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A Generalized Maximum Entropy Approach to Bregman Coclustering and Matrix Approximation
 In KDD
, 2004
"... Coclustering is a powerful data mining technique with varied applications such as text clustering, microarray analysis and recommender systems. Recently, an informationtheoretic coclustering approach applicable to empirical joint probability distributions was proposed. In many situations, coclust ..."
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Cited by 133 (29 self)
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Coclustering is a powerful data mining technique with varied applications such as text clustering, microarray analysis and recommender systems. Recently, an informationtheoretic coclustering approach applicable to empirical joint probability distributions was proposed. In many situations, coclustering of more general matrices is desired. In this paper, we present a substantially generalized coclustering framework wherein any Bregman divergence can be used in the objective function, and various conditional expectation based constraints can be considered based on the statistics that need to be preserved. Analysis of the coclustering problem leads to the minimum Bregman information principle, which generalizes the maximum entropy principle, and yields an elegant meta algorithm that is guaranteed to achieve local optimality. Our methodology yields new algorithms and also encompasses several previously known clustering and coclustering algorithms based on alternate minimization.
Skinning Mesh Animations
 ACM Trans. Graph
, 2005
"... We extend approaches for skinning characters to the general setting of skinning deformable mesh animations. We provide an automatic algorithm for generating progressive skinning approximations, that is particularly efficient for pseudoarticulated motions. Our contributions include the use of nonpar ..."
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Cited by 133 (6 self)
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We extend approaches for skinning characters to the general setting of skinning deformable mesh animations. We provide an automatic algorithm for generating progressive skinning approximations, that is particularly efficient for pseudoarticulated motions. Our contributions include the use of nonparametric mean shift clustering of highdimensional mesh rotation sequences to automatically identify statistically relevant bones, and robust least squares methods to determine bone transformations, bonevertex influence sets, and vertex weight values. We use a lowrank data reduction model defined in the undeformed mesh configuration to provide progressive convergence with a fixed number of bones. We show that the resulting skinned animations enable efficient hardware rendering, rest pose editing, and deformable collision detection. Finally, we present numerous examples where skins were automatically generated using a single set of parameter values.
A Fast FixedPoint Algorithm for Independent Component Analysis of Complex Valued Signals
, 2000
"... Separation of complex valued signals is a frequently arising problem in signal processing. For example, separation of convolutively mixed source signals involves computations on complex valued signals. In this article it is assumed that the original, complex valued source signals are mutually statis ..."
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Cited by 128 (1 self)
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Separation of complex valued signals is a frequently arising problem in signal processing. For example, separation of convolutively mixed source signals involves computations on complex valued signals. In this article it is assumed that the original, complex valued source signals are mutually statistically independent, and the problem is solved by the independent component analysis (ICA) model. ICA is a statistical method for transforming an observed multidimensional random vector into components that are mutually as independent as possible. In this article, a fast xedpoint type algorithm that is capable of separating complex valued, linearly mixed source signals is presented and its computational efficiency is shown by simulations. Also, the local consistency of the estimator given by the algorithm is proved.
Relational Learning via Collective Matrix Factorization
, 2008
"... Relational learning is concerned with predicting unknown values of a relation, given a database of entities and observed relations among entities. An example of relational learning is movie rating prediction, where entities could include users, movies, genres, and actors. Relations would then encode ..."
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Cited by 127 (4 self)
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Relational learning is concerned with predicting unknown values of a relation, given a database of entities and observed relations among entities. An example of relational learning is movie rating prediction, where entities could include users, movies, genres, and actors. Relations would then encode users ’ ratings of movies, movies ’ genres, and actors ’ roles in movies. A common prediction technique given one pairwise relation, for example a #users × #movies ratings matrix, is lowrank matrix factorization. In domains with multiple relations, represented as multiple matrices, we may improve predictive accuracy by exploiting information from one relation while predicting another. To this end, we propose a collective matrix factorization model: we simultaneously factor several matrices, sharing parameters among factors when an entity participates in multiple relations. Each relation can have a different value type and error distribution; so, we allow nonlinear relationships between the parameters and outputs, using Bregman divergences to measure error. We extend standard alternating projection algorithms to our model, and derive an efficient Newton update for the projection. Furthermore, we propose stochastic optimization methods to deal with large, sparse matrices. Our model generalizes several existing matrix factorization methods, and therefore yields new largescale optimization algorithms for these problems. Our model can handle any pairwise relational schema and a
Convex and SemiNonnegative Matrix Factorizations
, 2008
"... We present several new variations on the theme of nonnegative matrix factorization (NMF). Considering factorizations of the form X = F GT, we focus on algorithms in which G is restricted to contain nonnegative entries, but allow the data matrix X to have mixed signs, thus extending the applicable ra ..."
