Results 11  20
of
251
Face Recognition Using Kernel Eigenfaces
, 2000
"... Eigenceface or Principal Component Analysis (PCA) methods have demonstrated their success in face recognition, detection, and tracking. The representation in PCA is based on the second order statistics of the image set, and does not address higher order statistical dependencies such as the relations ..."
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Cited by 44 (0 self)
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Eigenceface or Principal Component Analysis (PCA) methods have demonstrated their success in face recognition, detection, and tracking. The representation in PCA is based on the second order statistics of the image set, and does not address higher order statistical dependencies such as the relationships among three or more pixels. Recently Higher Order Statistics (HOS) have been used as a more informative low dimensional representation than PCA for face and vehicle detection. In this paper we investigate a generalization of PCA, Kernel Principal Component Analysis (Kernel PCA), for learning low dimensional representations in the context of face recognition. In contrast to HOS, Kernel PCA computes the higher order statistics without the combinatorial explosion of time and memory complexity. While PCA aims to nd a second order correlation of patterns, Kernel PCA provides a replacement which takes into account higher order correlations. We compare the recognition results using kernel met...
Constructing Descriptive and Discriminative Nonlinear Features: Rayleigh Coefficients in Kernel Feature Spaces
, 2003
"... We incorporate prior knowledge to construct nonlinear algorithms for invariant feature extraction and discrimination. Employing a unified framework in terms of a nonlinearized variant of the Rayleigh coefficient, we propose nonlinear generalizations of Fisher's discriminant and oriented PCA using su ..."
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Cited by 43 (4 self)
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We incorporate prior knowledge to construct nonlinear algorithms for invariant feature extraction and discrimination. Employing a unified framework in terms of a nonlinearized variant of the Rayleigh coefficient, we propose nonlinear generalizations of Fisher's discriminant and oriented PCA using support vector kernel functions. Extensive simulations show the utility of our approach.
Quick shift and kernel methods for mode seeking
 In European Conference on Computer Vision, volume IV
, 2008
"... Abstract. We show that the complexity of the recently introduced medoidshift algorithm in clustering N points is O(N 2), with a small constant, if the underlying distance is Euclidean. This makes medoid shift considerably faster than mean shift, contrarily to what previously believed. We then explo ..."
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Cited by 43 (6 self)
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Abstract. We show that the complexity of the recently introduced medoidshift algorithm in clustering N points is O(N 2), with a small constant, if the underlying distance is Euclidean. This makes medoid shift considerably faster than mean shift, contrarily to what previously believed. We then exploit kernel methods to extend both mean shift and the improved medoid shift to a large family of distances, with complexity bounded by the effective rank of the resulting kernel matrix, and with explicit regularization constraints. Finally, we show that, under certain conditions, medoid shift fails to cluster data points belonging to the same mode, resulting in overfragmentation. We propose remedies for this problem, by introducing a novel, simple and extremely efficient clustering algorithm, called quick shift, that explicitly trades off under and overfragmentation. Like medoid shift, quick shift operates in nonEuclidean spaces in a straightforward manner. We also show that the accelerated medoid shift can be used to initialize mean shift for increased efficiency. We illustrate our algorithms to clustering data on manifolds, image segmentation, and the automatic discovery of visual categories. 1
Efficient and Robust Feature Extraction by Maximum Margin Criterion
 In Advances in Neural Information Processing Systems 16
, 2003
"... In pattern recognition, feature extraction techniques are widely employed to reduce the dimensionality of data and to enhance the discriminatory information. Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) are two most popular linear dimensionality reduction methods. Howev ..."
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Cited by 43 (4 self)
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In pattern recognition, feature extraction techniques are widely employed to reduce the dimensionality of data and to enhance the discriminatory information. Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) are two most popular linear dimensionality reduction methods. However, PCA is not very effective for the extraction of the most discriminant features and LDA is not stable due to the small sample size problem. In this paper, we propose some new (linear and nonlinear) feature extractors based on maximum margin criterion (MMC). Geometrically, feature extractors based on MMC maximize the (average) margin between classes after dimensionality reduction. It is shown that MMC can represent class separability better than PCA. As a connection to LDA, we may also derive LDA from MMC by incorporating some constraints. By using some other constraints, we establish a new linear feature extractor that does not suffer from the small sample size problem, which is known to cause serious stability problems for LDA. The kernelized (nonlinear) counterpart of this linear feature extractor is also established in the paper. Our extensive experiments demonstrate that the new feature extractors are effective, stable, and efficient.
Learning distance metrics with contextual constraints for image retrieval
 In Proc. CVPR2006
, 2006
"... Relevant Component Analysis (RCA) has been proposed for learning distance metrics with contextual constraints for image retrieval. However, RCA has two important disadvantages. One is the lack of exploiting negative constraints which can also be informative, and the other is its incapability of capt ..."
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Cited by 43 (18 self)
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Relevant Component Analysis (RCA) has been proposed for learning distance metrics with contextual constraints for image retrieval. However, RCA has two important disadvantages. One is the lack of exploiting negative constraints which can also be informative, and the other is its incapability of capturing complex nonlinear relationships between data instances with the contextual information. In this paper, we propose two algorithms to overcome these two disadvantages, i.e., Discriminative Component Analysis (DCA) and Kernel DCA. Compared with other complicated methods for distance metric learning, our algorithms are rather simple to understand and very easy to solve. We evaluate the performance of our algorithms on image retrieval in which experimental results show that our algorithms are effective and promising in learning good quality distance metrics for image retrieval. 1
Invariant Feature Extraction and Classification in Kernel Spaces
"... We incorporate prior knowledge to construct nonlinear algorithms for invariant feature extraction and discrimination. Employing a unified framework in terms of a nonlinear variant of the Rayleigh coefficient, we propose nonlinear generalizations of Fisher's discriminant and oriented PCA using S ..."
