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224
Detecting faces in images: A survey
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2002
"... Images containing faces are essential to intelligent visionbased human computer interaction, and research efforts in face processing include face recognition, face tracking, pose estimation, and expression recognition. However, many reported methods assume that the faces in an image or an image se ..."
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Cited by 611 (4 self)
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Images containing faces are essential to intelligent visionbased human computer interaction, and research efforts in face processing include face recognition, face tracking, pose estimation, and expression recognition. However, many reported methods assume that the faces in an image or an image sequence have been identified and localized. To build fully automated systems that analyze the information contained in face images, robust and efficient face detection algorithms are required. Given a single image, the goal of face detection is to identify all image regions which contain a face regardless of its threedimensional position, orientation, and the lighting conditions. Such a problem is challenging because faces are nonrigid and have a high degree of variability in size, shape, color, and texture. Numerous techniques have been developed to detect faces in a single image, and the purpose of this paper is to categorize and evaluate these algorithms. We also discuss relevant issues such as data collection, evaluation metrics, and benchmarking. After analyzing these algorithms and identifying their limitations, we conclude with several promising directions for future research.
Mixtures of Probabilistic Principal Component Analysers
, 1998
"... Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a com ..."
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Cited by 403 (6 self)
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Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a combination of local linear PCA projections. However, conventional PCA does not correspond to a probability density, and so there is no unique way to combine PCA models. Previous attempts to formulate mixture models for PCA have therefore to some extent been ad hoc. In this paper, PCA is formulated within a maximumlikelihood framework, based on a specific form of Gaussian latent variable model. This leads to a welldefined mixture model for probabilistic principal component analysers, whose parameters can be determined using an EM algorithm. We discuss the advantages of this model in the context of clustering, density modelling and local dimensionality reduction, and we demonstrate its applicat...
Think Globally, Fit Locally: Unsupervised Learning of Low Dimensional Manifolds
 Journal of Machine Learning Research
, 2003
"... The problem of dimensionality reduction arises in many fields of information processing, including machine learning, data compression, scientific visualization, pattern recognition, and neural computation. ..."
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Cited by 260 (9 self)
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The problem of dimensionality reduction arises in many fields of information processing, including machine learning, data compression, scientific visualization, pattern recognition, and neural computation.
NonLinear Dimensionality Reduction
 Advances in Neural Information Processing Systems 5
, 1993
"... A method for creating a non–linear encoder–decoder for multidimensional data with compact representations is presented. The commonly used technique of autoassociation is extended to allow non–linear representations, and an objective function which penalizes activations of individual hidden units is ..."
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Cited by 108 (1 self)
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A method for creating a non–linear encoder–decoder for multidimensional data with compact representations is presented. The commonly used technique of autoassociation is extended to allow non–linear representations, and an objective function which penalizes activations of individual hidden units is shown to result in minimum dimensional encodings with respect to allowable error in reconstruction. 1
Dimension Reduction by Local Principal Component Analysis
, 1997
"... Reducing or eliminating statistical redundancy between the components of highdimensional vector data enables a lowerdimensional representation without significant loss of information. Recognizing the limitations of principal component analysis (PCA), researchers in the statistics and neural networ ..."
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Cited by 102 (0 self)
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Reducing or eliminating statistical redundancy between the components of highdimensional vector data enables a lowerdimensional representation without significant loss of information. Recognizing the limitations of principal component analysis (PCA), researchers in the statistics and neural network communities have developed nonlinear extensions of PCA. This article develops a local linear approach to dimension reduction that provides accurate representations and is fast to compute. We exercise the algorithms on speech and image data, and compare performance with PCA and with neural network implementations of nonlinear PCA. We find that both nonlinear techniques can provide more accurate representations than PCA and show that the local linear techniques outperform neural network implementations.
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 89 (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 )
Principal manifolds and probabilistic subspaces for visual recognition
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2002
"... We investigate the use of linear and nonlinear principal manifolds for learning lowdimensional representations for visual recognition. Several leading techniques: Principal Component Analysis (PCA), Independent Component Analysis (ICA), and nonlinear Kernel PCA (KPCA) are examined and tested in a v ..."
