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Sparse dual-graph regularized quadratic dimensionality reduction algorithm based on subspace learning

Digital Signal processing: A Review Journal 2025年 164卷

作者： Ma, Ziping Huang, Yulei Ma, Jinlin Li, Huirong School of Mathematics and Information Science North Minzu University Yinchuan750030 China School of Mathematics and Statistics Ningxia University Yinchuan750030 China School of Computer Science and Engineering North Minzu University Yinchuan750030 China School of Mathematics and Computer Application Shangluo University Shangluo726000 China Ningxia Collaborative Innovation Center for Scientific Computing and Intelligent Information Processing North Minzu University Yinchuan750030 China

Nonnegative matrix factorization (NMF) has been attracting more and more attention due to its significant performance in dimensionality reduction. NMF performs dimensionality reduction by mapping high-dimensional data into low-dimensional space, which might lead to the uncontrollability, i.e. quantity and quality, of dimensions in dimensionality reduction. To address this issue, we innovatively propose a novel sparse dual-graph regularized quadratic dimensionality reduction (SDQDR) algorithm by embedding feature selection mechanism to semi-supervised NMF, which are fused as a whole rather than the simple combinations of NMF and feature selection in existing methods. The proposed SDQDR not only inherits the advantages of semi-supervised NMF but also demonstrates some special and important properties, such as controllability of dimensionality reduction, higher clustering performance, and significant dimensionality reduction with low time cost, etc. Then, to reinforce the sparsity structure and retain the manifold structures of both the data and the feature space simultaneously, 1-2,1/2 sparse constraint and dual graph regularization are incorporated into the proposed framework. Finally, the objective function, convergence proof, and iterative update rules are presented. In comparison with 15 state-of-the-art algorithms, relevant results demonstrate the proposed method is competitive, especially in terms of the efficiency of dimensionality reduction. © 2025 Elsevier Inc.

关键词： Non-negative matrix factorization

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Correction to: A metaheuristic-based framework for index tracking with practical constraints

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Complex & intelligent Systems 2022年第3期9卷 3469-3469页

作者： Yuen, Man-Chung Ng, Sin-Chun Leung, Man-Fai Che, Hangjun School of Science and Technology Hong Kong Metropolitan University Kowloon China School of Computing and Information Science Anglia Ruskin University Cambridge UK Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing College of Electronic and Information Engineering Southwest University Chongqing China

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Invariant-preserving schemes with arbitrarily high-order accuracy for the two-component Camassa–Holm system via Hamiltonian boundary value methods

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Communications in Nonlinear science and Numerical Simulation 2025年 150卷

作者： Luo, Qian Xiao, Aiguo Li, Min Yan, Xiaoqiang School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan411105 China Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Hunan411105 China School of Mathematics and Physics China University of Geosciences Wuhan430074 China National Center for Applied Mathematics in Hunan Xiangtan University Hunan411105 China

In this paper, we present an arbitrarily high-order numerical scheme for the two-component Camassa–Holm system, ensuring the preservation of three invariants: energy and two Casimir functions. The spatial discretization is achieved using Fourier–Galerkin methods, resulting in a semi-discrete system which retains a Hamiltonian structure and approximates the invariants of the original continuous system. Subsequently, an energy-preserving Runge–Kutta method, such as Hamiltonian boundary value methods, is applied to the semi-discrete system, yielding a fully discrete scheme of arbitrarily high order. The proposed scheme is validated through numerical simulations, demonstrating its accuracy and capability in capturing different types of solutions of the two-component Camassa–Holm equation. © 2025 Elsevier B.V.