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Cited by 109 (9 self)
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We present several new variations on the theme of nonnegative matrix factorization (NMF). Considering factorizations of the form X = F GT, we focus on algorithms in which G is restricted to contain nonnegative entries, but allow the data matrix X to have mixed signs, thus extending the applicable range of NMF methods. We also consider algorithms in which the basis vectors of F are constrained to be convex combinations of the data points. This is used for a kernel extension of NMF. We provide algorithms for computing these new factorizations and we provide supporting theoretical analysis. We also analyze the relationships between our algorithms and clustering algorithms, and consider the implications for sparseness of solutions. Finally, we present experimental results that explore the properties of these new methods.
Document clustering using nonnegative matrix factorization
 Inf. Proc. & Manag
, 2006
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Hyperspectral unmixing overview: Geometrical, statistical, and sparse regressionbased approaches
 IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens
, 2012
"... Abstract—Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). H ..."
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Cited by 104 (34 self)
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Abstract—Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, illposed
Generalized nonnegative matrix approximations with Bregman divergences
 In: Neural Information Proc. Systems
, 2005
"... Nonnegative matrix approximation (NNMA) is a recent technique for dimensionality reduction and data analysis that yields a parts based, sparse nonnegative representation for nonnegative input data. NNMA has found a wide variety of applications, including text analysis, document clustering, face/imag ..."
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Cited by 97 (5 self)
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Nonnegative matrix approximation (NNMA) is a recent technique for dimensionality reduction and data analysis that yields a parts based, sparse nonnegative representation for nonnegative input data. NNMA has found a wide variety of applications, including text analysis, document clustering, face/image recognition, language modeling, speech processing and many others. Despite these numerous applications, the algorithmic development for computing the NNMA factors has been relatively deficient. This paper makes algorithmic progress by modeling and solving (using multiplicative updates) new generalized NNMA problems that minimize Bregman divergences between the input matrix and its lowrank approximation. The multiplicative update formulae in the pioneering work by Lee and Seung [11] arise as a special case of our algorithms. In addition, the paper shows how to use penalty functions for incorporating constraints other than nonnegativity into the problem. Further, some interesting extensions to the use of “link ” functions for modeling nonlinear relationships are also discussed. 1
H: Sparse nonnegative matrix factorizations via alternating nonnegativityconstrained least squares for microarray data analysis
 Bioinformatics
"... Many practical pattern recognition problems require nonnegativity constraints. For example, pixels in digital images and chemical concentrations in bioinformatics are nonnegative. Nonnegative matrix factorization (NMF) is a useful technique in approximating these high dimensional data. Sparse N ..."
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Cited by 93 (11 self)
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Many practical pattern recognition problems require nonnegativity constraints. For example, pixels in digital images and chemical concentrations in bioinformatics are nonnegative. Nonnegative matrix factorization (NMF) is a useful technique in approximating these high dimensional data. Sparse NMFs are also useful when we need to control the degree of sparseness in nonnegative basis vectors or nonnegative lowerdimensional representations. In this paper, we introduce novel sparse NMFs via alternating nonnegativityconstrained least squares. We applied one of the proposed sparse NMFs to cancer class discovery and gene expression data analysis. Our experimental results illustrate that our proposed method achieves better clustering performance than NMF based on multiplicative update rules and sparse NMFs based on the gradient descent method. 1
Convolutive speech bases and their application to supervised speech separation
 IEEE Transactions on Audio, Speech and Language Processing
, 2007
"... In this paper we present a convolutive basis decomposition method and its application on simultaneous speakers separation from monophonic recordings. The model we propose is a convolutive version of the nonnegative matrix factorization algorithm. Due to the nonnegativity constraint this type of co ..."
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Cited by 92 (6 self)
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In this paper we present a convolutive basis decomposition method and its application on simultaneous speakers separation from monophonic recordings. The model we propose is a convolutive version of the nonnegative matrix factorization algorithm. Due to the nonnegativity constraint this type of coding is very well suited for intuitively and efficiently representing magnitude spectra. We present results that reveal the nature of these basis functions and we introduce their utility in separating monophonic mixtures of known speakers.