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Approximation Algorithms for Projective Clustering
 Proceedings of the ACM SIGMOD International Conference on Management of data, Philadelphia
, 2000
"... We consider the following two instances of the projective clustering problem: Given a set S of n points in R d and an integer k ? 0; cover S by k hyperstrips (resp. hypercylinders) so that the maximum width of a hyperstrip (resp., the maximum diameter of a hypercylinder) is minimized. Let w ..."
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Cited by 302 (22 self)
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We consider the following two instances of the projective clustering problem: Given a set S of n points in R d and an integer k ? 0; cover S by k hyperstrips (resp. hypercylinders) so that the maximum width of a hyperstrip (resp., the maximum diameter of a hypercylinder) is minimized. Let w
Finding Generalized Projected Clusters in High Dimensional Spaces
"... High dimensional data has always been a challenge for clustering algorithms because of the inherent sparsity of the points. Recent research results indicate that in high dimensional data, even the concept of proximity or clustering may not be meaningful. We discuss very general techniques for projec ..."
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Cited by 194 (8 self)
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for projected clustering which are able to construct clusters in arbitrarily aligned subspaces of lower dimensionality. The subspaces are specific to the clusters themselves. This definition is substantially more general and realistic than currently available techniques which limit the method to only
Projective Clustering by Histograms
 IEEE Transactions on Knowledge and Data Engineering
, 2005
"... Abstract — Recent research suggests that clustering for high dimensional data should involve searching for ”hidden ” subspaces with lower dimensionalities, in which patterns can be observed when data objects are projected onto the subspaces. Discovering such interattribute correlations and location ..."
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Cited by 9 (0 self)
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Abstract — Recent research suggests that clustering for high dimensional data should involve searching for ”hidden ” subspaces with lower dimensionalities, in which patterns can be observed when data objects are projected onto the subspaces. Discovering such interattribute correlations
Sublinear Projective Clustering with Outliers
"... Given a set of n points in ℜ d, a family of shapes S and a number of clusters k, the projective clustering problem is to find a collection of k shapes in S such that the maximum distance from a point to its nearest shape is minimized. Some special cases of the problem include the kline center probl ..."
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Cited by 1 (0 self)
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Given a set of n points in ℜ d, a family of shapes S and a number of clusters k, the projective clustering problem is to find a collection of k shapes in S such that the maximum distance from a point to its nearest shape is minimized. Some special cases of the problem include the kline center
A monte carlo algorithm for fast projective clustering
 In Proceedings of the 2002 ACM SIGMOD International conference on Management of data
, 2002
"... We propose a mathematical formulation for the notion of optimal projective cluster, starting from natural requirements on the density of points in subspaces. This allows us to develop a Monte Carlo algorithm for iteratively computing projective clusters. We prove that the computed clusters are good ..."
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Cited by 104 (1 self)
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We propose a mathematical formulation for the notion of optimal projective cluster, starting from natural requirements on the density of points in subspaces. This allows us to develop a Monte Carlo algorithm for iteratively computing projective clusters. We prove that the computed clusters are good
Efficient Algorithm for Projected Clustering
"... With high dimensional data, natural clusters are expected to exist in different subspaces. We propose the EPC (Efficient Projected Clustering) algorithm to discover the sets of correlated dimensions and the location of the clusters. This algorithm is quite different from previous approaches and has ..."
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With high dimensional data, natural clusters are expected to exist in different subspaces. We propose the EPC (Efficient Projected Clustering) algorithm to discover the sets of correlated dimensions and the location of the clusters. This algorithm is quite different from previous approaches and has
Iterative Projected Clustering by Subspace Mining
 IEEE Transactions on Knowledge and Data Engineering
, 2005
"... Abstract—Irrelevant attributes add noise to highdimensional clusters and render traditional clustering techniques inappropriate. Recently, several algorithms that discover projected clusters and their associated subspaces have been proposed. In this paper, we realize the analogy between mining freq ..."
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Cited by 14 (0 self)
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Abstract—Irrelevant attributes add noise to highdimensional clusters and render traditional clustering techniques inappropriate. Recently, several algorithms that discover projected clusters and their associated subspaces have been proposed. In this paper, we realize the analogy between mining
Linear Time Algorithm for Projective Clustering
"... Abstract. Projective clustering is a problem with both theoretical and practical importance and has received a great deal of attentions in recent years. Given a set of points P in Rd space, projective clustering is to find a set F of k lower dimensional jflats so that the average distance (or squar ..."
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Abstract. Projective clustering is a problem with both theoretical and practical importance and has received a great deal of attentions in recent years. Given a set of points P in Rd space, projective clustering is to find a set F of k lower dimensional jflats so that the average distance (or
Mixtures of Probabilistic Principal Component Analysers
, 1998
"... Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a com ..."
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Cited by 532 (6 self)
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combination of local linear PCA projections. However, conventional PCA does not correspond to a probability density, and so there is no unique way to combine PCA models. Previous attempts to formulate mixture models for PCA have therefore to some extent been ad hoc. In this paper, PCA is formulated within a
Clustering and Projected Clustering with Adaptive Neighbors
"... Many clustering methods partition the data groups based on the input data similarity matrix. Thus, the clustering results highly depend on the data similarity learning. Because the similarity measurement and data clustering are often conducted in two separated steps, the learned data similarity may ..."
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Cited by 3 (2 self)
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to optimize the proposed challenging problem, and show the theoretical analysis on the connections between our method and the Kmeans clustering, and spectral clustering. We also further extend the new clustering model for the projected clustering to handle the highdimensional data. Extensive empirical
Results 1  10
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6,036