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105
Robust face recognition via sparse representation,” (preprint
 IEEE Trans. Pattern Analysis and Machine Intelligence
"... Abstract — We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models, and argue that new theory from sp ..."
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Cited by 321 (22 self)
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Abstract — We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models, and argue that new theory from sparse signal representation offers the key to addressing this problem. Based on a sparse representation computed by ℓ 1minimization, we propose a general classification algorithm for (imagebased) object recognition. This new framework provides new insights into two crucial issues in face recognition: feature extraction and robustness to occlusion. For feature extraction, we show that if sparsity in the recognition problem is properly harnessed, the choice of features is no longer critical. What is critical, however, is whether the number of features is sufficiently large and whether the sparse representation is correctly computed. Unconventional features such as downsampled images and random projections perform just as well as conventional features such as Eigenfaces and Laplacianfaces, as long as the dimension of the feature space surpasses certain threshold, predicted by the theory of sparse representation. This framework can handle errors due to occlusion and corruption uniformly, by exploiting the fact that these errors are often sparse w.r.t. to the standard (pixel) basis. The theory of sparse representation helps predict how much occlusion the recognition algorithm can handle and how to choose the training images to maximize robustness to occlusion. We conduct extensive experiments on publicly available databases to verify the efficacy of the proposed algorithm, and corroborate the above claims.
Locality Preserving Projections
, 2002
"... Many problems in information processing involve some form of dimensionality reduction. In this paper, we introduce Locality Preserving Projections (LPP). These are linear projective maps that arise by solving a variational problem that optimally preserves the neighborhood structure of the data s ..."
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Cited by 209 (15 self)
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Many problems in information processing involve some form of dimensionality reduction. In this paper, we introduce Locality Preserving Projections (LPP). These are linear projective maps that arise by solving a variational problem that optimally preserves the neighborhood structure of the data set. LPP should be seen as an alternative to Principal Component Analysis (PCA)  a classical linear technique that projects the data along the directions of maximal variance. When the high dimensional data lies on a low dimensional manifold embedded in the ambient space, the Locality Preserving Projections are obtained by finding the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operator on the manifold. As a result, LPP shares many of the data representation properties of nonlinear techniques such as Laplacian Eigenmaps or Locally Linear Embedding. Yet LPP is linear and more crucially is defined everywhere in ambient space rather than just on the training data points. This is borne out by illustrative examples on some high dimensional data sets.
Random projection for high dimensional data clustering: A cluster ensemble approach
 In: Proceedings of the 20th International Conference on Machine Learning (ICML
"... We investigate how random projection can best be used for clustering high dimensional data. Random projection has been shown to have promising theoretical properties. In practice, however, we find that it results in highly unstable clustering performance. Our solution is to use random projection in ..."
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Cited by 97 (4 self)
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We investigate how random projection can best be used for clustering high dimensional data. Random projection has been shown to have promising theoretical properties. In practice, however, we find that it results in highly unstable clustering performance. Our solution is to use random projection in a cluster ensemble approach. Empirical results show that the proposed approach achieves better and more robust clustering performance compared to not only single runs of random projection/clustering but also clustering with PCA, a traditional data reduction method for high dimensional data. To gain insights into the performance improvement obtained by our ensemble method, we analyze and identify the influence of the quality and the diversity of the individual clustering solutions on the final ensemble performance. 1.
Properties of embedding methods for similarity searching in metric spaces
 PAMI
, 2003
"... Complex data types—such as images, documents, DNA sequences, etc.—are becoming increasingly important in modern database applications. A typical query in many of these applications seeks to find objects that are similar to some target object, where (dis)similarity is defined by some distance functi ..."
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Cited by 80 (4 self)
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Complex data types—such as images, documents, DNA sequences, etc.—are becoming increasingly important in modern database applications. A typical query in many of these applications seeks to find objects that are similar to some target object, where (dis)similarity is defined by some distance function. Often, the cost of evaluating the distance between two objects is very high. Thus, the number of distance evaluations should be kept at a minimum, while (ideally) maintaining the quality of the result. One way to approach this goal is to embed the data objects in a vector space so that the distances of the embedded objects approximates the actual distances. Thus, queries can be performed (for the most part) on the embedded objects. In this paper, we are especially interested in examining the issue of whether or not the embedding methods will ensure that no relevant objects are left out (i.e., there are no false dismissals and, hence, the correct result is reported). Particular attention is paid to the SparseMap, FastMap, and MetricMap embedding methods. SparseMap is a variant of Lipschitz embeddings, while FastMap and MetricMap are inspired by dimension reduction methods for Euclidean spaces (using KLT or the related PCA and SVD). We show that, in general, none of these embedding methods guarantee that queries on the embedded objects have no false dismissals, while also demonstrating the limited cases in which the guarantee does hold. Moreover, we describe a variant of SparseMap that allows queries with no false dismissals. In addition, we show that with FastMap and MetricMap, the distances of the embedded objects can be much greater than the actual distances. This makes it impossible (or at least impractical) to modify FastMap and MetricMap to guarantee no false dismissals.
On Scaling Latent Semantic Indexing for Large PeerToPeer Systems
 Proc. 27th Annual International ACM SIGIR Conference
, 2004
"... The exponential growth of data demands scalable infrastructures capable of indexing and searching rich content such as text, music, and images. A promising direction is to combine information retrieval with peertopeer technology for scalability, faulttolerance, and low administration cost. One pi ..."