关键词： Runge Kutta methods

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Hard instance learning for quantum adiabatic prime factorization

arXiv

引用

arXiv 2021年

作者： Lin, Jian Zhang, Zhengfeng Zhang, Junping Li, Xiaopeng State Key Laboratory of Surface Physics Institute of Nanoelectronics and Quantum Computing Department of Physics Fudan University Shanghai200433 China Shanghai Key Lab of Intelligent Information Processing School of Computer Science Fudan University Shanghai200433 China Shanghai Qi Zhi Institute AI Tower Xuhui District Shanghai200232 China

Prime factorization is a difficult problem with classical computing, whose exponential hardness is the foundation of Rivest-Shamir-Adleman (RSA) cryptography. With programmable quantum devices, adiabatic quantum computing has been proposed as a plausible approach to solve prime factorization, having promising advantage over classical computing. Here, we find there are certain hard instances that are consistently intractable for both classical simulated annealing and un-configured adiabatic quantum computing (AQC). Aiming at an automated architecture for optimal configuration of quantum adiabatic factorization, we apply a deep reinforcement learning (RL) method to configure the AQC algorithm. By setting the success probability of the worst-case problem instances as the reward to RL, we show the AQC performance on the hard instances is dramatically improved by RL configuration. The success probability also becomes more evenly distributed over different problem instances, meaning the configured AQC is more stable as compared to the un-configured case. Through a technique of transfer learning, we find prominent evidence that the framework of AQC configuration is scalable—the configured AQC as trained on five qubits remains working efficiently on nine qubits with a minimal amount of additional training cost. Copyright © 2021, The Authors. All rights reserved.

关键词： Factorization

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General Greedy De-bias Learning

arXiv

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arXiv 2021年

作者： Han, Xinzhe Wang, Shuhui Su, Chi Huang, Qingming Tian, Qi The School of Computer Science and Technology University of Chinese Academy of Sciences Beijing101408 China The Key Laboratory of Intelligent Information Processing Institute of Computing Technology Chinese Academy of Sciences Beijing100190 China Peng Cheng Laboratory Shenzhen518066 China SmartMore Beijing100085 China Huawei Cloud & AI Shenzhen518129 China

Neural networks often make predictions relying on the spurious correlations from the datasets rather than the intrinsic properties of the task of interest, facing with sharp degradation on out-of-distribution (OOD) test data. Existing de-bias learning frameworks try to capture specific dataset bias by annotations but they fail to handle complicated OOD scenarios. Others implicitly identify the dataset bias by special design low capability biased models or losses, but they degrade when the training and testing data are from the same distribution. In this paper, we propose a General Greedy De-bias learning framework (GGD), which greedily trains the biased models and base model. The base model is encouraged to focus on examples that are hard to solve with biased models, thus remaining robust against spurious correlations in the test stage. GGD largely improves models' OOD generalization ability on various tasks, but sometimes over-estimates the bias level and degrades on the in-distribution test. We further re-analyze the ensemble process of GGD and introduce the Curriculum Regularization inspired by curriculum learning, which achieves a good trade-off between in-distribution (ID) and out-of-distribution performance. Extensive experiments on image classification, adversarial question answering, and visual question answering demonstrate the effectiveness of our method. GGD can learn a more robust base model under the settings of both task-specific biased models with prior knowledge and self-ensemble biased model without prior knowledge. Codes are available at https://***/GeraldHan/GGD. Copyright © 2021, The Authors. All rights reserved.

关键词： Curricula

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Locality-aware channel-wise dropout for occluded face recognition

arXiv

引用

arXiv 2021年

作者： He, Mingjie Zhang, Jie Shan, Shiguang Liu, Xiao Wu, Zhongqin Chen, Xilin Key Laboratory of Intelligent Information Processing Chinese Academy of Sciences Institute of Computing Technology CAS Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China CAS Center for Excellence in Brain Science and Intelligence Technology Shanghai200031 China Peng Cheng Laboratory Shenzhen518055 China Beijing100080 China

