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112
Semi-Supervised Clustering via Matrix Factorization
, 2008
"... The recent years have witnessed a surge of interests of semi-supervised clustering methods, which aim to cluster the data set under the guidance of some supervisory information. Usually those supervisory information takes the form of pairwise constraints that indicate the similarity/dissimilarity be ..."
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Cited by 30 (4 self)
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The recent years have witnessed a surge of interests of semi-supervised clustering methods, which aim to cluster the data set under the guidance of some supervisory information. Usually those supervisory information takes the form of pairwise constraints that indicate the similarity/dissimilarity between the two points. In this paper, we propose a novel matrix factorization based approach for semi-supervised clustering. In addition, we extend our algorithm to co-cluster the data sets of different types with constraints. Finally the experiments on UCI data sets and real world Bulletin Board Systems (BBS) data sets show the superiority of our proposed method.
Blind reflectometry
- In ECCV
, 2010
"... Abstract. Different materials reflect light in different ways, so reflectance is a useful surface descriptor. Existing systems for measuring reflectance are cumbersome, however, and although the process can be streamlined using cameras, projectors and clever catadioptrics, it generally requires comp ..."
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Cited by 30 (2 self)
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Abstract. Different materials reflect light in different ways, so reflectance is a useful surface descriptor. Existing systems for measuring reflectance are cumbersome, however, and although the process can be streamlined using cameras, projectors and clever catadioptrics, it generally requires complex infrastructure. In this paper we propose a simpler method for inferring reflectance from images, one that eliminates the need for active lighting and exploits natural illumination instead. The method’s distinguishing property is its ability to handle a broad class of isotropic reflectance functions, including those that are neither radially-symmetric nor well-represented by low-parameter reflectance models. The key to the approach is a bi-variate representation of isotropic reflectance that enables a tractable inference algorithm while maintaining generality. The resulting method requires only a camera, a light probe, and as little as one HDR image of a known, curved, homogeneous surface. 1
Weighted consensus clustering
, 2008
"... Consensus clustering has emerged as an important extension of the classical clustering problem. We propose weighted consensus clustering, where each input clustering is weighted and the weights are determined in such a way that the final consensus clustering provides a better quality solution, in wh ..."
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Cited by 29 (10 self)
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Consensus clustering has emerged as an important extension of the classical clustering problem. We propose weighted consensus clustering, where each input clustering is weighted and the weights are determined in such a way that the final consensus clustering provides a better quality solution, in which clusters are better separated comparing to standard consensus clustering. Theoretically, we show that a reformulation of the wellknown L1 regularization LASSO problem is equivalent to the weight optimization of our weighted consensus clustering, and thus our approach provides sparse solutions which may resolve the difficult situation when the input clusterings diverge significantly. We also show that the weighted consensus clustering resolves the redundancy problem when many input clusterings correlate highly. Detailed algorithms are given. Experiments are carried out to demonstrate the effectiveness of the weighted consensus clustering.
Unsupervised sentiment analysis with emotional signals
- In Proceedings of the 22nd international conference on World Wide Web, WWW’13. ACM
"... The explosion of social media services presents a great opportunity to understand the sentiment of the public via analyzing its large-scale and opinion-rich data. In social media, it is easy to amass vast quantities of unlabeled data, but very costly to obtain sentiment labels, which makes unsupervi ..."
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Cited by 27 (5 self)
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The explosion of social media services presents a great opportunity to understand the sentiment of the public via analyzing its large-scale and opinion-rich data. In social media, it is easy to amass vast quantities of unlabeled data, but very costly to obtain sentiment labels, which makes unsupervised sentiment analysis essential for various applications. It is challenging for traditional lexicon-based unsupervised methods due to the fact that expressions in social media are unstructured, informal, and fast-evolving. Emoticons and product ratings are examples of emotional signals that are associated with sentiments expressed in posts or words. Inspired by the wide availability of emotional signals in social media, we propose to study the problem of unsupervised sentiment analysis with emotional signals. In particular, we investigate whether the signals can potentially help sentiment analysis by providing a unified way to model two main categories of emotional signals, i.e., emotion indication and emotion correlation. We further incorporate the signals into an unsupervised learning framework for sentiment analysis. In the experiment, we compare the proposed framework with the state-of-the-art methods on two Twitter datasets and empirically evaluate our proposed framework to gain a deep understanding of the effects of emotional signals.
Convex sparse matrix factorizations
"... We present a convex formulation of dictionary learning for sparse signal decomposition. Convexity is obtained by replacing the usual explicit upper bound on the dictionary size by a convex rank-reducing term similar to the trace norm. In particular, our formulation introduces an explicit trade-off b ..."
