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79
A twostage linear discriminant analysis via QRdecomposition
 IEEE TRANSACTION ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2005
"... Linear Discriminant Analysis (LDA) is a wellknown method for feature extraction and dimension reduction. It has been used widely in many applications involving highdimensional data, such as image and text classification. An intrinsic limitation of classical LDA is the socalled singularity proble ..."
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Cited by 27 (0 self)
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Linear Discriminant Analysis (LDA) is a wellknown method for feature extraction and dimension reduction. It has been used widely in many applications involving highdimensional data, such as image and text classification. An intrinsic limitation of classical LDA is the socalled singularity problems; that is, it fails when all scatter matrices are singular. Many LDA extensions were proposed in the past to overcome the singularity problems. Among these extensions, PCA+LDA, a twostage method, received relatively more attention. In PCA+LDA, the LDA stage is preceded by an intermediate dimension reduction stage using Principal Component Analysis (PCA). Most previous LDA extensions are computationally expensive, and not scalable, due to the use of Singular Value Decomposition or Generalized Singular Value Decomposition. In this paper, we propose a twostage LDA method, namely LDA/QR, which aims to overcome the singularity problems of classical LDA, while achieving efficiency and scalability simultaneously. The key difference between LDA/QR and PCA+LDA lies in the first stage, where LDA/QR applies QR decomposition to a small matrix involving the class centroids, while PCA+LDA applies PCA to the total scatter matrix involving all training data points. We further justify the proposed algorithm by showing the relationship among LDA/QR and previous LDA methods. Extensive experiments on face images and text documents are presented to show the effectiveness of the proposed algorithm.
Fusing Gabor and LBP Feature Sets for KernelBased Face Recognition
"... Abstract. Extending recognition to uncontrolled situations is a key challenge for practical face recognition systems. Finding efficient and discriminative facial appearance descriptors is crucial for this. Most existing approaches use features of just one type. Here we argue that robust recognition ..."
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Abstract. Extending recognition to uncontrolled situations is a key challenge for practical face recognition systems. Finding efficient and discriminative facial appearance descriptors is crucial for this. Most existing approaches use features of just one type. Here we argue that robust recognition requires several different kinds of appearance information to be taken into account, suggesting the use of heterogeneous feature sets. We show that combining two of the most successful local face representations, Gabor wavelets and Local Binary Patterns (LBP), gives considerably better performance than either alone: they are complimentary in the sense that LBP captures small appearance details while Gabor features encode facial shape over a broader range of scales. Both feature sets are high dimensional so it is beneficial to use PCA to reduce the dimensionality prior to normalization and integration. The Kernel Discriminative Common Vector method is then applied to the combined feature vector to extract discriminant nonlinear features for recognition. The method is evaluated on several challenging face datasets including FRGC 1.0.4, FRGC 2.0.4 and FERET, with promising results. 1
SemiSupervised Discriminant Analysis Using Robust PathBased Similarity
 Proc. IEEE Conf. Computer Vision and Pattern Recognition
, 2008
"... Linear Discriminant Analysis (LDA), which works by maximizing the withinclass similarity and minimizing the betweenclass similarity simultaneously, is a popular dimensionality reduction technique in pattern recognition and machine learning. In realworld applications when labeled data are limited, ..."
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Linear Discriminant Analysis (LDA), which works by maximizing the withinclass similarity and minimizing the betweenclass similarity simultaneously, is a popular dimensionality reduction technique in pattern recognition and machine learning. In realworld applications when labeled data are limited, LDA does not work well. Under many situations, however, it is easy to obtain unlabeled data in large quantities. In this paper, we propose a novel dimensionality reduction method, called SemiSupervised Discriminant Analysis (SSDA), which can utilize both labeled and unlabeled data to perform dimensionality reduction in the semisupervised setting. Our method uses a robust pathbased similarity measure to capture the manifold structure of the data and then uses the obtained similarity to maximize the separability between different classes. A kernel extension of the proposed method for nonlinear dimensionality reduction in the semisupervised setting is also presented. Experiments on face recognition demonstrate the effectiveness of the proposed method. 1.
