PPT-Graph Theory and Spectral Methods for Pattern Recognition

Richard C Wilson Dept of Computer Science University of York Graphs and Networks Graphs and networks are all around us Simple networks 10s to 100s of vertices Graphs and networks. Spielman September 5 2012 31 About these notes These notes are not necessarily an accurate representation of what happened in class The notes written before class say what I think I should say The notes written after class way what I wish I said Be 1 Introduction Spectral graph theory has a long history In the early days matrix theory and linear algebra were used to analyze adjacency matrices of graphs Algebraic meth ods have proven to be especially e64256ective in treating graphs which are reg INTRODUCTION Pattern recognition stems from the need for automated machine recognition of objects signals or images or the need for automated decisionmaking based on a given set of parameters Despite over half a century of productive research patter KChung Author address University of Pennsylvania Philadelphia Pennsylvania 19104 Email address chungmathupennedu brPage 2br Contents Chapter 1 Eigenvalues and the Laplacian of a graph 1 11 Introduction 1 12 The Laplacian and eigenvalue . Pattern Recognition. John Beech. School of Psychology. PS1000.  . 2. Pattern Recognition. The term “pattern recognition” can refer to being able to . recognise. 2-D patterns, in particular alphanumerical characters. But “pattern recognition” is also understood to be the study of how we . Gregory Moore, Rutgers University. Strings-Math, Bonn, July, 2012. P. . Aspinwall,W. .-y. . Chuang,E.Diaconescu,J. . . Manschot. , . Y. . . Soibelman. D. . Gaiotto. & A. . Neitzke. D. Van den . . social . and neural network data. Darren A. Narayan. Rochester Institute of Technology. Joint work with Roger Vargas, Williams College, Bradford Mahon and Frank Garcea, Rochester Center for Brain Imaging, University of Rochester. Or, Why Can’t I Read My Statistics Notes?. Overview. How Do We Read?. More specifically, how does the brain recognize letters?. Pattern Recognition. How does pattern recognition in the brain work?. One of these things is not like the other…. spectral clustering (a la Ng-Jordan-Weiss). data. similarity graph. edges have weights . w. (. i. ,. j. ). e.g.. the . Laplacian. diagonal matrix . D. Normalized . . social . and neural network data. Darren A. Narayan. Rochester Institute of Technology. Joint work with Roger Vargas, Williams College, Bradford Mahon and Frank Garcea, Rochester Center for Brain Imaging, University of Rochester. Richard C. Wilson. Dept. of Computer Science. University of York. Graphs and Networks. Graphs . and. networks . are all around us. ‘Simple’ networks. 10s to 100s of vertices. Graphs and networks. Disorders. Richard J. Barohn, MD. Chair, Department of Neurology. Gertrude and Dewey Ziegler Professor of Neurology. University Distinguished Professor. Vice Chancellor for Research. University of Kansas Medical Center. Gregory Moore, Rutgers University. Strings-Math, Bonn, July, 2012. P. . Aspinwall,W. .-y. . Chuang,E.Diaconescu,J. . . Manschot. , . Y. . . Soibelman. D. . Gaiotto. & A. . Neitzke. D. Van den . Representation. Chumphol Bunkhumpornpat, Ph.D.. Department of Computer Science. Faculty of Science. Chiang Mai University. Learning Objectives. KDD Process. Know that patterns can be represented as. Vectors.