In this paper, we consider a class of sparse group $ell_0$ regularized optimization problems. Firstly, we give a continuous relaxation model of the considered problem and establish the equivalence of these two problems in the sense of global minimize
rs. Then, we define a class of stationary points of the relaxation problem, and prove that any defined stationary point is a local minimizer of the considered sparse group $ell_0$ regularized problem and satisfies a desirable property of its global minimizers. Further, based on the difference-of-convex (DC) structure of the relaxation problem, we design two DC algorithms to solve the relaxation problem. We prove that any accumulation point of the iterates generated by them is a stationary point of the relaxation problem. In particular, all accumulation points have a common support set and a unified lower bound for the nonzero entries, and their zero entries can be attained within finite iterations. Moreover, we prove the convergence of the entire iterates generated by the proposed algorithms. Finally, we give some numerical experiments to show the efficiency of the proposed algorithms.
We investigate a class of constrained sparse regression problem with cardinality penalty, where the feasible set is defined by box constraint, and the loss function is convex, but not necessarily smooth. First, we put forward a smoothing fast iterati
ve hard thresholding (SFIHT) algorithm for solving such optimization problems, which combines smoothing approximations, extrapolation techniques and iterative hard thresholding methods. The extrapolation coefficients can be chosen to satisfy $sup_k beta_k=1$ in the proposed algorithm. We discuss the convergence behavior of the algorithm with different extrapolation coefficients, and give sufficient conditions to ensure that any accumulation point of the iterates is a local minimizer of the original cardinality penalized problem. In particular, for a class of fixed extrapolation coefficients, we discuss several different update rules of the smoothing parameter and obtain the convergence rate of $O(ln k/k)$ on the loss and objective function values. Second, we consider the case in which the loss function is Lipschitz continuously differentiable, and develop a fast iterative hard thresholding (FIHT) algorithm to solve it. We prove that the iterates of FIHT converge to a local minimizer of the problem that satisfies a desirable lower bound property. Moreover, we show that the convergence rate of loss and objective function values are $o(k^{-2})$. Finally, some numerical examples are presented to illustrate the theoretical results.
High purity iron is obtained from vanadium-titanium magnetite (VTM) by one-step coal-based direct reduction-smelting process with coal as reductant and sodium carbonate (Na2CO3) as additives. Industrial experiments show that the process of treating m
olten iron with a large amount of Na2CO3 is effective in removing titanium from molten iron. However, the studies are rarely conducted in thermodynamic relationship between titanium and other components of molten iron, under the condition of a large amount of Na2CO3 additives. In this study, through the thermodynamic database software Factsage8.0, the effects of melting temperature, sodium content and oxygen content on the removal of titanium from molten iron are studied. The results of thermodynamic calculation show that the removal of titanium from molten iron needs to be under the condition of oxidation, and the temperature should be below the critical temperature of titanium removal (the highest temperature at which titanium can be removed). Relatively low temperature and high oxygen content contribute to the removal of titanium from molten iron. The high oxygen content is conducive to the simultaneous removal of titanium and phosphorus from molten iron. In addition, from a thermodynamic point of view, excessive sodium addition inhibits the removal of titanium from molten iron.
Recent learning-based approaches show promising performance improvement for scene text removal task. However, these methods usually leave some remnants of text and obtain visually unpleasant results. In this work, we propose a novel end-to-end framew
ork based on accurate text stroke detection. Specifically, we decouple the text removal problem into text stroke detection and stroke removal. We design a text stroke detection network and a text removal generation network to solve these two sub-problems separately. Then, we combine these two networks as a processing unit, and cascade this unit to obtain the final model for text removal. Experimental results demonstrate that the proposed method significantly outperforms the state-of-the-art approaches for locating and erasing scene text. Since current publicly available datasets are all synthetic and cannot properly measure the performance of different methods, we therefore construct a new real-world dataset, which will be released to facilitate the relevant research.
Community is a common characteristic of networks including social networks, biological networks, computer and information networks, to name a few. Community detection is a basic step for exploring and analysing these network data. Typically, homogeno
us network is a type of networks which consists of only one type of objects with one type of links connecting them. There has been a large body of developments in models and algorithms to detect communities over it. However, real-world networks naturally exhibit heterogeneous qualities appearing as multiple types of objects with multi-relational links connecting them. Those heterogeneous information could facilitate the community detection for its constituent homogeneous networks, but has not been fully explored. In this paper, we exploit heterogeneous multi-relational networks (HMRNet) and propose an efficient message passing based algorithm to simultaneously detect communities for all homogeneous networks. Specifically, an HMRNet is reorganized into a hierarchical structure with homogeneous networks as its layers and heterogeneous links connecting them. To detect communities in such an HMRNet, the problem is formulated as a maximum a posterior (MAP) over a factor graph. Finally a message passing based algorithm is derived to find a best solution of the MAP problem. Evaluation on both synthetic and real-world networks confirms the effectiveness of the proposed method.
Labeling of sequential data is a prevalent meta-problem for a wide range of real world applications. While the first-order Hidden Markov Models (HMM) provides a fundamental approach for unsupervised sequential labeling, the basic model does not show
satisfying performance when it is directly applied to real world problems, such as part-of-speech tagging (PoS tagging) and optical character recognition (OCR). Aiming at improving performance, important extensions of HMM have been proposed in the literatures. One of the common key features in these extensions is the incorporation of proper prior information. In this paper, we propose a new extension of HMM, termed diversified Hidden Markov Models (dHMM), which utilizes a diversity-encouraging prior over the state-transition probabilities and thus facilitates more dynamic sequential labellings. Specifically, the diversity is modeled by a continuous determinantal point process prior, which we apply to both unsupervised and supervised scenarios. Learning and inference algorithms for dHMM are derived. Empirical evaluations on benchmark datasets for unsupervised PoS tagging and supervised OCR confirmed the effectiveness of dHMM, with competitive performance to the state-of-the-art.
