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IEEE International Conference on Data Mining

作者： Zhao Kang Chong Peng Qiang Cheng Department of Computer Science Southern Illinois University

ISBN: (纸本)9781467395052

Numerous applications in data mining and machine learning require recovering a matrix of minimal rank. Robust principal component analysis (RPCA) is a general framework for handling this kind of problems. Nuclear norm based convex surrogate of the rank function in RPCA is widely investigated. Under certain assumptions, it can recover the underlying true low rank matrix with high probability. However, those assumptions may not hold in real-world applications. Since the nuclear norm approximates the rank by adding all singular values together, which is essentially a l_1-norm of the singular values, the resulting approximation error is not trivial and thus the resulting matrix estimator can be significantly biased. To seek a closer approximation and to alleviate the above-mentioned limitations of the nuclear norm, we propose a nonconvex rank approximation. This approximation to the matrix rank is tighter than the nuclear norm. To solve the associated nonconvex minimization problem, we develop an efficient augmented Lagrange multiplier based optimization algorithm. Experimental results demonstrate that our method outperforms current state-of-the-art algorithms in both accuracy and efficiency.

关键词： Rank of data data mining approximation principal components analysis Approximation error Atomic nuclei matrices optimization algorithms

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Adaptive Maximization of Pointwise Submodular Functions With Budget Constraint 16

Adaptive Maximization of Pointwise Submodular Functions With...

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Annual Conference on Neural Information Processing Systems

作者： Nguyen Viet Cuong Huan Xu Department of Engineering University of Cambridge Stewart School of Industrial & Systems Engineering Georgia Institute of Technology

ISBN: (纸本)9781510838819

We study the worst-case adaptive optimization problem with budget constraint that is useful for modeling various practical applications in artificial intelligence and machine learning. We investigate the near-optimality of greedy algorithms for this problem with both modular and non-modular cost functions. In both cases, we prove that two simple greedy algorithms are not near-optimal but the best between them is near-optimal if the utility function satisfies pointwise submodularity and pointwise cost-sensitive submodularity respectively. This implies a combined algorithm that is near-optimal with respect to the optimal algorithm that uses half of the budget. We discuss applications of our theoretical results and also report experiments comparing the greedy algorithms on the active learning problem.

关键词： greedy algorithm Budgets Artificial Intelligence optimization algorithms Modularity

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CT SLICE RETRIEVAL BY SHAPE ELLIPSES DESCRIPTORS FOR SKULL REPAIRING

CT SLICE RETRIEVAL BY SHAPE ELLIPSES DESCRIPTORS FOR SKULL R...

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IEEE International Conference on Image Processing

作者： Marcelo Rudek Osiris Canciglieri Andreas Jahnen Gerson Linck Bichinho Industrial and Systems Engineering Graduate Program - Pontifical Catholic University of Parana PUCPR Brazil. Ressource Centre for HealthCare Technologies (SANTEC) Public Research Centre Henri Tudor Luxembourg. Technology in Healthcare Postgraduate Program - Pontifical Catholic University of Parana PUCPR Brazil.

ISBN: (纸本)9781479923427

This paper addresses the problem of automated prosthesis modelling and manufacturing, whose machining parameters are based on images extracted from different medical databases. The specific case of 3D surface restoration of a defective skull was used as study case. A method based on adjusted ellipses on skull bone curvature performs the symbolic representation of searching parameters. The superellipse concept permits to define geometric parameters to fit an ellipse on each Computed Tomography slice. Those ellipse descriptors can be used as a template for the retrieval of similar images from databases whose parameters match the sampled image. The similarity is measured according to the best fitness values through an optimization algorithm. The slices found by similarity are retrieved from all databases in order to build the 3D model. Experiments show that the proposed method is a promising technique for content based image retrieval.

关键词： Prosthesis Modelling Image Retrieval Ellipse 3D Medical Imaging Ellipse image retrieval Medical imaging content-based image retrieval Skull retrieval Database X-Ray Computed Tomography Three Dimensions Descriptors images geometric parameter optimization algorithms

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Solving Traveling Salesman Problem with Hybrid Estimation of Distribution Algorithm

Solving Traveling Salesman Problem with Hybrid Estimation of...

