讲座时间：7月20日上午9：30-11：50
讲座地点：曹光彪主楼218教室
讲座人：Ohio州立大学教授Prof.Yusu WANG, Prof. Mikhail Belkin
9:30~10:30
Mikhail Belkin: “Geometry, Manifold and Semi-supervised Learning”
10:50~11:50
Yusu Wang: “Laplace, Gradients, and Integral from Point Clouds Data --- A Geometric View”
此次讲座纳入研究生读书报告范围，盖章在九月开学以后到研究生科贺老师处盖章。
Abstract:
1、Title:
Geometry, Manifold and Semi-supervised Learning
Abstract:
In recent years there has been a considerable amount of work on understanding structure in multidimensional non-linear data.
In this talk I will discuss the role of data geometry in machine learning with particular emphasis on the manifold setting, where data is assumed to lie on or
near a low dimensional manifold in a high dimensional space. I will discuss why this setting is interesting and, arguably, ubiquitous, and how such
structures can be used to develop algorithms for various inferential tasks. In particular, I will talk about the role of the Laplace operator and the
heat equation in manifold learning and their applications to various problems, including semi-supervised learning and clustering. I will also mention some recent theoretical advances, such as spectral convergence.
Brief Bio:
Mikhail Belkin received his Ph.D from the Mathematics department at University of Chicago. He is currently an Assistant Professor in Computer Science and Statistics at Ohio State University. He was a co-organizer of the Chicago Machine Learning Summer School in 2005, the Workshop on Geometry, Random Matrices, and Statistical Inference in SAMSI in 2007, and the 2009 Machine Learning Summer School/Workshop on Theory and Practice of Computational Learning.
His primary research interests are artificial intelligence and statistical pattern recognition. Together with Partha Niyogi, he proposed the Laplacian Eigenmap method for dimensionality reduction, and his recent research focuses on designing and analyzing algorithms for machine learning based on non-linear structure of multi-dimensional data, such as manifold and spectral methods. Mikhail Belkin received the National Science Foundation (NSF) Career Award in 2006. His research is currently supported by the National Science Foundation and the U.S Airforce Research Foundation.
2、Yusu Wang
Title: Laplace, Gradients, and Integral from Point Clouds Data --- A Geometric View
Abstract: The Laplace-Beltrami operator of a given manifold (e.g, a surface) is a fundamental object encoding the intrinsic geometry of the underlying manifold. It has many properties useful for practical applications from areas such as graphics and machine learning. For example, its relation to the heat diffusion makes it a primary tool for surface smoothing in graphics. It has recently been used for a broad range of graphics and geometric optimization applications, such as mesh editing, compression, matching, segmentaion, and etc.
However, many a time, the underlying manifold is only accessible through a discrete approximation, either as a mesh or simply as a set of points. The important question is then how to approximate the Laplace operator and other geometric invariants from such discrete setting. Previously, much work has been done on approximating Laplace operator from points sampled from some probabilistic distribution. In this talk, we initiate the study of a spectral point clouds processing framework in a more general non-statistical setting: I will first describe our recent results on approximating the Laplace operator for general point clouds by a geometric approach. Since the Laplace operator encodes all intrinsic geometry information of the input manifold, once it is approximated, we can then estimate other geometric information from it. I will next focus on two such applications: estimating gradients and integral of an input function from simply the point clouds data.
Brief Bio: Yusu Wang is mainly interested in computational geometry, computational topology, as well as their applications in visualization, graphics and structural biology. She obtained her Ph.D degree from the Computer Science Dept. at Duke University in 2004 (where she received the best Ph.D Dissertation Award). From 2004 - 2005, she was a postdoctoral fellow in the Geometric Computing Lab in the CS Dept. at Stanford University. She joined the Computer Science and Engineering Dept. at the Ohio State University in 2005. She received the U.S Department of Energy (DOE) Early Career Award in 2006 and the U.S National Science Foundation (NSF) Career Award in 2008. She is currently on the Editorial board for Journal of Computational Geometry.
