Lecture notes: Laplacian Matrix for Dimensionality Reduction and Clustering

Thoughts, Laplacian Matrix


Here you can find the lecture notes "Laplacian Matrix for Dimensionality Reduction and Clustering" by Prof. Dr. Laurenz Wiskott from the Institute of Neuroinformatics at Ruhr-Universität Bochum. Another version can be found on the arXiv: https://arxiv.org/abs/1909.08381.

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 the Laplacian matrix is introduced and then a small number of algorithms presented designed around it.

Furthermore, you can find exercises and solutions to the lecture.


Prof. Dr. Laurenz Wiskott


Information Science & Technology

Natural Sciences




cc by-sa

Laurenz Wiskott, This work (except for all figures from other sources, if present) is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License

Date of publication

Fri, 27. Sep 2019

Sprache des Angebots