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Robust Recovery of Signals From a Structured Union of Subspaces
, 2008
"... Traditional sampling theories consider the problem of reconstructing an unknown signal x from a series of samples. A prevalent assumption which often guarantees recovery from the given measurements is that x lies in a known subspace. Recently, there has been growing interest in nonlinear but structu ..."
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Cited by 221 (47 self)
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Traditional sampling theories consider the problem of reconstructing an unknown signal x from a series of samples. A prevalent assumption which often guarantees recovery from the given measurements is that x lies in a known subspace. Recently, there has been growing interest in nonlinear
Entropybased Subspace Clustering for Mining Numerical Data
, 1999
"... Mining numerical data is a relatively difficult problem in data mining. Clustering is one of the techniques. We consider a database with numerical attributes, in which each transaction is viewed as a multidimensional vector. By studying the clusters formed by these vectors, we can discover certain ..."
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Cited by 162 (1 self)
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dimensional data set. This problem is known as subspace clustering. We follow the basic assumptions of previous work CLIQUE. It is found that the number of subspaces with clustering is very large, and a criterion called the coverage is proposed in CLIQUE for the pruning. In addition to coverage, we identify new
Robust Subspace Segmentation by LowRank Representation
"... We propose lowrank representation (LRR) to segment data drawn from a union of multiple linear (or affine) subspaces. Given a set of data vectors, LRR seeks the lowestrank representation among all the candidates that represent all vectors as the linear combination of the bases in a dictionary. Unlik ..."
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Cited by 145 (25 self)
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We propose lowrank representation (LRR) to segment data drawn from a union of multiple linear (or affine) subspaces. Given a set of data vectors, LRR seeks the lowestrank representation among all the candidates that represent all vectors as the linear combination of the bases in a dictionary
Multilinear Subspace Analysis of Image Ensembles
 PROCEEDINGS OF 2003 IEEE COMPUTER SOCIETY CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION
, 2003
"... Multilinear algebra, the algebra of higherorder tensors, offers a potent mathematical framework for analyzing ensembles of images resulting from the interaction of any number of underlying factors. We present a dimensionality reduction algorithm that enables subspace analysis within the multilinear ..."
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Cited by 119 (2 self)
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the multilinear framework. This Nmode orthogonal iteration algorithm is based on a tensor decomposition known as the Nmode SVD, the natural extension to tensors of the conventional matrix singular value decomposition (SVD). We demonstrate the power of multilinear subspace analysis in the context of facial image
YET ANOTHER SUBSPACE TRACKER
"... This paper introduces a new algorithm for tracking the major subspace of the correlation matrix associated with time series. This algorithm greatly outperforms many wellknown subspace trackers in terms of subspace estimation. Moreover, it guarantees the orthonormality of the subspace weighting matr ..."
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This paper introduces a new algorithm for tracking the major subspace of the correlation matrix associated with time series. This algorithm greatly outperforms many wellknown subspace trackers in terms of subspace estimation. Moreover, it guarantees the orthonormality of the subspace weighting
Frames and Stable Bases for ShiftInvariant Subspaces of . . .
, 1994
"... Let X be a countable fundamental set in a Hilbert space H, and let T be the operator T : ` 2 (X) ! H : c 7! X x2X c(x)x: Whenever T is welldefined and bounded, X is said to be a Bessel sequence. If, in addition, ran T is closed, then X is a frame. Finally, a frame whose corresponding T is inje ..."
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Cited by 133 (29 self)
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T is injective is a stable basis (also known as a Riesz basis). This paper considers the above three properties for subspaces H of L 2 (IR d ), and for sets X of the form X = fOE(\Delta \Gamma ff) : OE 2 \Phi; ff 2 ZZ d g; with \Phi either a singleton, a finite set, or, more generally, a countable set
Generalized principal component analysis (GPCA)
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2003
"... This paper presents an algebrogeometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points. We represent the subspaces with a set of homogeneous polynomials whose degree is the number of subspaces and whose derivatives at a ..."
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Cited by 206 (36 self)
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at a data point give normal vectors to the subspace passing through the point. When the number of subspaces is known, we show that these polynomials can be estimated linearly from data; hence, subspace segmentation is reduced to classifying one point per subspace. We select these points optimally from
Deflated and augmented Krylov subspace techniques
 Numer. Linear Algebra Appl
, 1996
"... We present a general framework for a number of techniques based on projection methods on `augmented Krylov subspaces'. These methods include the deflated GMRES algorithm, an innerouter FGMRES iteration algorithm, and the class of block Krylov methods. Augmented Krylov subspace methods often ..."
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Cited by 73 (11 self)
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subspace Flexible GMRES 1 Introduction There are three techniques which are sometimes used to enhance the robustness of Krylov subspace methods. The first is to exploit block versions of Krylov subspace methods. These block methods are known to be generally more reliable than their scalar equivalents
Subspace clustering with gravitation
, 2010
"... Data mining is a process of discovering and exploiting hidden patterns from data. Clustering as an important task of data mining divides the observations into groups (clusters), which is according to the principle that the observations in the same cluster are similar, and the ones from different clu ..."
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clusters are dissimilar to each other. Subspace clustering enables clustering in subspaces within a data set, which means the clusters could be found not only in the whole space but also in subspaces. The wellknown subspace clustering methods have a common problem, the parameters are hard to be decided
ASCLU: Alternative subspace clustering
 In MultiClust at KDD
, 2010
"... Finding groups of similar objects in databases is one of the most important data mining tasks. Recently, traditional clustering approaches have been extended to generate alternative clustering solutions. The basic observation is that for each database object multiple meaningful groupings might exist ..."
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Cited by 6 (4 self)
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attributes per object are recorded, traditional clustering is known to generate no meaningful results. Instead, the analysis of subspace projections of the data with subspace or projected clustering techniques is more suitable. In this paper, we develop the first method that detects alternative subspace
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