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Cited by 42 (8 self)
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We incorporate prior knowledge to construct nonlinear algorithms for invariant feature extraction and discrimination. Employing a unified framework in terms of a nonlinear variant of the Rayleigh coefficient, we propose nonlinear generalizations of Fisher's discriminant and oriented PCA using Support Vector kernel functions.
A Kernel Method For Canonical Correlation Analysis
 In Proceedings of the International Meeting of the Psychometric Society (IMPS2001
, 2001
"... roduce a quadratic regularization term #(a + b )/2 into the cost function of CCA. By the quadratic regularization, it follows that a can be written by a weighted sum of # x (x i ) where x i is the ith sample, and b can be written by a weighted sum of # y (y i ). Therefore, a # x (x) = # ..."
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Cited by 41 (0 self)
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roduce a quadratic regularization term #(a + b )/2 into the cost function of CCA. By the quadratic regularization, it follows that a can be written by a weighted sum of # x (x i ) where x i is the ith sample, and b can be written by a weighted sum of # y (y i ). Therefore, a # x (x) = # i # i # x (x i ) # x (x). This fact enables us to use a "kernel trick": Let k(z, w) be a kernel function which is symmetric and positive definite, then there exists # z (z) and k(z, w) = # z (z) # z (w). Using a kernel, we can calculate # x (x i ) # x (x) directly without knowing #. This means the complexity problem of calculation is solved as well, because we do not need to calculate # anymore. 6. Consequently, we obtain KCCA: 1. Calculate matrices of kernels K x = (k x (x i , x j )) and K y = (k y (y i , y j )), where k x and k y are kernels. 2. Solve the generalized eigen problem, M# = #L# and M # = #N#, where M = (1/n)K x JK y , L = (1/n)K x JK x + (#/#)K x , N = (1/n)K y
Capitalize on dimensionality increasing techniques for improving face recognition grand challenge performance
 IEEE TPAMI
, 2006
"... Abstract—This paper presents a novel pattern recognition framework by capitalizing on dimensionality increasing techniques. In particular, the framework integrates Gabor image representation, a novel multiclass Kernel Fisher Analysis (KFA) method, and fractional power polynomial models for improving ..."
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Cited by 40 (2 self)
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Abstract—This paper presents a novel pattern recognition framework by capitalizing on dimensionality increasing techniques. In particular, the framework integrates Gabor image representation, a novel multiclass Kernel Fisher Analysis (KFA) method, and fractional power polynomial models for improving pattern recognition performance. Gabor image representation, which increases dimensionality by incorporating Gabor filters with different scales and orientations, is characterized by spatial frequency, spatial locality, and orientational selectivity for coping with image variabilities such as illumination variations. The KFA method first performs nonlinear mapping from the input space to a highdimensional feature space, and then implements the multiclass Fisher discriminant analysis in the feature space. The significance of the nonlinear mapping is that it increases the discriminating power of the KFA method, which is linear in the feature space but nonlinear in the input space. The novelty of the KFA method comes from the fact that 1) it extends the twoclass kernel Fisher methods by addressing multiclass pattern classification problems and 2) it improves upon the traditional Generalized Discriminant Analysis (GDA) method by deriving a unique solution (compared to the GDA solution, which is not unique). The fractional power polynomial models further improve performance of the proposed pattern recognition framework. Experiments on face recognition using both the FERET database and the FRGC (Face Recognition Grand Challenge) databases show the feasibility of the proposed framework. In particular, experimental results using the FERET database show that the KFA method performs better than the GDA method and the fractional power polynomial models help both the KFA method and the GDA method improve their face recognition performance. Experimental results using the FRGC databases show that the proposed pattern recognition framework improves face
Object Classification from a Single Example Utilizing Class Relevance Metrics
 In Advances in Neural Information Processing Systems (NIPS
, 2004
"... We describe a framework for learning an object classifier from a single example, by emphasizing relevant dimensions using available examples of related classes. Learning to accurately classify objects from a single training example is often unfeasible due to overfitting effects. However, if the ..."
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Cited by 35 (0 self)
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We describe a framework for learning an object classifier from a single example, by emphasizing relevant dimensions using available examples of related classes. Learning to accurately classify objects from a single training example is often unfeasible due to overfitting effects. However, if the instance representation provides that the distance between each two instances of the same class is smaller than the distance between any two instances from different classes, then a nearest neighbor classifier could achieve perfect performance with a single training example. We therefore suggest a two stage strategy. First, learn a metric over the instances that achieves the distance criterion mentioned above, from available examples of other related classes. Then, using the single examples, define a nearest neighbor classifier where distance is evaluated by the learned class relevance metric. Finding a metric that emphasizes the relevant dimensions for classification might not be possible when restricted to linear projections. We therefore make use of a kernel based metric learning algorithm. Our setting encodes object instances as sets of locality based descriptors and adopts an appropriate image kernel for the class relevance metric learning. The proposed framework for learning from a single example is demonstrated in a synthetic setting and on a character classification task.
An Improved Training Algorithm for Kernel Fisher Discriminants
 In Proceedings AISTATS 2001
, 2001
"... We present a fast training algorithm for the kernel Fisher discriminant classifier. It uses a greedy approximation technique and has an empirical scaling behavior which improves upon the state of the art by more than an order of magnitude, thus rendering the kernel Fisher algorithm a viable option a ..."
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Cited by 32 (3 self)
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We present a fast training algorithm for the kernel Fisher discriminant classifier. It uses a greedy approximation technique and has an empirical scaling behavior which improves upon the state of the art by more than an order of magnitude, thus rendering the kernel Fisher algorithm a viable option also for large datasets. 1