讲座地点：曹光彪主楼218教室
讲座人：Ohio州立大学教授Prof.Yusu WANG, Prof. Mikhail Belkin
9:30~10:30
Mikhail Belkin: “Geometry, Manifold and Semi-supervised Learning”
10:50~11:50
Yusu Wang: “Laplace, Gradients, and Integral from Point Clouds Data --- A Geometric View”
此次讲座纳入研究生读书报告范围，盖章在九月开学以后到研究生科贺老师处盖章。
Abstract:
1、Title:
Geometry, Manifold and Semi-supervised Learning
Abstract:
In recent years there has been a considerable amount of work on understanding structure in multidimensional non-linear data.
In this talk I will discuss the role of data geometry in machine learning with particular emphasis on the manifold setting, where data is assumed to lie on or
near a low dimensional manifold in a high dimensional space. I will discuss why this setting is interesting and, arguably, ubiquitous, and how such
structures can be used to develop algorithms for various inferential tasks. In particular, I will talk about the role of the Laplace operator and the
heat equation in manifold learning and their applications to various problems, including semi-supervised learning and clustering. I will also mention some recent theoretical advances, such as spectral convergence.
Brief Bio:
Mikhail Belkin received his Ph.D from the Mathematics department at University of Chicago. He is currently an Assistant Professor in Computer Science and Statistics at Ohio State University. He was a co-organizer of the Chicago Machine Learning Summer School in 2005, the Workshop on Geometry, Random Matrices, and Statistical Inference in SAMSI in 2007, and the 2009 Machine Learning Summer School/Workshop on Theory and Practice of Computational Learning.
His primary research interests are artificial intelligence and statistical pattern recognition. Together with Partha Niyogi, he proposed the Laplacian Eigenmap method for dimensionality reduction, and his recent research focuses on designing and analyzing algorithms for machine learning based on non-linear structure of multi-dimensional data, such as manifold and spectral methods. Mikhail Belkin received the National Science Foundation (NSF) Career Award in 2006. His research is currently supported by the National Science Foundation and the U.S Airforce Research Foundation.
2、Yusu Wang
Title: Laplace, Gradients, and Integral from Point Clouds Data --- A Geometric View
Abstract: The Laplace-Beltrami operator of a given manifold (e.g, a surface) is a fundamental object encoding the intrinsic geometry of the underlying manifold. It has many properties useful for practical applications from areas such as graphics and machine learning. For example, its relation to the heat diffusion makes it a primary tool for surface smoothing in graphics. It has recently been used for a broad range of graphics and geometric optimization applications, such as mesh editing, compression, matching, segmentaion, and etc.
However, many a time, the underlying manifold is only accessible through a discrete approximation, either as a mesh or simply as a set of points. The important question is then how to approximate the Laplace operator and other geometric invariants from such discrete setting. Previously, much work has been done on approximating Laplace operator from points sampled from some probabilistic distribution. In this talk, we initiate the study of a spectral point clouds processing framework in a more general non-statistical setting: I will first describe our recent results on approximating the Laplace operator for general point clouds by a geometric approach. Since the Laplace operator encodes all intrinsic geometry information of the input manifold, once it is approximated, we can then estimate other geometric information from it. I will next focus on two such applications: estimating gradients and integral of an input function from simply the point clouds data.
Brief Bio: Yusu Wang is mainly interested in computational geometry, computational topology, as well as their applications in visualization, graphics and structural biology. She obtained her Ph.D degree from the Computer Science Dept. at Duke University in 2004 (where she received the best Ph.D Dissertation Award). From 2004 - 2005, she was a postdoctoral fellow in the Geometric Computing Lab in the CS Dept. at Stanford University. She joined the Computer Science and Engineering Dept. at the Ohio State University in 2005. She received the U.S Department of Energy (DOE) Early Career Award in 2006 and the U.S National Science Foundation (NSF) Career Award in 2008. She is currently on the Editorial board for Journal of Computational Geometry.
