Laplacian Matrix for Dimensionality Reduction and Clustering

2019/09/18 by Laurenz Wiskott, Wiskott, Laurenz, Fabian Schönfeld +1
Computer Science · Mathematics · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #cs.LG #stat.ML

paper · pdf · doi:10.48550/arxiv.1909.08381

lecture notes, 30 pages, 9 figures

arxiv created 2019/09/18 · arxiv updated 2019/09/19

Abstract

Many problems in machine learning can be expressed by means of a graph with nodes representing training samples and edges representing the relationship between samples in terms of similarity, temporal proximity, or label information. Graphs can in turn be represented by matrices. A special example is the Laplacian matrix, which allows us to assign each node a value that varies only little between strongly connected nodes and more between distant nodes. Such an assignment can be used to extract a useful feature representation, find a good embedding of data in a low dimensional space, or perform clustering on the original samples. In these lecture notes we first introduce the Laplacian matrix and then present a small number of algorithms designed around it.

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