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Cited by 77 (2 self)
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We investigate the use of linear and nonlinear principal manifolds for learning lowdimensional representations for visual recognition. Several leading techniques: Principal Component Analysis (PCA), Independent Component Analysis (ICA), and nonlinear Kernel PCA (KPCA) are examined and tested in a visual recognition experiment using 1800+ facial images from the “FERET ” database. We compare the recognition performance of nearestneighbour matching with each principal manifold representation to that of a maximum a posteriori (MAP) matching rule using a Bayesian similarity measure derived from dual probabilistic subspaces. The experimental results demonstrate the simplicity, computational economy and performance superiority of the Bayesian subspace method over principal manifold techniques for visual matching.
A unified model for probabilistic principal surfaces
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2001
"... AbstractÐPrincipal curves and surfaces are nonlinear generalizations of principal components and subspaces, respectively. They can provide insightful summary of highdimensional data not typically attainable by classical linear methods. Solutions to several problems, such as proof of existence and c ..."
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Cited by 42 (6 self)
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AbstractÐPrincipal curves and surfaces are nonlinear generalizations of principal components and subspaces, respectively. They can provide insightful summary of highdimensional data not typically attainable by classical linear methods. Solutions to several problems, such as proof of existence and convergence, faced by the original principal curve formulation have been proposed in the past few years. Nevertheless, these solutions are not generally extensible to principal surfaces, the mere computation of which presents a formidable obstacle. Consequently, relatively few studies of principal surfaces are available. Recently, we proposed the probabilistic principal surface (PPS) to address a number of issues associated with current principal surface algorithms. PPS uses a manifold oriented covariance noise model, based on the generative topographical mapping (GTM), which can be viewed as a parametric formulation of Kohonen's selforganizing map. Building on the PPS, we introduce a unified covariance model that implements PPS … 0< <1†, GTM … ˆ 1†, and the manifoldaligned GTM …>1† by varying the clamping parameter. Then, we comprehensively evaluate the empirical performance (reconstruction error) of PPS, GTM, and the manifoldaligned GTM on three popular benchmark data sets. It is shown in two different comparisons that the PPS outperforms the GTM under identical parameter settings. Convergence of the PPS is found to be identical to that of the GTM and the computational overhead incurred by the PPS decreases to 40 percent or less for more complex manifolds. These results show that the generalized PPS provides a flexible and effective way of obtaining principal surfaces. Index TermsÐPrincipal curve, principal surface, probabilistic, dimensionality reduction, nonlinear manifold, generative topographic mapping. 1
FeedForward Neural Networks and Topographic Mappings for Exploratory Data Analysis
 Neural Computing and Applications
, 1996
"... A recent novel approach to the visualisation and analysis of datasets, and one which is particularly applicable to those of a high dimension, is discussed in the context of real applications. A feedforward neural network is utilised to effect a topographic, structurepreserving, dimensionreducing ..."
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Cited by 42 (2 self)
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A recent novel approach to the visualisation and analysis of datasets, and one which is particularly applicable to those of a high dimension, is discussed in the context of real applications. A feedforward neural network is utilised to effect a topographic, structurepreserving, dimensionreducing transformation of the data, with an additional facility to incorporate different degrees of associated subjective information. The properties of this transformation are illustrated on synthetic and real datasets, including the 1992 UK Research Assessment Exercise for funding in higher education. The method is compared and contrasted to established techniques for feature extraction, and related to topographic mappings, the Sammon projection and the statistical field of multidimensional scaling. 1 INTRODUCTION The visualisation and analysis of highdimensional data is a difficult problem and one that may be helpfully viewed in the context of feature extraction, which provides a useful commo...
Principal Manifolds and Bayesian Subspaces for Visual Recognition
 International Conference on Computer Vision
, 1999
"... We investigate the use of linear and nonlinear principal manifolds for learning lowdimensional representations for visual recognition. Three techniques: Principal Component Analysis (PCA), Independent Component Analysis (ICA) and Nonlinear PCA (NLPCA) are examined and tested in a visual recognition ..."
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Cited by 41 (1 self)
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We investigate the use of linear and nonlinear principal manifolds for learning lowdimensional representations for visual recognition. Three techniques: Principal Component Analysis (PCA), Independent Component Analysis (ICA) and Nonlinear PCA (NLPCA) are examined and tested in a visual recognition experiment using a large gallery of facial images from the ¨FERET¨database. We compare the recognition performance of a nearestneighbour matching rule with each principal manifold representation to that of a maximum a posteriori (MAP) matching rule using a Bayesian similarity measure derived from probabilistic subspaces and demonstrate the superiority of the latter.