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Cited by 33 (0 self)
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The exponential growth of data demands scalable infrastructures capable of indexing and searching rich content such as text, music, and images. A promising direction is to combine information retrieval with peertopeer technology for scalability, faulttolerance, and low administration cost. One pioneering work along this direction is pSearch [32, 33]. pSearch places documents onto a peerto peer overlay network according to semantic vectors produced using Latent Semantic Indexing (LSI). The search cost for a query is reduced since documents related to the query are likely to be colocated on a small number of nodes. Unfortunately, because of its reliance on LSI, pSearch also inherits the limitations of LSI. (1) When the corpus is large and heterogeneous, LSI's retrieval quality is inferior to methods such as Okapi. (2) The Singular Value Decomposition (SVD) used in LSI is unscalable in terms of both memory consumption and computation time.
Locality Preserving Indexing for Document Representation
 In Proc. of the 27rd ACM SIGIR
, 2004
"... Document representation and indexing is a key problem for document analysis and processing, such as clustering, classification and retrieval. Conventionally, Latent Semantic Indexing (LSI) is considered effective in deriving such an indexing. LSI essentially detects the most representative features ..."
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Cited by 29 (12 self)
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Document representation and indexing is a key problem for document analysis and processing, such as clustering, classification and retrieval. Conventionally, Latent Semantic Indexing (LSI) is considered effective in deriving such an indexing. LSI essentially detects the most representative features for document representation rather than the most discriminative features. Therefore, LSI might not be optimal in discriminating documents with different semantics. In this paper, a novel algorithm called Locality Preserving Indexing (LPI) is proposed for document indexing. Each document is represented by a vector with low dimensionality. In contrast to LSI which discovers the global structure of the document space, LPI discovers the local structure and obtains a compact document representation subspace that best detects the essential semantic structure. We compare the proposed LPI approach with LSI on two standard databases. Experimental results show that LPI provides better representation in the sense of semantic structure.
The fast JohnsonLindenstrauss transform and approximate nearest neighbors
 SIAM J. Comput
, 2009
"... Abstract. We introduce a new lowdistortion embedding of ℓd n) 2 into ℓO(log p (p =1, 2) called the fast Johnson–Lindenstrauss transform (FJLT). The FJLT is faster than standard random projections and just as easy to implement. It is based upon the preconditioning of a sparse projection matrix with ..."
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Cited by 22 (0 self)
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Abstract. We introduce a new lowdistortion embedding of ℓd n) 2 into ℓO(log p (p =1, 2) called the fast Johnson–Lindenstrauss transform (FJLT). The FJLT is faster than standard random projections and just as easy to implement. It is based upon the preconditioning of a sparse projection matrix with a randomized Fourier transform. Sparse random projections are unsuitable for lowdistortion embeddings. We overcome this handicap by exploiting the “Heisenberg principle ” of the Fourier transform, i.e., its localglobal duality. The FJLT can be used to speed up search algorithms based on lowdistortion embeddings in ℓ1 and ℓ2. We consider the case of approximate nearest neighbors in ℓd 2. We provide a faster algorithm using classical projections, which we then speed up further by plugging in the FJLT. We also give a faster algorithm for searching over the hypercube.
Feature selection in face recognition: A sparse representation perspective
, 2007
"... In this paper, we examine the role of feature selection in face recognition from the perspective of sparse representation. We cast the recognition problem as finding a sparse representation of the test image features w.r.t. the training set. The sparse representation can be accurately and efficientl ..."
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Cited by 19 (1 self)
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In this paper, we examine the role of feature selection in face recognition from the perspective of sparse representation. We cast the recognition problem as finding a sparse representation of the test image features w.r.t. the training set. The sparse representation can be accurately and efficiently computed by ℓ 1minimization. The proposed simple algorithm generalizes conventional face recognition classifiers such as nearest neighbors and nearest subspaces. Using face recognition under varying illumination and expression as an example, we show that if sparsity in the recognition problem is properly harnessed, the choice of features is no longer critical. What is critical, however, is whether the number of features is sufficient and whether the sparse representation is correctly found. We conduct extensive experiments to validate the significance of imposing sparsity using the Extended Yale B database and the AR database. Our thorough evaluation shows that, using conventional features such as Eigenfaces and facial parts, the proposed algorithm achieves much higher recognition accuracy on face images with variation in either illumination or expression. Furthermore, other unconventional features such as severely downsampled images and randomly projected features perform almost equally well with the increase of feature dimensions. The differences in performance between different features become insignificant as the featurespace dimension is sufficiently large.
Using BagofConcepts to Improve the Performance of Support Vector Machines in Text Categorization
 IN PROC. OF THE 20TH COLING
, 2004
"... This paper investigates the use of conceptbased representations for text categorization. We introduce ..."
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Cited by 17 (2 self)
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This paper investigates the use of conceptbased representations for text categorization. We introduce
CoarsetoFine Syntactic Machine Translation using Language Projections
"... The intersection of tree transducerbased translation models with ngram language models results in huge dynamic programs for machine translation decoding. We propose a multipass, coarsetofine approach in which the language model complexity is incrementally introduced. In contrast to previous orde ..."
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Cited by 17 (5 self)
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The intersection of tree transducerbased translation models with ngram language models results in huge dynamic programs for machine translation decoding. We propose a multipass, coarsetofine approach in which the language model complexity is incrementally introduced. In contrast to previous orderbased bigramtotrigram approaches, we focus on encodingbased methods, which use a clustered encoding of the target language. Across various encoding schemes, and for multiple language pairs, we show speedups of up to 50 times over singlepass decoding while improving BLEU score. Moreover, our entire decoding cascade for trigram language models is faster than the corresponding bigram pass alone of a bigramtotrigram decoder. 1