Face recognition remains a challenging task in unconstrained scenarios, especially when faces are partially occluded. To improve the robustness against occlusion, augmenting the training images with artificial occlusions has been proved as a useful approach. However, these artificial occlusions are commonly generated by adding a black rectangle or several object templates including sunglasses, scarfs and phones, which cannot well simulate the realistic occlusions. In this paper, based on the argument that the occlusion essentially damages a group of neurons, we propose a novel and elegant occlusion-simulation method via dropping the activations of a group of neurons in some elaborately selected channel. Specifically, we first employ a spatial regularization to encourage each feature channel to respond to local and different face regions. In this way, the activations affected by an occlusion in a local region are more likely to be located in a single feature channel. Then, the locality-aware channel-wise dropout (LCD) is designed to simulate the occlusion by dropping out the entire feature channel. Furthermore, by randomly dropping out several feature channels, our method can well simulate the occlusion of larger area. The proposed LCD can encourage its succeeding layers to minimize the intra-class feature variance caused by occlusions, thus leading to improved robustness against occlusion. In addition, we design an auxiliary spatial attention module by learning a channel-wise attention vector to reweight the feature channels, which improves the contributions of non-occluded regions. Extensive experiments on various benchmarks show that the proposed method outperforms state-of-the-art methods with a remarkable improvement. Copyright © 2021, The Authors. All rights reserved.

关键词： Chemical activation

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Optimizing Partial Area Under the Top-k Curve: Theory and Practice

arXiv

引用

arXiv 2022年

作者： Wang, Zitai Xu, Qianqian Yang, Zhiyong He, Yuan Cao, Xiaochun Huang, Qingming Institute of Information Engineering Chinese Academy of Sciences Beijing100093 China School of Cyber Security University of Chinese Academy of Sciences Beijing100049 China The Key Laboratory of Intelligent Information Processing Institute of Computing Technology Chinese Academy of Sciences Beijing100190 China School of Computer Science and Technology University of Chinese Academy of Sciences Beijing100049 China The Security Department Alibaba Group Hangzhou311121 China School of Cyber Science and Technology Sun Yat-Sen University Shenzhen Campus Shenzhen518107 China University of Chinese Academy of Sciences Beijing101408 China Peng Cheng Laboratory Shenzhen518055 China

Top-k error has become a popular metric for large-scale classification benchmarks due to the inevitable semantic ambiguity among classes. Existing literature on top-k optimization generally focuses on the optimization method of the top-k objective, while ignoring the limitations of the metric itself. In this paper, we point out that the top-k objective lacks enough discrimination such that the induced predictions may give a totally irrelevant label a top rank. To fix this issue, we develop a novel metric named partial Area Under the top-k Curve (AUTKC). Theoretical analysis shows that AUTKC has a better discrimination ability, and its Bayes optimal score function could give a correct top-K ranking with respect to the conditional probability. This shows that AUTKC does not allow irrelevant labels to appear in the top list. Furthermore, we present an empirical surrogate risk minimization framework to optimize the proposed metric. Theoretically, we present (1) a sufficient condition for Fisher consistency of the Bayes optimal score function;(2) a generalization upper bound which is insensitive to the number of classes under a simple hyperparameter setting. Finally, the experimental results on four benchmark datasets validate the effectiveness of our proposed framework. © 2022, CC BY.

关键词： Machine learning

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Global stability of the periodic solution of the three level food chain model with extinction of top predator

arXiv

引用

arXiv 2021年

作者： Cheng, Kaijen You, Hongming Yang, Ting-Hui School of Mathematics and Statistics Zhaoqing University Guangdong Zhaoqing526061 China College of Mathematics and Computer Science Quanzhou Normal University Quanzhou362000 China Department of Mathematics Tamkang University No. 151 Yingzhuan Road Tamsui Dist. New Taipei City25137 Taiwan Fujian Provincial Key Laboratory of Data-Intensive Computing Key Laboratory of Intelligent Computing and Information Processing School of Mathematics and Computer Science Quanzhou Normal University Quanzhou China

