Results 1  10
of
1,021,963
A simple D 2sampling based PTAS for kmeans and other Clustering problems
"... Abstract. Given a set of points P ⊂ R d, the kmeans clustering problem is to find a set of k centers C = {c1,..., ck}, ci ∈ R d, such that the objective function ∑ x∈P d(x, C)2, where d(x, C) denotes the distance between x and the closest center in C, is minimized. This is one of the most prominent ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Abstract. Given a set of points P ⊂ R d, the kmeans clustering problem is to find a set of k centers C = {c1,..., ck}, ci ∈ R d, such that the objective function ∑ x∈P d(x, C)2, where d(x, C) denotes the distance between x and the closest center in C, is minimized. This is one of the most
A simple D2sampling based PTAS for kmeans and other clustering problems. Algorithmica
, 2013
"... ar ..."
Xmeans: Extending Kmeans with Efficient Estimation of the Number of Clusters
 In Proceedings of the 17th International Conf. on Machine Learning
, 2000
"... Despite its popularity for general clustering, Kmeans suffers three major shortcomings; it scales poorly computationally, the number of clusters K has to be supplied by the user, and the search is prone to local minima. We propose solutions for the first two problems, and a partial remedy for the t ..."
Abstract

Cited by 412 (5 self)
 Add to MetaCart
Despite its popularity for general clustering, Kmeans suffers three major shortcomings; it scales poorly computationally, the number of clusters K has to be supplied by the user, and the search is prone to local minima. We propose solutions for the first two problems, and a partial remedy
Mean shift, mode seeking, and clustering
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1995
"... AbstractMean 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 kmeans like clustering algorithms its special cases. It is shown that mean shift is a modeseeki ..."
Abstract

Cited by 620 (0 self)
 Add to MetaCart
AbstractMean 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 kmeans like clustering algorithms its special cases. It is shown that mean shift is a mode
Refining Initial Points for KMeans Clustering
, 1998
"... Practical approaches to clustering use an iterative procedure (e.g. KMeans, EM) which converges to one of numerous local minima. It is known that these iterative techniques are especially sensitive to initial starting conditions. We present a procedure for computing a refined starting condition fro ..."
Abstract

Cited by 308 (5 self)
 Add to MetaCart
Practical approaches to clustering use an iterative procedure (e.g. KMeans, EM) which converges to one of numerous local minima. It is known that these iterative techniques are especially sensitive to initial starting conditions. We present a procedure for computing a refined starting condition
A ptas for kmeans clustering based on weak coresets
 DELIS – Dynamically Evolving, LargeScale Information Systems
, 2007
"... Given a point set P ⊆ R d the kmeans clustering problem is to find a set C = {c1,..., ck} of k points and a partition of P into k clusters C1,..., Ck such that the sum of squared errors �k � i=1 p∈C �p − ci� i 2 2 is minimized. For given centers this cost function is minimized by assigning points t ..."
Abstract

Cited by 30 (11 self)
 Add to MetaCart
Given a point set P ⊆ R d the kmeans clustering problem is to find a set C = {c1,..., ck} of k points and a partition of P into k clusters C1,..., Ck such that the sum of squared errors �k � i=1 p∈C �p − ci� i 2 2 is minimized. For given centers this cost function is minimized by assigning points
ModelBased 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

Cited by 557 (28 self)
 Add to MetaCart
for modelbased 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
 ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 15
, 2003
"... 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 Kmeans initially fails to find one that is meaningful to a user, the only recourse may be for the us ..."
Abstract

Cited by 799 (14 self)
 Add to MetaCart
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 Kmeans initially fails to find one that is meaningful to a user, the only recourse may
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

Cited by 1697 (13 self)
 Add to MetaCart
in slightly different ways. Second, many of these algorithms have no proof that they will actually compute a reasonable clustering. In this paper, we present a simple spectral clustering algorithm that can be implemented using a few lines of Matlab. Using tools from matrix perturbation theory, we analyze
Results 1  10
of
1,021,963