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Event(s) on October 2006
- Tuesday, 3rd October, 2006
Title: Algorithms and Applications for Nonnegative Matrix Factorization Speaker: Dr. Rafal Zdunek, Brain Science Institute, RIKEN, Wako-shi, Saitama, Japan Time/Place: 11:30 - 12:30
Abstract: Nonnegative Matrix Factorization (NMF) solves the following linear algebra problem: find such nonnegative matrices MR~+¸ℜA and RT~+¸ℜX that , given only YAXMT~¸ℜY and the assigned index R. This method has found a wide spectrum of applications in signal and image processing, such as blind source separation, spectra recovering, pattern recognition, segmentation or clustering. The NMF is usually performed with an alternating gradient descent technique that is applied to the squared Euclidean distance or Kullback-Leibler (KL) divergence. This approach has been used in the most known Lee-Seung NMF algorithms that belong to a class of multiplicative iterative algorithms which are extensions of the well-known ISRA and EMML algorithms. It is obvious that such a factorization can be performed with minimization of different kinds of cost functions, depending on the underlying nature of noise and distribution of nonnegative components (or factors). Also, different algorithms can be applied to the minimization task, which leads to various NMF algorithms with different degrees of their complexity, robustness, and convergence properties. Their performance is also strongly application-dependent. The talk will be focused on the NMF algorithms that can be derived from the alpha- and beta-divergences that unify many well-known cost functions, such as the generalized KL and dual KL divergences, Pearsonfs, Hellingerfs, and Itakura-Saito distances. We will show the related algorithms that are obtained with applying different approaches to perform the optimization task, e.g. gradient descent, exponetiated gradient, projected gradient, or interior-point techniques. Also, we will present the NMF algorithms based on second-order optimization methods: projected quasi-Newton and QP-based methods, and their improved versions (Q-less QR factorization and GPCG method) which allow us to avoid a direct inversion of the Hessian. Additionally, a new very robust multilayer NMF with multi initializations will be also briefly discussed. Some results obtained with our NMF algorithms, which were applied to a Blind Source Separation (BSS) problem with mixed signals and images, will be demonstrated. In the end, we will shortly discuss our shareware Matlab software: NMFLAB for Signal and Image Processing, and NTFLAB for Signal Processing, where most of the presented algorithms have been implemented.
- Tuesday, 3rd October, 2006
Title: Knowledge Discovery and Systems Biology: An Application on Crops and Medicinal Plants Speaker: Prof. Diane Dianjing Guo, Department of Biology, The Chinese University of Hong Kong, HKSAR, China Time/Place: 15:30 - 16:30
- Thursday, 12th October, 2006
Title: Distinguished Lecture Series: Mathematics in the Real World and the Fake World Speaker: Prof. Stanley Osher, Department of Mathematics, University of California, Los Angeles, USA Time/Place: 16:30 - 17:30
Abstract: A good example of the applications of mathematics involves a new approach to image science and free boundary problems in nature. This is exemplified by the level set method for capturing moving fronts, which was introduced in 1987 by Osher and Sethian. It has proven to be phenomenally successful as a numerical device. For example, typing in "Level Set Methods" on google's search engine gives roughly 190,000 responses. Applications range from capturing multiphase fluid dynamical flows, to special effects in Hollywood to visualization,image processing, control, epitaxial growth, computer vision and many more. In this talk we shall give a quick overview of the numerical technology, its relation with the field of PDE based imaging science and some application. The real world is exemplified by image analysis and the fake world is exemplified by computer graphics.
- Friday, 13th October, 2006
Title: Wofoo Distinguished Applied Mathematics Lecture Series: Bregman Iteration, Inverse Scale Space, Cartoon/Texture Decomposition, Recovery of Signal from "Noise" and Other New Techniques in PDE Based Image Restoration Speaker: Prof. Stanley Osher, Department of Mathematics, University of California, Los Angeles, USA Time/Place: 16:00 - 18:00
Abstract: In recent years there has been an explosion of activity related to PDE and variational based methods in image processing. In this talk we will begin with standard BV/L2 minimization and discuss various related and significant improvements, largely provoked by Yves Meyer's 2001 monograph
- Tuesday, 17th October, 2006
Title: In Search of the Optimal Coordinate System in Computational Fluid Dynamics Speaker: Prof. W. H. Hui, Department of Mechanical Engineering, Hong Kong Polytechnic University, HKSAR, China Time/Place: 11:30 - 12:30
Abstract: It is well-known that the numerical solution to a flow depends on the relation between the flow and the coordinate system used to compute it. An important issue in CFD is, therefore, the search for the optimal coordinate system. This paper reviews the advantages and drawbacks of Eulerian and Lagrangian coordinate systems in CFD, leading to the construction of a unified coordinate system which combines the advantages of these two systems and beyond. Specifically, using the unified coordinate system it is shown that: (a) The governing equations can be written as a system of conservation partial differential equations (PDE); in particular, the system of Lagrangian gas dynamic equations is written, for the first time, in conservation PDE form. (b) Contact discontinuities and material interfaces (including free surfaces), as well as shock waves, are resolved sharply. (c) Automatic grid generation is achieved for flow past a body. Several numerical examples are given to confirm these properties.
- Tuesday, 24th October, 2006
Title: An Integrated Smoothed Maximum Score Estimator For A Generalized Censored Quantile Regression Model Speaker: Prof. Chen Songnian, Department of Economics, The Hong Kong University of Science and Technology, HKSAR, China Time/Place: 11:30 - 12:30
Abstract: In this paper we consider semiparametric estimation of a general quantile regression model with censored data. We propose an integrated smoothed maximum score estimator following the insight of Horowitz (1992) and Manski (1985) for the binary choice under a quantile restriction. Similar to Horowitz (1992), we only use one-dimensional kernels. While the approaches of Chaudhuri et al (1997) and Khan (2001) are also applicable, their first-step estimates involve nonparametric estimation of quantile regression using multivariate kernel functions, thus their methods are not very useful in practice when there are multiple regressors due to curse-of-dimensionality.
- Tuesday, 31st October, 2006
Title: Iterative Methods for Tikhonov Regularization Speaker: Prof. Lothar Reichel, Department of Mathematics, Kent State University, USA Time/Place: 11:30 - 12:30
Abstract: Image deblurring problems give rise to large ill-posed systems of equations, whose solution recently has received considerable attention. We discuss the determination of an approximate solution by Tikhonov regularization and survey available iterative methods that both determine a suitable value of the regularization parameter and an associated approximate solution. The iterative methods explore the connections between orthogonal polynomials, Gauss quadrature, and Lanczos bidiagonalization. Methods for both unconstrained and constrained problems will be discussed.