On the consistency of spectral clustering in the continuum limit

Bamdad Hosseini , Caltech
Event time: 
Monday, November 9, 2020 - 2:30pm
https://yale.zoom.us/j/93776687491 See map
Event description: 

Abstract:  Spectral clustering is a popular unsupervised learning technique for finding meaningful structure in large datasets. A weighted graph is constructed on the dataset, encoding the similarities between the data points. A graph Laplacian operator is then defined on this graph whose spectral geometric content reveals the number and shape of clusters in the data set. In this talk I will present some spectral analysis of graph Laplacians in the  continuum limit where the number of vertices of the graph goes to infinity. In the first part I will discuss how the different normalizations of the graph Laplacian will affect the spectrum of the continuum operator and introduce a notion of a balanced normalization that has desirable qualities in large data settings. In the second part of the talk I will focus on a specific choice of the graph Laplacian and present some results on the consistency of spectral clustering by first studying the continuum limit operator and extending its properties to discrete approximations.

Event Type: 
Applied Mathematics