Communications of the ACM
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
A Spectral Technique for Coloring Random 3-Colorable Graphs
SIAM Journal on Computing
A constant-factor approximation algorithm for the k-median problem (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Learning mixtures of arbitrary gaussians
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
AI Game Programming Wisdom
Diffusion Kernels on Graphs and Other Discrete Input Spaces
ICML '02 Proceedings of the Nineteenth International Conference on Machine Learning
Approximation schemes for clustering problems
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Learning Mixtures of Gaussians
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Spectral Partitioning of Random Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Clustering with Qualitative Information
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Random sampling and approximation of MAX-CSPs
Journal of Computer and System Sciences - STOC 2002
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
Correlation Clustering: maximizing agreements via semidefinite programming
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
On clusterings: Good, bad and spectral
Journal of the ACM (JACM)
Machine Learning
A spectral algorithm for learning mixture models
Journal of Computer and System Sciences - Special issue on FOCS 2002
Aggregating inconsistent information: ranking and clustering
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On Learning Mixtures of Heavy-Tailed Distributions
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
On a theory of learning with similarity functions
ICML '06 Proceedings of the 23rd international conference on Machine learning
A divide-and-merge methodology for clustering
ACM Transactions on Database Systems (TODS)
Spectral clustering by recursive partitioning
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
How good is a kernel when used as a similarity measure?
COLT'07 Proceedings of the 20th annual conference on Learning theory
The spectral method for general mixture models
COLT'05 Proceedings of the 18th annual conference on Learning Theory
On spectral learning of mixtures of distributions
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Structural risk minimization over data-dependent hierarchies
IEEE Transactions on Information Theory
A theory of learning with similarity functions
Machine Learning
Clustering with Interactive Feedback
ALT '08 Proceedings of the 19th international conference on Algorithmic Learning Theory
Combinatorial algorithms for nearest neighbors, near-duplicates and small-world design
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Approximate clustering without the approximation
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Combinatorial Framework for Similarity Search
SISAP '09 Proceedings of the 2009 Second International Workshop on Similarity Search and Applications
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
Fast euclidean minimum spanning tree: algorithm, analysis, and applications
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
Nearest neighbor search: algorithmic perspective
SIGSPATIAL Special
Clustering with or without the approximation
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Predicting the labels of an unknown graph via adaptive exploration
Theoretical Computer Science
Center-based clustering under perturbation stability
Information Processing Letters
Center-Wise intra-inter silhouettes
SUM'12 Proceedings of the 6th international conference on Scalable Uncertainty Management
Data stability in clustering: a closer look
ALT'12 Proceedings of the 23rd international conference on Algorithmic Learning Theory
Clustering under approximation stability
Journal of the ACM (JACM)
The Journal of Machine Learning Research
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Problems of clustering data from pairwise similarity information are ubiquitous in Computer Science. Theoretical treatments typically view the similarity information as ground-truth and then design algorithms to (approximately) optimize various graph-based objective functions. However, in most applications, this similarity information is merely based on some heuristic; the ground truth is really the unknown correct clustering of the data points and the real goal is to achieve low error on the data. In this work, we develop a theoretical approach to clustering from this perspective. In particular, motivated by recent work in learning theory that asks "what natural properties of a similarity (or kernel) function are sufficient to be able to learn well?" we ask "what natural properties of a similarity function are sufficient to be able to cluster well?" To study this question we develop a theoretical framework that can be viewed as an analog of the PAC learning model for clustering, where the object of study, rather than being a concept class, is a class of (concept, similarity function) pairs, or equivalently, a property the similarity function should satisfy with respect to the ground truth clustering. We then analyze both algorithmic and information theoretic issues in our model. While quite strong properties are needed if the goal is to produce a single approximately-correct clustering, we find that a number of reasonable properties are sufficient under two natural relaxations: (a) list clustering: analogous to the notion of list-decoding, the algorithm can produce a small list of clusterings (which a user can select from) and (b) hierarchical clustering: the algorithm's goal is to produce a hierarchy such that desired clustering is some pruning of this tree (which a user could navigate). We develop a notion of the clustering complexity of a given property (analogous to notions of capacity in learning theory), that characterizes its information-theoretic usefulness for clustering. We analyze this quantity for several natural game-theoretic and learning-theoretic properties, as well as design new efficient algorithms that are able to take advantage of them. Our algorithms for hierarchical clustering combine recent learning-theoretic approaches with linkage-style methods. We also show how our algorithms can be extended to the inductive case, i.e., by using just a constant-sized sample, as in property testing. The analysis here uses regularity-type results of [FK] and [AFKK].