Combined subspace method using global and local features for face recognition
 in: Proceedings of the International Joint Conference on Neural Networks, 2005
"... Abstract — This paper proposes a combined subspace method using both global and local features for face recognition. The global and local features are obtained by applying the LDAbased method to either the whole or part of a face image, respectively. The combined subspace is constructed with the pro ..."
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Abstract — This paper proposes a combined subspace method using both global and local features for face recognition. The global and local features are obtained by applying the LDAbased method to either the whole or part of a face image, respectively. The combined subspace is constructed with the projection vectors corresponding to large eigenvalues of the betweenclass scatter matrix in each subspace. It is based on the fact that the eigenvectors corresponding to larger eigenvalues have more discriminating power. The combined subspace is evaluated in view of the Bayes error, which shows how well samples can be classified. The combined subspace gives small Bayes error than the subspaces composed of either the global or local features. Comparative experiments are also performed using the Color FERET database of facial images. The experimental results show that the combined subspace method gives better recognition rate than other subspace methods. I.
Manifold based local classifiers: Linear and nonlinear approaches
 In Pattern Recognition in review
, 2007
"... Abstract In case of insufficient data samples in highdimensional classification problems, sparse scatters of samples tend to have many ‘holes’—regions that have few or no nearby training samples from the class. When such regions lie close to interclass boundaries, the nearest neighbors of a query m ..."
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Cited by 6 (1 self)
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Abstract In case of insufficient data samples in highdimensional classification problems, sparse scatters of samples tend to have many ‘holes’—regions that have few or no nearby training samples from the class. When such regions lie close to interclass boundaries, the nearest neighbors of a query may lie in the wrong class, thus leading to errors in the Nearest Neighbor classification rule. The Klocal hyperplane distance nearest neighbor (HKNN) algorithm tackles this problem by approximating each class with a smooth nonlinear manifold, which is considered to be locally linear. The method takes advantage of the local linearity assumption by using the distances from a query sample to the affine hulls of query’s nearest neighbors for
Generalized 2D Principal Component Analysis
"... Abstract — Recently, a TwoDimensional Principal Component Analysis (2DPCA) [1] was proposed and the authors have demonstrated its superiority over the conventional Principal Component Analysis (PCA) in face recognition. But the theoretical proof why 2DPCA is better than PCA has not been given until ..."
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Abstract — Recently, a TwoDimensional Principal Component Analysis (2DPCA) [1] was proposed and the authors have demonstrated its superiority over the conventional Principal Component Analysis (PCA) in face recognition. But the theoretical proof why 2DPCA is better than PCA has not been given until now. In this paper, The essence of 2DPCA is analyzed and a framework of Generalized 2D Principal Component Analysis (G2DPCA) is proposed to extend the original 2DPCA in two perspectives: a Bilateralprojectionbased 2DPCA (B2DPCA) and a Kernelbased 2DPCA (K2DPCA) schemes are introduced. Experimental results in face recognition show its excellent performance. I.
Subspace Learning from Image gradient orientations
, 2012
"... We introduce the notion of subspace learning from image gradient orientations for appearancebased object recognition. As image data is typically noisy and noise is substantially different from Gaussian, traditional subspace learning from pixel intensities fails very often to estimate reliably the ..."
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Cited by 5 (3 self)
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We introduce the notion of subspace learning from image gradient orientations for appearancebased object recognition. As image data is typically noisy and noise is substantially different from Gaussian, traditional subspace learning from pixel intensities fails very often to estimate reliably the lowdimensional subspace of a given data population. We show that replacing pixel intensities with gradient orientations and the ℓ2 norm with a cosinebased distance measure offers, to some extend, a remedy to this problem. Within this framework, which we coin IGO (Image Gradient Orientations) subspace learning, we first formulate and study the properties of Principal Component Analysis of image gradient orientations (IGOPCA). We then show its connection to previously proposed robust PCA techniques both theoretically and experimentally. Finally, we derive a number of other popular subspace learning techniques, namely Linear Discriminant Analysis (LDA), Locally Linear Embedding (LLE) and Laplacian Eigenmaps (LE). Experimental results show that our algorithms outperform significantly popular methods such as Gabor features and Local Binary Patterns and achieve stateoftheart performance for difficult problems such as illumination and occlusionrobust face recognition. In addition to this, the proposed IGOmethods require the eigendecomposition of simple covariance matrices and are as computationally efficient as their corresponding ℓ2 norm intensitybased counterparts. Matlab code for the methods presented in this paper can be found at
SemiSupervised Discriminant Analysis via CCCP
"... Linear discriminant analysis (LDA) is commonly used for dimensionality reduction. In realworld applications where labeled data are scarce, LDA does not work very well. However, unlabeled data are often available in large quantities. We propose a novel semisupervised discriminant analysis algorith ..."
