Results 1  10
of
5,248
Consistency of spectral clustering
, 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
Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms
 IEEE Transactions on Information Theory
, 2005
"... Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems t ..."
Abstract

Cited by 585 (13 self)
 Add to MetaCart
the Bethe approximation, and corresponding generalized belief propagation (GBP) algorithms. We emphasize the conditions a free energy approximation must satisfy in order to be a “valid ” or “maxentnormal ” approximation. We describe the relationship between four different methods that can be used
Adapting kmedians to generate normalized cluster centers
 In Proceedings of the Sixth SIAM International Conference on Data Mining
"... Many applications of clustering require the use of normalized data, such as text or mass spectra mining. The spherical Kmeans algorithm [6], an adaptation of the traditional Kmeans algorithm, is highly useful for data of this kind because it produces normalized cluster centers. The Kmedians clust ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Many applications of clustering require the use of normalized data, such as text or mass spectra mining. The spherical Kmeans algorithm [6], an adaptation of the traditional Kmeans algorithm, is highly useful for data of this kind because it produces normalized cluster centers. The K
Generating Normalized Cluster Centers with kMedians
"... Many applications of clustering require the use of normalized data, such as text or mass spectra mining. The spherical kmeans algorithm [6], an adaptation of the traditional kmeans algorithm, is highly useful for data of this kind because it produces normalized cluster centers. The kmedians clust ..."
Abstract
 Add to MetaCart
Many applications of clustering require the use of normalized data, such as text or mass spectra mining. The spherical kmeans algorithm [6], an adaptation of the traditional kmeans algorithm, is highly useful for data of this kind because it produces normalized cluster centers. The k
Concept Decompositions for Large Sparse Text Data using Clustering
 Machine Learning
, 2000
"... . Unlabeled document collections are becoming increasingly common and available; mining such data sets represents a major contemporary challenge. Using words as features, text documents are often represented as highdimensional and sparse vectorsa few thousand dimensions and a sparsity of 95 to 99 ..."
Abstract

Cited by 407 (27 self)
 Add to MetaCart
to 99% is typical. In this paper, we study a certain spherical kmeans algorithm for clustering such document vectors. The algorithm outputs k disjoint clusters each with a concept vector that is the centroid of the cluster normalized to have unit Euclidean norm. As our first contribution, we
Clustering by compression
 IEEE Transactions on Information Theory
, 2005
"... Abstract—We present a new method for clustering based on compression. The method does not use subjectspecific features or background knowledge, and works as follows: First, we determine a parameterfree, universal, similarity distance, the normalized compression distance or NCD, computed from the l ..."
Abstract

Cited by 297 (25 self)
 Add to MetaCart
Abstract—We present a new method for clustering based on compression. The method does not use subjectspecific features or background knowledge, and works as follows: First, we determine a parameterfree, universal, similarity distance, the normalized compression distance or NCD, computed from
Segmentation using eigenvectors: A unifying view
 In ICCV
, 1999
"... Automatic grouping and segmentation of images remains a challenging problem in computer vision. Recently, a number of authors have demonstrated good performance on this task using methods that are based on eigenvectors of the a nity matrix. These approaches are extremely attractive in that they are ..."
Abstract

Cited by 380 (1 self)
 Add to MetaCart
on eigenvectors of the (possibly normalized) \a nity matrix". Figure 1a shows two clusters of points and gure 1b shows the a nity matrix de ned by:
Eigentaste: A Constant Time Collaborative Filtering Algorithm
, 2000
"... Eigentaste is a collaborative filtering algorithm that uses universal queries to elicit realvalued user ratings on a common set of items and applies principal component analysis (PCA) to the resulting dense subset of the ratings matrix. PCA facilitates dimensionality reduction for offline clusterin ..."
Abstract

Cited by 378 (6 self)
 Add to MetaCart
clustering of users and rapid computation of recommendations. For a database of n users, standard nearestneighbor techniques require O(n) processing time to compute recommendations, whereas Eigentaste requires O(1) (constant) time. We compare Eigentaste to alternative algorithms using data from Jester
Multiclass spectral clustering
 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
Results 1  10
of
5,248