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Cited by 25 (13 self)
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We present a convex formulation of dictionary learning for sparse signal decomposition. Convexity is obtained by replacing the usual explicit upper bound on the dictionary size by a convex rank-reducing term similar to the trace norm. In particular, our formulation introduces an explicit trade-off between size and sparsity of the decomposition of rectangular matrices. Using a large set of synthetic examples, we compare the estimation abilities of the convex and nonconvex approaches, showing that while the convex formulation has a single local minimum, this may lead in some cases to performance which is inferior to the local minima of the non-convex formulation. 1
Linear and Nonlinear Projective Nonnegative Matrix Factorization
"... Abstract—A variant of nonnegative matrix factorization (NMF) which was proposed earlier is analyzed here. It is called Projective Nonnegative Matrix Factorization (PNMF). The new method approximately factorizes a projection matrix, minimizing the reconstruction error, into a positive low-rank matrix ..."
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Cited by 21 (3 self)
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Abstract—A variant of nonnegative matrix factorization (NMF) which was proposed earlier is analyzed here. It is called Projective Nonnegative Matrix Factorization (PNMF). The new method approximately factorizes a projection matrix, minimizing the reconstruction error, into a positive low-rank matrix and its transpose. The dissimilarity between the original data matrix and its approximation can be measured by the Frobenius matrix norm or the modified Kullback-Leibler divergence. Both measures are minimized by multiplicative update rules, whose convergence is proven for the first time. Enforcing orthonormality to the basic objective is shown to lead to an even more efficient update rule, which is also readily extended to nonlinear cases. The formulation of the PNMF objective is shown to be connected to a variety of existing nonnegative matrix factorization methods and clustering approaches. In addition, the derivation using Lagrangian multipliers reveals the relation between reconstruction and sparseness. For kernel principal component analysis with the binary constraint, useful in graph partitioning problems, the nonlinear kernel PNMF provides a good approximation which outperforms an existing discretization approach. Empirical study on three real-world databases shows that PNMF can achieve the best or close to the best in clustering. The proposed algorithm runs more efficiently than the compared nonnegative matrix factorization methods, especially for high-dimensional data. Moreover, contrary to the basic NMF, the trained projection matrix can be readily used for newly coming samples and demonstrates good generalization. I.
Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework
- J GLOB OPTIM
, 2013
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Nonnegative Matrix Factorization: A Comprehensive Review
- IEEE TRANS. KNOWLEDGE AND DATA ENG
, 2013
"... Nonnegative Matrix Factorization (NMF), a relatively novel paradigm for dimensionality reduction, has been in the ascendant since its inception. It incorporates the nonnegativity constraint and thus obtains the parts-based representation as well as enhancing the interpretability of the issue corres ..."
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Cited by 17 (2 self)
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Nonnegative Matrix Factorization (NMF), a relatively novel paradigm for dimensionality reduction, has been in the ascendant since its inception. It incorporates the nonnegativity constraint and thus obtains the parts-based representation as well as enhancing the interpretability of the issue correspondingly. This survey paper mainly focuses on the theoretical research into NMF over the last 5 years, where the principles, basic models, properties, and algorithms of NMF along with its various modifications, extensions, and generalizations are summarized systematically. The existing NMF algorithms are divided into four categories: Basic NMF (BNMF),
Exemplar-based Visualization of Large Document Corpus
"... Abstract—With the rapid growth of the World Wide Web and electronic information services, text corpus is becoming available online at an incredible rate. By displaying text data in a logical layout (e.g., color graphs), text visualization presents a direct way to observe the documents as well as und ..."
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Cited by 15 (2 self)
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Abstract—With the rapid growth of the World Wide Web and electronic information services, text corpus is becoming available online at an incredible rate. By displaying text data in a logical layout (e.g., color graphs), text visualization presents a direct way to observe the documents as well as understand the relationship between them. In this paper, we propose a novel technique, Exemplarbased Visualization (EV), to visualize an extremely large text corpus. Capitalizing on recent advances in matrix approximation and decomposition, EV presents a probabilistic multidimensional projection model in the low-rank text subspace with a sound objective function. The probability of each document proportion to the topics is obtained through iterative optimization and embedded to a low dimensional space using parameter embedding. By selecting the representative exemplars, we obtain a compact approximation of the data. This makes the visualization highly efficient and flexible. In addition, the selected exemplars neatly summarize the entire data set and greatly reduce the cognitive overload in the visualization, leading to an easier interpretation of large text corpus. Empirically, we demonstrate the superior performance of EV through extensive experiments performed on the publicly available text data sets. Index Terms—Exemplar, large-scale document visualization, multidimensional projection. 1
Convolutive non-negative sparse coding,”
- in IEEE International Joint Conference on Neural Networks.,
, 2008
"... Abstract-Sparse Coding (SC), which models the data vectors as sparse linear combinations over basis vectors, has been widely applied in machine learning, signal processing and neuroscience. In this paper, we propose a dual random projection method to provide an efficient solution to Nonnegative Spa ..."
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Cited by 14 (3 self)
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Abstract-Sparse Coding (SC), which models the data vectors as sparse linear combinations over basis vectors, has been widely applied in machine learning, signal processing and neuroscience. In this paper, we propose a dual random projection method to provide an efficient solution to Nonnegative Sparse Coding (NSC) using small memory. Experiments on real world data demonstrate the effectiveness of the proposed method.