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IEEE International Conference on Cyber Technology in Automation, Control, and Intelligent Systems

作者： Libo Song Chang Liu Jun Zhu Haibo Shi Shenyang Institute of Automation Chinese Academy of Sciences Shenyang China

ISBN: (纸本)9781538604915

A hybrid distribution estimation algorithm for traveling salesman problem is proposed. Firstly, based on the distributed estimation algorithm, a new effective probability model is proposed to solve the traveling salesman problem. Secondly, in order to speed up the optimization of the algorithm to prevent the algorithm falling into the local optimal, the extreme optimization algorithm is combined to form a hybrid distribution estimation algorithm to improve the effectiveness of the algorithm. Then through the public TSPLIB data set, it is proved that the hybrid distribution estimation algorithm is effective, and the algorithm can solve this kind of problem well. Finally, a new idea is proposed to verify the validity of the traveling salesman problem, and the algorithm is tested by the proposed algorithm. The experimental results show that the proposed hybrid distribution estimation algorithm has a good performance in solving the traveling salesman problem.

关键词： Urban areas Estimation Traveling salesman problems optimization Sociology Statistics Encoding travelling salesman problems Sociology algorithms urban area Allocation Algorithm coding optimization algorithms HYBRID Hybrid electric vehicles

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Last Iterate Convergence of Incremental Methods and Applications in Continual Learning

arXiv

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arXiv 2024年

作者： Cai, Xufeng Diakonikolas, Jelena Department of Computer Sciences University of Wisconsin-Madison United States

Incremental gradient and incremental proximal methods are a fundamental class of optimization algorithms used for solving finite sum problems, broadly studied in the literature. Yet, without strong convexity, their convergence guarantees have primarily been established for the ergodic (average) iterate. Motivated by applications in continual learning, we obtain the first convergence guarantees for the last iterate of both incremental gradient and incremental proximal methods, in general convex smooth (for both) and convex Lipschitz (for the proximal variants) settings. Our oracle complexity bounds for the last iterate nearly match (i.e., match up to a square-root-log or a log factor) the best known oracle complexity bounds for the average iterate, for both classes of methods. We further obtain generalizations of our results to weighted averaging of the iterates with increasing weights and for randomly permuted ordering of updates. We study incremental proximal methods as a model of continual learning with generalization and argue that large amount of regularization is crucial to preventing catastrophic forgetting. Our results generalize last iterate guarantees for incremental methods compared to state of the art, as such results were previously known only for overparameterized linear models, which correspond to convex quadratic problems with infinitely many solutions. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

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Distributed Minimum Cost Multicasting with Lossless Source Coding and Network Coding

Distributed Minimum Cost Multicasting with Lossless Source C...

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Proceedings of the 46th IEEE Conference on Decision and Control, Pages 5511-5970

作者： Tao Cui Tracey Ho Lijun Chen Division of Engineering and Applied Science California State University Sacramento USA

ISBN: (纸本)9781424414970;1424414970

In this paper, we consider minimum cost lossless source coding for multiple multicast sessions. Each session comprises a set of correlated sources whose information is demanded by a set of sink nodes. We propose a distributed end-to-end algorithm which operates over given multicast trees, and a back-pressure algorithm which optimizes routing and coding over the whole network. Unlike other existing algorithms, the source rates need not be centrally coordinated;the sinks control transmission rates across the sources. With random network coding, the proposed approach yields completely distributed and optimal algorithms for intra-session network coding. We prove the convergence of our proposed algorithms. Some practical considerations are also discussed. Experimental results are provided to complement our theoretical analysis.

