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arXiv · 1909.08381

Laplacian Matrix for Dimensionality Reduction and Clustering

Laurenz Wiskott·Fabian Schönfeld
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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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Laurenz Wiskott, Fabian Schönfeld. 2019-09-18. Laplacian Matrix for Dimensionality Reduction and Clustering. https://arxiv.org/abs/1909.08381

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