In this work, we revisit the classical Holling type II three species food chain model from a different viewpoint. Two critical parameters λ1 and λ2 dependent on all parameters are defined. The existence and local stabilities of all equilibria can be reformulated by λ1 and λ2, and the complete classifications of parameters and its corresponding dynamics are given. Moreover, with the extinction of top-predator, there is an invariant two dimensional subsystem containing the prey and the intermediate predator. We prove the global stability of the boundary equilibrium in 3+ by differential inequality as well as Butler-McGehee lemma if it is stable. Alternatively, there is a unique limit cycle when the boundary equilibrium lost its stability, and we also show the global stability of the limit cycle in 3+ by differential inequality and computing the Floquet Multipliers. Finally, some interesting numerical simulations, the chaotic and the bi-stability phenomena, are presented numerically. A brief discussion and biological implications are also *** Codes 92D25 Copyright © 2021, The Authors. All rights reserved.

关键词： Stability

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Contrastive Learning for Robust Android Malware Familial Classification

arXiv

引用

arXiv 2021年

作者： Wu, Yueming Dou, Shihan Zou, Deqing Yang, Wei Qiang, Weizhong Jin, Hai National Engineering Research Center for Big Data Technology and System Services Computing Technology and System Lab Hubei Engineering Research Center on Big Data Security School of Cyber Science and Engineering Huazhong University of Science and Technology Wuhan430074 China Shanghai Key Laboratory of Intelligent Information Processing School of Computer Science Fudan University Shanghai200433 China University of Texas at Dallas Dallas United States National Engineering Research Center for Big Data Technology and System Services Computing Technology and System Lab Cluster and Grid Computing Lab School of Computer Science and Technology Huazhong University of Science and Technology Wuhan430074 China

Due to its open-source nature, Android operating system has been the main target of attackers to exploit. Malware creators always perform different code obfuscations on their apps to hide malicious activities. Features extracted from these obfuscated samples through program analysis contain many useless and disguised features, which leads to many false negatives. To address the issue, in this paper, we demonstrate that obfuscation-resilient malware family analysis can be achieved through contrastive learning. The key insight behind our analysis is that contrastive learning can be used to reduce the difference introduced by obfuscation while amplifying the difference between malware and other types of malware. Based on the proposed analysis, we design a system that can achieve robust and interpretable classification of Android malware. To achieve robust classification, we perform contrastive learning on malware samples to learn an encoder that can automatically extract robust features from malware samples. To achieve interpretable classification, we transform the function call graph of a sample into an image by centrality analysis. Then the corresponding heatmaps can be obtained by visualization techniques. These heatmaps can help users understand why the malware is classified as this family. We implement IFDroid and perform extensive evaluations on two datasets. Experimental results show that IFDroid is superior to state-of-the-art Android malware familial classification systems. Moreover, IFDroid is capable of maintaining a 98.4% F1 on classifying 69,421 obfuscated malware samples. © 2021, CC0.

关键词： Android (operating system)

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Control of space-dependent four-wave mixing in a four-level atomic system

引用

Physical Review A 2020年第3期102卷 033516-033516页

作者： Jing Qiu Zhiping Wang Dongsheng Ding Zhixiang Huang Benli Yu Key Laboratory of Opto-Electronic Information Acquisition and Manipulation Ministry of Education Anhui University Hefei 230601 China Key Laboratory of Quantum Information University of Science and Technology of China Hefei Anhui 230026 China Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education Anhui University Hefei 230039 China

We propose a scheme to demonstrate the manipulation of space-dependent four-wave mixing (FWM) in a four-level atomic system. By adjusting the detuning of the control field, one can effectively control the FWM output field transferred from a pump beam carrying orbital angular momentum. More interestingly, by appropriate choice of the intensity of the control field, the FWM field can be significantly enhanced and phase twist is almost completely suppressed. Furthermore, the superposition modes created by the interference between the FWM field and a same-frequency Gaussian beam are also discussed, showing many interesting properties. Our results may open some possibilities for phase imprinting in Bose-Einstein condensates or atom manipulation with optical tweezers.

关键词： Angular momentum of light Atom optics Coherent control Optical coherence

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