum fractal dimension of the fracture were located. Therefore, the dominant channel belt of gas migration was divided into low-layer target areas, middle-layer target areas, and high-layer target areas according to the level of the spatial horizon. Finally, based on the theory of mining fracture ellipse belts and the dominant gas migration channel zone at the working face side, the mathematical equation of the target area in inclined thick coal seams was established considering the coal seam dip angle, and the basis for selection of pressure relief gas drainage methods in the targeted area was formed. It provided a reference for optimizing the parameters of pressure relief gas drainage in an inclined, thick coal seam working face