关键词： lossless source coding Multicast Network coding optimization algorithms Random Network coding TRANSMISSION RATE multicast communication solidification Distribute algorithms Network routing Theoretical analysis Sinks source rate

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COMPLEXITY AND NUMERICAL EXPERIMENTS OF A NEW ADAPTIVE GENERIC PROXIMAL BUNDLE METHOD

arXiv

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arXiv 2024年

作者： Guigues, Vincent Monteiro, Renato D.C. Tran, Benoit School of Applied Mathematics FGV Praia de Botafogo Rio de Janeiro Brazil Georgia Institute of Technology AtlantaGA30332-0205 United States

This paper develops an adaptive generic proximal bundle method, shows its complexity, and presents numerical experiments comparing this method with two bundle methods on a set of optimization problems. Copyright ©... 详细信息

关键词： optimization algorithms

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Discrete MRF Inference of Marginal Densities for Non-uniformly Discretized Variable Space

Discrete MRF Inference of Marginal Densities for Non-uniform...

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IEEE Conference on Computer Vision and Pattern Recognition

作者： Masaki Saito Takayuki Okatani Koichiro Deguchi Tohoku University Japan

ISBN: (纸本)9781467364102

This paper is concerned with the inference of marginal densities based on MRF models. The optimization algorithms for continuous variables are only applicable to a limited number of problems, whereas those for discrete variables are versatile. Thus, it is quite common to convert the continuous variables into discrete ones for the problems that ideally should be solved in the continuous domain, such as stereo matching and optical flow estimation. In this paper, we show a novel formulation for this continuous-discrete conversion. The key idea is to estimate the marginal densities in the continuous domain by approximating them with mixtures of rectangular densities. Based on this formulation, we derive a mean field (MF) algorithm and a belief propagation (BP) algorithm. These algorithms can correctly handle the case where the variable space is discretized in a non-uniform manner. By intentionally using such a non-uniform discretization, a higher balance between computational efficiency and accuracy of marginal density estimates could be achieved. We present a method for actually doing this, which dynamically discretizes the variable space in a coarse-to-fine manner in the course of the computation. Experimental results show the effectiveness of our approach.

关键词： problems efficiency accuracy discrete transforms Traffic estimation optimization algorithms Computational efficiency

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The Computation of Full-complexity Polytopic Robust Control Invariant Sets

The Computation of Full-complexity Polytopic Robust Control ...

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IEEE Annual Conference on Decision and Control

作者： Chengyuan Liu Imad M. Jaimoukha Department of Electrical and Electronic Engineering Imperial College London SW7 2AZ UK

ISBN: (纸本)9781479978878

This paper considers the problem of evaluating robust control invariant (RCI) sets for linear discrete-time systems subject to state and input constraints as well as additive disturbances. An RCI set has the property that if the system state is inside the set at any one time, then it is guaranteed to remain in the set for all future times using a predefined state feedback control law. This problem is important in many control applications. We present a numerically efficient algorithm for the computation of full-complexity polytopic RCI sets. Farkas' Theorem is first used to derive necessary and sufficient conditions for the existence of an admissible polytopic RCI set in the form of nonlinear matrix inequalities. An Elimination Lemma is then used to derive sufficient conditions, in the form of linear matrix inequalities, for the existence of the solution. An optimization algorithm to approximate maximal RCI sets is also proposed. Numerical examples are given to illustrate the effectiveness of the proposed algorithm.

关键词： SETTING Sufficient conditions Robust control state feedback control Invariant linear matrix inequalities optimization algorithms

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A Nonlinear Estimator Concept for Active Vehicle Suspension Control

A Nonlinear Estimator Concept for Active Vehicle Suspension ...

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American Control Conference

作者： Guido Koch Tobias Kloiber Enrico Pellegrini Boris Lohmann Institute of Automatic Control Technische Universitat Munchen 86748 Garching Germany

ISBN: (纸本)9781424474264

A new Kalman filter based signal estimation concept for active vehicle suspension control is presented in this paper considering the nonlinear damper characteristic of a vehicle suspension setup. The application of a multi-objective genetic optimization algorithm for the tuning of the estimator shows that three parallel Kalman filters enhance the estimation performance for the variables of interest (states, dynamic wheel load and road profile). The Kalman filter structure is validated in simulations and on a testrig for an active suspension configuration using measurements of real road profiles as disturbance input. The advantages of the concept are its low computational effort compared to Extended or Unscented Kalman filters and its good estimation accuracy despite the presence of nonlinearities in the suspension setup.

关键词： Automobile suspensions Kalman filters nonlinearity Road optimization algorithms

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