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Cited by 4 (2 self)
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Linear discriminant analysis (LDA) is commonly used for dimensionality reduction. In realworld applications where labeled data are scarce, LDA does not work very well. However, unlabeled data are often available in large quantities. We propose a novel semisupervised discriminant analysis algorithm called SSDACCCP. We utilize unlabeled data to maximize an optimality criterion of LDA and use the constrained concaveconvex procedure to solve the optimization problem. The optimization procedure leads to estimation of the class labels for the unlabeled data. We propose a novel confidence measure for selecting those unlabeled data points with high confidence. The selected unlabeled data can then be used to augment the original labeled data set for performing LDA. We also propose a variant of SSDACCCP, called MSSDACCCP, which adopts the manifold assumption to utilize the unlabeled data. Extensive experiments on many benchmark data sets demonstrate the effectiveness of our proposed methods.
Discriminant common vecotors versus neighbourhood components analysis and laplacianfaces: A comparative study in small sample size problem
 Image and Vision Computing
"... and Laplacianfaces (LAP) are three recently proposed methods which can effectively learn linear projection matrices for dimensionality reduction in face recognition, where the dimension of the sample space is typically larger than the number of samples in the training set and consequently the socal ..."
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and Laplacianfaces (LAP) are three recently proposed methods which can effectively learn linear projection matrices for dimensionality reduction in face recognition, where the dimension of the sample space is typically larger than the number of samples in the training set and consequently the socalled small sample size (SSS) problem exists. The three methods obtained their respective projection matrices based on different objective functions and all claimed to be superior to such methods as Principal Component Analysis (PCA) and PCA plus Linear Discriminant Analysis (PCA+LDA) in terms of classification accuracy. However, in literature, no comparative study is carried out among them. In this paper, we carry out a comparative study among them in face recognition (or generally in the SSS problem), and argue that the projection matrix yielded by DCV is the optimal solution to both NCA and LAP in terms of their respective objective functions, whereas neither NCA nor LAP may get their own optimal solutions. In addition, we show that DCV is more efficient than both NCA and LAP for both linear dimensionality reduction and subsequent classification in SSS problem. Finally, experiments are conducted on ORL, AR and YALE face databases to verify our arguments and to present some insights for future study.
Nearest Hyperdisk Methods for HighDimensional Classification
"... In highdimensional classification problems it is infeasible to include enough training samples to cover the class regions densely. Irregularities in the resulting sparse sample distributions cause local classifiers such as Nearest Neighbors (NN) and kernel methods to have irregular decision boundar ..."
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In highdimensional classification problems it is infeasible to include enough training samples to cover the class regions densely. Irregularities in the resulting sparse sample distributions cause local classifiers such as Nearest Neighbors (NN) and kernel methods to have irregular decision boundaries. One solution is to “fill in the holes” by building a convex model of the region spanned by the training samples of each class and classifying examples based on their distances to these approximate models. Methods of this kind based on affine and convex hulls and bounding hyperspheres have already been studied. Here we propose a method based on the bounding hyperdisk of each class – the intersection of the affine hull and the smallest bounding hypersphere of its training samples. We argue that in many cases hyperdisks are preferable to affine and convex hulls and hyperspheres: they bound the classes more tightly than affine hulls or hyperspheres while avoiding much of the sample overfitting and computational complexity that is inherent in highdimensional convex hulls. We show that the hyperdisk method can be kernelized to provide nonlinear classifiers based on nonEuclidean distance metrics. Experiments on several classification problems show promising results. 1.