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169
Robust face recognition via sparse representation
 IEEE TRANS. PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2008
"... 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 signa ..."
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Cited by 936 (40 self)
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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.
Data Streams: Algorithms and Applications
, 2005
"... In the data stream scenario, input arrives very rapidly and there is limited memory to store the input. Algorithms have to work with one or few passes over the data, space less than linear in the input size or time significantly less than the input size. In the past few years, a new theory has emerg ..."
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Cited by 533 (22 self)
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In the data stream scenario, input arrives very rapidly and there is limited memory to store the input. Algorithms have to work with one or few passes over the data, space less than linear in the input size or time significantly less than the input size. In the past few years, a new theory has emerged for reasoning about algorithms that work within these constraints on space, time, and number of passes. Some of the methods rely on metric embeddings, pseudorandom computations, sparse approximation theory and communication complexity. The applications for this scenario include IP network traffic analysis, mining text message streams and processing massive data sets in general. Researchers in Theoretical Computer Science, Databases, IP Networking and Computer Systems are working on the data stream challenges. This article is an overview and survey of data stream algorithmics and is an updated version of [175].1
Sure independence screening for ultrahigh dimensional feature space
, 2006
"... Variable selection plays an important role in high dimensional statistical modeling which nowadays appears in many areas and is key to various scientific discoveries. For problems of large scale or dimensionality p, estimation accuracy and computational cost are two top concerns. In a recent paper, ..."
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Cited by 283 (26 self)
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Variable selection plays an important role in high dimensional statistical modeling which nowadays appears in many areas and is key to various scientific discoveries. For problems of large scale or dimensionality p, estimation accuracy and computational cost are two top concerns. In a recent paper, Candes and Tao (2007) propose the Dantzig selector using L1 regularization and show that it achieves the ideal risk up to a logarithmic factor log p. Their innovative procedure and remarkable result are challenged when the dimensionality is ultra high as the factor log p can be large and their uniform uncertainty principle can fail. Motivated by these concerns, we introduce the concept of sure screening and propose a sure screening method based on a correlation learning, called the Sure Independence Screening (SIS), to reduce dimensionality from high to a moderate scale that is below sample size. In a fairly general asymptotic framework, the SIS is shown to have the sure screening property for even exponentially growing dimensionality. As a methodological extension, an iterative SIS (ISIS) is also proposed to enhance its finite sample performance. With dimension reduced accurately from high to below sample size, variable selection can be improved on both speed and accuracy, and can then be ac
Structural Analysis of Network Traffic Flows
, 2003
"... Network traffic arises from the superposition of OriginDestination (OD) flows. Hence, a thorough understanding of OD flows is essential for modeling network traffic, and for addressing a wide variety of problems including traffic engineering, traffic matrix estimation, capacity planning, forecas ..."
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Cited by 165 (21 self)
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Network traffic arises from the superposition of OriginDestination (OD) flows. Hence, a thorough understanding of OD flows is essential for modeling network traffic, and for addressing a wide variety of problems including traffic engineering, traffic matrix estimation, capacity planning, forecasting and anomaly detection. However, to date, OD flows have not been closely studied, and there is very little known about their properties. We present
Robust principal component analysis: Exact recovery of corrupted lowrank matrices via convex optimization
 Advances in Neural Information Processing Systems 22
, 2009
"... The supplementary material to the NIPS version of this paper [4] contains a critical error, which was discovered several days before the conference. Unfortunately, it was too late to withdraw the paper from the proceedings. Fortunately, since that time, a correct analysis of the proposed convex prog ..."
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Cited by 149 (4 self)
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The supplementary material to the NIPS version of this paper [4] contains a critical error, which was discovered several days before the conference. Unfortunately, it was too late to withdraw the paper from the proceedings. Fortunately, since that time, a correct analysis of the proposed convex programming relaxation has been developed by Emmanuel Candes of Stanford University. That analysis is reported in a joint paper, Robust Principal Component Analysis? by Emmanuel Candes, Xiaodong Li, Yi Ma and John Wright,
A Survey of Dimension Reduction Techniques
, 2002
"... this paper, we assume that we have n observations, each being a realization of the p dimensional random variable x = (x 1 , . . . , x p ) with mean E(x) = = ( 1 , . . . , p ) and covariance matrix E{(x )(x = # pp . We denote such an observation matrix by X = i,j : 1 p, 1 ..."
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Cited by 141 (0 self)
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this paper, we assume that we have n observations, each being a realization of the p dimensional random variable x = (x 1 , . . . , x p ) with mean E(x) = = ( 1 , . . . , p ) and covariance matrix E{(x )(x = # pp . We denote such an observation matrix by X = i,j : 1 p, 1 n}. If i and # i = # (i,i) denote the mean and the standard deviation of the ith random variable, respectively, then we will often standardize the observations x i,j by (x i,j i )/ # i , where i = x i = 1/n j=1 x i,j , and # i = 1/n j=1 (x i,j x i )
Optimal multimodal fusion for multimedia data analysis
 In ACM Multimedia
, 2004
"... Considerable research has been devoted to utilizing multimodal features for better understanding multimedia data. However, two core research issues have not yet been adequately addressed. First, given a set of features extracted from multiple media sources (e.g., extracted from the visual, audio, an ..."
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Cited by 84 (1 self)
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Considerable research has been devoted to utilizing multimodal features for better understanding multimedia data. However, two core research issues have not yet been adequately addressed. First, given a set of features extracted from multiple media sources (e.g., extracted from the visual, audio, and caption track of videos), how do we determine the best modalities? Second, once a set of modalities has been identified, how do we best fuse them to map to semantics? In this paper, we propose a twostep approach. The first step finds statistically independent modalities from raw features. In the second step, we use superkernel fusion to determine the optimal combination of individual modalities. We carefully analyze the tradeoffs between three design factors that affect fusion performance: modality independence, curse of dimensionality, and fusionmodel complexity. Through analytical and empirical studies, we demonstrate that our twostep approach, which achieves a careful balance of the three design factors, can improve classprediction accuracy over traditional techniques.
A SELECTIVE OVERVIEW OF VARIABLE SELECTION IN HIGH DIMENSIONAL FEATURE SPACE
, 2010
"... High dimensional statistical problems arise from diverse fields of scientific research and technological development. Variable selection plays a pivotal role in contemporary statistical learning and scientific discoveries. The traditional idea of best subset selection methods, which can be regarded ..."
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Cited by 70 (6 self)
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High dimensional statistical problems arise from diverse fields of scientific research and technological development. Variable selection plays a pivotal role in contemporary statistical learning and scientific discoveries. The traditional idea of best subset selection methods, which can be regarded as a specific form of penalized likelihood, is computationally too expensive for many modern statistical applications. Other forms of penalized likelihood methods have been successfully developed over the last decade to cope with high dimensionality. They have been widely applied for simultaneously selecting important variables and estimating their effects in high dimensional statistical inference. In this article, we present a brief account of the recent developments of theory, methods, and implementations for high dimensional variable selection. What limits of the dimensionality such methods can handle, what the role of penalty functions is, and what the statistical properties are rapidly drive the advances of the field. The properties of nonconcave penalized likelihood and its roles in high dimensional statistical modeling are emphasized. We also review some recent advances in ultrahigh dimensional variable selection, with emphasis on independence screening and twoscale methods.