Clustering and ranking is often based on pairwise similarities (metric data) or comparisons (ordinal data). Most methods assume that the entire collection of all possible pairwise similarities or comparisons are known, but in high-dimensional settings there may be missing data and/or the costs of collecting this information may be prohibitive. T...
Creator:
Nowak, Robert (University of Wisconsin, Madison)
Created:
2011-09-26
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Clustering, or finding groups in data, is as old as machine learningitself. However, as more people use clustering in a variety ofsettings, the last few years we have brought unprecedenteddevelopments in this field.This tutorial will survey the most important clustering methods in usetoday from a unifying perspective, and will then present some ...
Creator:
Meila, Marina (University of Washington)
Created:
2013-10-04
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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-exis...
Creator:
Mémoli, Facundo (The Ohio State University)
Created:
2014-03-05
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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 lin...
Creator:
Vidal, René (Johns Hopkins University)
Created:
2008-10-28
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
To, effectively, combat the opioid epidemic and associated infectious diseases we must elucidate factors associated with therapeutic initiation, adherence and completion of therapy. However, the patient population compounds the problem of elucidation of these factors. Substance users are characterized by lack of medical care, generally limited f...
Creator:
Markatou, Marianthi (University at Buffalo (SUNY))
Created:
2018-11-08
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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 sugges...
Creator:
Koditschek, Daniel E. (University of Pennsylvania)
Created:
2014-02-10
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Identification of subgroups in a biomedical study with subjects sampled from a heterogeneous population has attracted considerable attention in recent years. Technically, subgroup group analysis may be formulated as a type of supervised clustering analysis with group labels being latent. The method of finite mixture model is the most widely used...
Creator:
Song, Peter (University of Michigan)
Created:
2018-11-08
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
1) What have have been recent advances on manifold clustering?a) Algebraic approachesb) Spectral approachesc) Probabilistic approaches2) What have been successful applications of manifoldclustering?3) What is the role of topology, geometry, and statistics, inmanifold learning, i.e.,a) clustering based on the dimensions of the manifoldsb) cluster...
Creator:
Vidal, René (Johns Hopkins University)
Created:
2008-10-29
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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 an...
Creator:
Lerman, Gilad (University of Minnesota, Twin Cities)
Created:
2008-10-29
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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 robus...
Creator:
Lerman, Gilad (University of Minnesota, Twin Cities)
Created:
2011-10-27
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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 cluster...
Creator:
Singh, Aarti (Carnegie Mellon University)
Created:
2011-10-24
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The cluster of receptors and associated proteins at the 'frontend' of the E. coli chemotaxis pathway is a paradigm formembrane complexes in cells. Like focal adhesions and synapses,it acts as a solid-state computational device that amplifies,integrates, and parses chemical signals from the environmentand relays the output to the rest of the cell...
Creator:
Bray, Dennis
Created:
2008-05-30
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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 underlyinggraph-distances. For example, internet hosts can be clustered by measured latencies or traffic correlations and genes can...
Creator:
Eriksson, Brian (University of Wisconsin, Madison); Nowak, Robert (University of Wisconsin, Madison)
Created:
2011-10-24
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In recent years network analysis have become the focus of muchresearch in many fields including biology, communication studies, economics, information science, organizational studies, and social psychology. Communities or clusters of highly connected actors form an essential feature in the structure of several empirical networks. Spectral cluste...
Creator:
Yu, Bin (University of California, Berkeley)
Created:
2011-09-26
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
