Euclidean Distance Matrix Optimization: Theory, Algorithms and Applications
Euclidean Distance Matrix (EDM) optimization has become a robust approach for analysing dissimilarity data due to its capacity of handling hard constraints, fast algorithms available and guaranteed error bounds. It has found applications in machine learning (dimension reduction), engineering (sensor network localization), social sciences (multidimensional scaling) and others. This talk will start with a brief introduction of EDM, mainly motivated by the classical multidimensional scaling. We then introduce a fast algorithm (Semismooth Newton-CG) for computing the nearest EDM (NEDM) problem. We will highlight the importance of sparsity in implementing this algorithm. We further extend the NEDM to the setting of embedding high-dimensional data in a low-dimensional space and establish a non-asymptotic error bound for quality embedding. For this extension, an alternating direction method of multiplier is a suitable algorithmic framework. We will also demonstrate a few interesting applications including data visualization of image data and sensor network localization.
Houduo Qi received the BSc in Statistics from Peking University in 1990, MSc in Operational Research and Optimal Control from Qufu Normal University in 1993, and PhD in Operational Research and Optimal Control from Institute of Applied Mathematics, Chinese Academy of Sciences (CAS) in 1996. From 1996 to 1998, he was a Chinese Postdoctoral Fellow at the Institute of Computational Mathematics, CAS. From 1998 to 2003, he was a research fellow and then the Australian Postdoctoral Fellow respectively at The Hong Kong Polytechnic University and The University of New South Wales. In 2004, he was awarded Queen Elizabeth II Fellowship (QEII Fellow) by the Australian Research Council. In September 2004, he joined the University of Southampton (UoS) as a lecturer in Operational Research. He now is Professor and Chair of Optimization at UoS. He is mainly interested in Mathematical Optimization, especially in matrix optimization with applications to finance and statistics. He has been the Area Editor (Optimization) of Asia-Pacific Journal of Operational Research from 2016, Associate Editor for Mathematical Programming Computation (since 2013) and Journal of Operations Research Society of China (since 2016). From 2010, he has been a college member of Engineering and Physical Sciences Research Council, UK.
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