Clustering and Classification From the Core to the Edge - Thomas Strohmer, California University

Explore cutting-edge advances in data science mathematics through this 41-minute conference talk by Thomas Strohmer from California University. Delve into unsupervised learning techniques, including diffusion maps and spectral clustering, while examining their applications in data shape analysis, community detection, and graph cuts. Investigate the limitations of k-means clustering and discover alternative approaches like kernel k-means and nonlinear embedding. Learn about Laplacian eigenmaps and their connection to spectral clustering, and understand the mathematical foundations of graph cuts and community detection in stochastic block models. Gain insights into semi-supervised clustering and the challenges of on-device machine learning in the age of surveillance capitalism. Discover compressive machine learning techniques, including compressive classification and deep learning, and their potential applications in edge computing. Conclude with an exploration of structured manifold projection and its initial results on the MNIST dataset, providing a comprehensive overview of current trends and future directions in data science and machine learning.

Intro
Outline
Unsupervised Learning via diffusion maps
Spectral clustering: learning the shape of data
Spectral clustering, graph cuts, community detection
Data clustering and unsupervised learning
Limitation of k-means
Kernel k-means and nonlinear embedding
Laplacian eigenmaps, k-means, spectral clustering
Comments on spectral clustering
A graph cut perspective
RatioCut and the graph Laplacian
Convex relaxation of RatioCut
Intuition
Finding the optimal graph cut via SDP relaxation
A short tour of the proof - Game of Cones
Spectral clustering for two concentric circles
Community detection under stochastic block model
Graph cuts and the stochastic block model
Semisupervised clustering
The Age of Surveillance Capitalism
What happens on the edge, stays on the edge!
Al on the edge
Challenges of on-device machine learning
Compressive machine learning
Compressive classification
Compressive deep learning
Construction of projection matrix
Structured manifold projection
Initial results on MNIST dataset
Conclusion and Outlook