Results 1 - 10 of 3,882

Consistency of spectral clustering

by Ulrike von Luxburg, Mikhail Belkin, Olivier Bousquet , 2004
"... Consistency is a key property of statistical algorithms, when the data is drawn from some underlying probability distribution. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of a popular family of spe ..."
Abstract - Cited by 572 (15 self) - Add to MetaCart
of spectral clustering algorithms, which cluster the data with the help of eigenvectors of graph Laplacian matrices. We show that one of the two of major classes of spectral clustering (normalized clustering) converges under some very general conditions, while the other (unnormalized), is only consistent

On Spectral Clustering: Analysis and an algorithm

by Andrew Y. Ng, Michael I. Jordan, Yair Weiss - 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 - Cited by 1713 (13 self) - Add to MetaCart
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

Self-tuning spectral clustering

by Lihi Zelnik-manor, Pietro Perona - Advances in Neural Information Processing Systems 17 , 2004
"... We study a number of open issues in spectral clustering: (i) Selecting the appropriate scale of analysis, (ii) Handling multi-scale data, (iii) Clustering with irregular background clutter, and, (iv) Finding automatically the number of groups. We first propose that a ‘local ’ scale should be used to ..."
Abstract - Cited by 362 (2 self) - Add to MetaCart
We study a number of open issues in spectral clustering: (i) Selecting the appropriate scale of analysis, (ii) Handling multi-scale data, (iii) Clustering with irregular background clutter, and, (iv) Finding automatically the number of groups. We first propose that a ‘local ’ scale should be used

Multiclass spectral clustering

by Stella X. Yu, Jianbo Shi - In Proc. Int. Conf. Computer Vision , 2003
"... We propose a principled account on multiclass spectral clustering. Given a discrete clustering formulation, we first solve a relaxed continuous optimization problem by eigendecomposition. We clarify the role of eigenvectors as a generator of all optimal solutions through orthonormal transforms. We t ..."
Abstract - Cited by 265 (7 self) - Add to MetaCart
We propose a principled account on multiclass spectral clustering. Given a discrete clustering formulation, we first solve a relaxed continuous optimization problem by eigendecomposition. We clarify the role of eigenvectors as a generator of all optimal solutions through orthonormal transforms. We

Learning spectral clustering

by Francis R. Bach, Michael I. Jordan , 2003
"... Spectral clustering refers to a class of techniques which rely on the eigenstructure of a similarity matrix to partition points into disjoint clusters with points in the same cluster having high similarity and points in different clusters having low similarity. In this paper, we derive a new cost fu ..."
Abstract - Cited by 118 (4 self) - Add to MetaCart
Spectral clustering refers to a class of techniques which rely on the eigenstructure of a similarity matrix to partition points into disjoint clusters with points in the same cluster having high similarity and points in different clusters having low similarity. In this paper, we derive a new cost

spectral clustering

by Ying Liu, Eran Eyal, Ivet Bahar , 2008
"... Motivation: The ability of human immunodeficiency virus-1 (HIV-1) protease to develop mutations that confer multi-drug resistance 15 (MDR) has been a major obstacle in designing rational therapies against HIV. Resistance is usually imparted by a cooperative mechanism that can be elucidated by a cova ..."
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covariance analysis by evaluat-ing the mutual information (MI) between all residue pairs. Spectral clustering of the resulting covariance matrices disclosed two 25 distinctive clusters of correlated residues: the first, observed in set 1 but absent in set 2, contained residues involved in MDR acquisition

Fast Approximate Spectral Clustering

by Donghui Yan, Ling Huang, Michael I. Jordan , 2009
"... Spectral clustering refers to a flexible class of clustering procedures that can produce high-quality clusterings on small data sets but which has limited applicability to large-scale problems due to its computational complexity of O(n 3), with n the number of data points. We extend the range of spe ..."
Abstract - Cited by 58 (1 self) - Add to MetaCart
Spectral clustering refers to a flexible class of clustering procedures that can produce high-quality clusterings on small data sets but which has limited applicability to large-scale problems due to its computational complexity of O(n 3), with n the number of data points. We extend the range

Correlational spectral clustering

by Matthew B. Blaschko, Christoph H. Lampert - In CVPR ’08
"... We present a new method for spectral clustering with paired data based on kernel canonical correlation analysis, called correlational spectral clustering. Paired data are common in real world data sources, such as images with text captions. Traditional spectral clustering algorithms either assume th ..."
Abstract - Cited by 31 (2 self) - Add to MetaCart
We present a new method for spectral clustering with paired data based on kernel canonical correlation analysis, called correlational spectral clustering. Paired data are common in real world data sources, such as images with text captions. Traditional spectral clustering algorithms either assume

Parallel Spectral Clustering

by Yangqiu Song, Wen-yen Chen, Hongjie Bai, Chih-jen Lin, Edward Y. Chang
"... Abstract. Spectral clustering algorithm has been shown to be more effective in finding clusters than most traditional algorithms. However, spectral clustering suffers from a scalability problem in both memory use and computational time when a dataset size is large. To perform clustering on large dat ..."
Abstract - Cited by 38 (2 self) - Add to MetaCart
Abstract. Spectral clustering algorithm has been shown to be more effective in finding clusters than most traditional algorithms. However, spectral clustering suffers from a scalability problem in both memory use and computational time when a dataset size is large. To perform clustering on large

Flexible constrained spectral clustering

by Xiang Wang, Ian Davidson - in KDD, 2010
"... Constrained clustering has been well-studied for algorithms like K-means and hierarchical agglomerative clustering. However, how to encode constraints into spectral clustering remains a developing area. In this paper, we propose a flexible and generalized framework for constrained spectral clusterin ..."
Abstract - Cited by 38 (4 self) - Add to MetaCart
Constrained clustering has been well-studied for algorithms like K-means and hierarchical agglomerative clustering. However, how to encode constraints into spectral clustering remains a developing area. In this paper, we propose a flexible and generalized framework for constrained spectral
Results 1 - 10 of 3,882