Campuses:

Clustering

Monday, June 1, 2015 - 10:00am - 11:00am
Dylan Rupel (Northeastern University)
Wednesday, October 29, 2008 - 5:15pm - 6:15pm
René Vidal (Johns Hopkins University)

1) What have have been recent advances on manifold
clustering?

a) Algebraic approaches

b) Spectral approaches

c) Probabilistic approaches


2) What have been successful applications of manifold
clustering?


3) What is the role of topology, geometry, and statistics, in
manifold learning, i.e.,

a) clustering based on the dimensions of the manifolds

b) clustering based on geometry

c) clustering based on statistics

Wednesday, October 29, 2008 - 10:55am - 11:45am
Gilad Lerman (University of Minnesota, Twin Cities)
We propose a fast multi-way spectral clustering algorithm for multi-manifold data modeling. We describe the supporting theory as well as the practical choices guided by it. We emphasize the case of hybrid linear modeling, i.e., when the manifolds are affine subspaces in a Euclidean space, and then extend this setting to more general manifolds and other embedding metric spaces. We exemplify applications of the algorithm to several real-world problems while comparing it with other methods.
Tuesday, October 28, 2008 - 12:15pm - 1:05pm
René Vidal (Johns Hopkins University)
Over the past few years, various techniques have been developed for learning a low-dimensional representation of data lying in a nonlinear manifold embedded in a high-dimensional space. Unfortunately, most of these techniques are limited to the analysis of a single submanifold of a Euclidean space and suffer from degeneracies when applied to linear manifolds (subspaces). The simultaneous segmentation and estimation of a collection of submanifolds from sample data points is a challenging problem that is often thought of as chicken-and-egg.
Wednesday, March 5, 2014 - 10:15am - 11:05am
Facundo Mémoli (The Ohio State University)
I'll describe a framework for studying what happens when one imposes various structural conditions on clustering schemes and tries to identify all methods that comply with such conditions. Within this framework, it is possible to prove a theorem analogous to one of J. Kleinberg, in which one obtains existence and uniqueness instead of a non-existence result. We also obtain a full classification of all clustering schemes satisfying a condition we
refer to as excisiveness. The classification can be changed by varying the notion
Monday, February 10, 2014 - 11:30am - 12:20pm
Daniel Koditschek (University of Pennsylvania)
Hierarchical clustering is a well-known and widely used method of unsupervised data mining and pattern analysis. Less attention has been paid its potential role in specifying and controlling the coordination of swarms of actively controlled particles. Nevertheless, the near ubiquity of hierarchical command structure in human organizations suggests the potential value of formalizing this “relaxed” but “organized “ mode of large group coordination and control.
Friday, October 4, 2013 - 9:00am - 10:15am
Marina Meila (University of Washington)
Clustering, or finding groups in data, is as old as machine learning
itself. However, as more people use clustering in a variety of
settings, the last few years we have brought unprecedented
developments in this field.

This tutorial will survey the most important clustering methods in use
today from a unifying perspective, and will then present some of the
current paradigms shifts in data clustering.
Thursday, October 27, 2011 - 4:15pm - 5:15pm
Gilad Lerman (University of Minnesota, Twin Cities)
Motivated by talks from the first day of this workshop, we discuss in more detail modelling data by multiple subspaces, a.k.a., subspace clustering. We emphasize various theoretical results supporting the performance of some of these algorithms. In particular, we study in depth the minimizer obtained by a common energy minimization and its robustness to noise and outliers. We relate this work to recent works on robust PCA.
Monday, October 24, 2011 - 1:30pm - 2:30pm
Aarti Singh (Carnegie-Mellon University)
Despite the empirical success of spectral clustering, its performance under noise and incomplete data is not well understood. This talk will provide a precise characterization of the misclustering rate of spectral clustering for large graphs. Using minimax theory, we establish information theoretic lower bounds on the amount of noise any clustering algorithm can tolerate and demonstrate that spectral clustering is near-optimal. The gap relative to the optimal performance is the statistical price that needs to be paid for computational efficiency.
Monday, October 24, 2011 - 9:00am - 10:00am
Brian Eriksson (University of Wisconsin, Madison), Robert Nowak (University of Wisconsin, Madison)
Graphs are commonly used to represent complex networks, such as the internet or
biological systems. The structure of a graph can be inferred by clustering
vertices based on dissimilarity measures correlated with the underlying
graph-distances. For example, internet hosts can be clustered by measured
latencies or traffic correlations and genes can be clustered according to
responses to varied experimental conditions. These clusters reveal the
structure of the underlying graph; e.g., internet routing or functional

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