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20,525
On Spectral Clustering: Analysis and an algorithm
- ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS
, 2001
"... Despite many empirical successes of spectral clustering methods -- algorithms that cluster points using eigenvectors of matrices derived from the distances between the points -- there are several unresolved issues. First, there is a wide variety of algorithms that use the eigenvectors in slightly ..."
Abstract
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Cited by 1713 (13 self)
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the algorithm, and give conditions under which it can be expected to do well. We also show surprisingly good experimental results on a number of challenging clustering problems.
TO CLUSTERING PROBLEMS
"... This paper deals with the relationship between cluster analysis and computational geometry describfng clustering strategies using a Voronoi diagram approach in general and a line separation approach to improve the efficiency in a special case. We state the following theorems: 1. The set of all centr ..."
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This paper deals with the relationship between cluster analysis and computational geometry describfng clustering strategies using a Voronoi diagram approach in general and a line separation approach to improve the efficiency in a special case. We state the following theorems: 1. The set of all
The Clustering Problem
, 2012
"... ◮ Y ∼ F = {f(y|θ), θ ∈ Θ}, where Θ ∈ Rk ◮ We observe a sample of n independent data y = (y1, y2,...,yn) ◮ We look at the sample as being split into clusters, ..."
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◮ Y ∼ F = {f(y|θ), θ ∈ Θ}, where Θ ∈ Rk ◮ We observe a sample of n independent data y = (y1, y2,...,yn) ◮ We look at the sample as being split into clusters,
Survey of clustering algorithms
- IEEE TRANSACTIONS ON NEURAL NETWORKS
, 2005
"... Data analysis plays an indispensable role for understanding various phenomena. Cluster analysis, primitive exploration with little or no prior knowledge, consists of research developed across a wide variety of communities. The diversity, on one hand, equips us with many tools. On the other hand, the ..."
Abstract
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Cited by 499 (4 self)
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, the profusion of options causes confusion. We survey clustering algorithms for data sets appearing in statistics, computer science, and machine learning, and illustrate their applications in some benchmark data sets, the traveling salesman problem, and bioinformatics, a new field attracting intensive efforts
Mean shift, mode seeking, and clustering
- IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1995
"... Mean shift, a simple iterative procedure that shifts each data point to the average of data points in its neighborhood, is generalized and analyzed in this paper. This generalization makes some k-means like clustering algorithms its special cases. It is shown that mean shift is a mode-seeking proce ..."
Abstract
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Cited by 624 (0 self)
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-seeking process on a surface constructed with a “shadow ” kernel. For Gaussian kernels, mean shift is a gradient mapping. Convergence is studied for mean shift iterations. Cluster analysis is treated as a deterministic problem of finding a fixed point of mean shift that characterizes the data. Applications
Model-Based Clustering, Discriminant Analysis, and Density Estimation
- JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 2000
"... Cluster analysis is the automated search for groups of related observations in a data set. Most clustering done in practice is based largely on heuristic but intuitively reasonable procedures and most clustering methods available in commercial software are also of this type. However, there is little ..."
Abstract
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Cited by 573 (29 self)
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for model-based clustering that provides a principled statistical approach to these issues. We also show that this can be useful for other problems in multivariate analysis, such as discriminant analysis and multivariate density estimation. We give examples from medical diagnosis, mineeld detection, cluster
Distance metric learning, with application to clustering with sideinformation,”
- in Advances in Neural Information Processing Systems 15,
, 2002
"... Abstract Many algorithms rely critically on being given a good metric over their inputs. For instance, data can often be clustered in many "plausible" ways, and if a clustering algorithm such as K-means initially fails to find one that is meaningful to a user, the only recourse may be for ..."
Abstract
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Cited by 818 (13 self)
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Abstract Many algorithms rely critically on being given a good metric over their inputs. For instance, data can often be clustered in many "plausible" ways, and if a clustering algorithm such as K-means initially fails to find one that is meaningful to a user, the only recourse may
Laplacian eigenmaps and spectral techniques for embedding and clustering.
- Proceeding of Neural Information Processing Systems,
, 2001
"... Abstract Drawing on the correspondence between the graph Laplacian, the Laplace-Beltrami op erator on a manifold , and the connections to the heat equation , we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in ..."
Abstract
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Cited by 668 (7 self)
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in a higher dimensional space. The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering. Several applications are considered. In many areas of artificial intelligence, information
Constrained Clustering Problems
"... Summary: In the paper a view, based on the optimization approach, is given on different types of constrained clustering problems and methods for their solution. ..."
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Cited by 3 (0 self)
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Summary: In the paper a view, based on the optimization approach, is given on different types of constrained clustering problems and methods for their solution.
Clustering with Bregman Divergences
- JOURNAL OF MACHINE LEARNING RESEARCH
, 2005
"... A wide variety of distortion functions are used for clustering, e.g., squared Euclidean distance, Mahalanobis distance and relative entropy. In this paper, we propose and analyze parametric hard and soft clustering algorithms based on a large class of distortion functions known as Bregman divergence ..."
Abstract
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Cited by 443 (57 self)
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generalizing the basic idea to a very large class of clustering loss functions. There are two main contributions in this paper. First, we pose the hard clustering problem in terms of minimizing the loss in Bregman information, a quantity motivated by rate-distortion theory, and present an algorithm to minimize
Results 1 - 10
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20,525
