Colloquium/Seminar

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Event(s) on October 2014


  • Friday, 3rd October, 2014

    Title: CMIV Lecture 1: Total Variation Data Analysis - A Non-linear Spectral Framework for Machine Learning
    Speaker: Dr. Xavier Bresson, Universite de Lausanne, Switzerland
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: With enormous and daily flows of data in finance, security, health, social network and multimedia (sound/text/image/video), there is a strong need to process information as efficiently as possible for smart decisions to be made. Machine Learning develops analytical methods and strong algorithms to deal with this massive large-scale, multi-dimensional and multi-modal data. This field has recently seen tremendous advances with the emergence of new powerful techniques combining the key mathematical tools of sparsity, convex optimization and relaxation methods. In this talk, I will present how these concepts can be applied to find excellent approximate solutions of NP-hard balanced cut problems for unsupervised data clustering, significantly overcoming state-of-the-art spectral clustering methods including Shi-Malik's normalized cut. I will also show how to design fast algorithms for the proposed non-convex and non-differentiable optimization problems based on recent breakthroughs in total variation optimization problems borrowed from the compressed sensing field. This new total variation clustering technique paves the way to a new generation of learning algorithms that can provide simultaneously accurate, fast and robust solutions to other fundamental problems in data science such as Support Vector Machine data classification. These new methodologies have a wide range of applications including data retrieval (search engines), neuroimaging (diseases detection and analysis) and social network analysis (community detection). This is a joint work with Thomas Laurent, James von Brecht, Arthur Szlam, David Uminsky, Dejan Slepcev, Nicolas Garcia Trillos, Xue-Cheng Tai and Tony Chan.


  • Friday, 3rd October, 2014

    Title: CMIV Lecture 2: Matrix Completion on Graphs
    Speaker: Dr. Xavier Bresson, Universite de Lausanne, Switzerland
    Time/Place: 15:30  -  16:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem is NP-hard, Candès and Recht showed that it can be exactly relaxed if the matrix is low-rank and the number of observed entries is sufficiently large. In this work, we introduce a novel matrix completion model that makes use of proximity information about rows and columns by assuming they form communities. This assumption makes sense in several real-world problems like in recommender systems, where there are communities of people sharing preferences, while products form clusters that receive similar ratings. Our main goal is thus to find a low-rank solution that is structured by the proximities of rows and columns encoded by graphs. We borrow ideas from manifold learning to constrain our solution to be smooth on these graphs, in order to implicitly force row and column proximities. Our matrix recovery model is formulated as a convex non-smooth optimization problem, for which a well-posed iterative scheme is provided. We study and evaluate the proposed matrix completion on synthetic and real data, showing that the proposed structured low-rank recovery model outperforms the standard matrix completion model in many situations. This is a joint work with Vassilis Kalofolias, Michael Bronstein, and Pierre Vandergheynst.


  • Monday, 13th October, 2014

    Title: CMIV Distinguished Lecture: An Inverse Problem in Bar Code Decoding
    Speaker: Prof. Fadil Santosa, School of Mathematics, University of Minnesota, United States
    Time/Place: 16:30  -  17:30 (Preceded by Tea Reception at 4:00 p.m.)
    SCT909, Cha Chi-ming Science Tower, HSH Campus, Hong Kong Baptist University
    Abstract: Bar codes are ubiquitous -- they are used to identify products in stores, parts in a warehouse, and books in a library, etc. In this talk, the speaker will describe how information is encoded in a bar code and how it is read by a scanner. The presentation will go over how the decoding process, from scanner signal to coded information, can be formulated as an inverse problem. The inverse problem involves finding the "word" hidden in the signal. What makes this inverse problem, and the approach to solve it, somewhat unusual is that the unknown has a finite number of states.


  • Monday, 20th October, 2014

    Title: Seeing Beyond the Diffraction Limit
    Speaker: Prof. Peijun Li, Department of Mathematics, Purdue University, USA
    Time/Place: 15:30  -  16:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In this talk, our recent progress on a class of inverse surface scattering problems will be discussed. I will present new approaches to achieve subwavelength resolution for the inverse problems. The methods require only a single incident field and are realized by using the fast Fourier transform. The error estimates of the solution for the model equation will be addressed. I will also highlight ongoing projects in rough surface imaging, random medium imaging, and near-field and nano- optics modeling.


  • Wednesday, 29th October, 2014

    Title: Isospectral non-diffeomorphic nilmanifolds with respect to sub-Laplacians
    Speaker: Prof. Kenro Furutani , Department of Mathematics, Tokyo University of Science, Japan
    Time/Place: 14:30  -  15:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: I start by explaining a rough history of isospectral problem posed by Mark Kac and present a new example of isospectral non-diffeomorphic manifolds with respect to sub-Laplacians and Laplacians too.