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KPCA plus LDA: a complete kernel Fisher discriminant framework for feature extraction and recognition

by Jian Yang, Alejandro F. Frangi, Jing-yu Yang, David Zhang, Zhong Jin - IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE , 2005
"... This paper examines the theory of kernel Fisher discriminant analysis (KFD) in a Hilbert space and develops a two-phase KFD framework, i.e., kernel principal component analysis (KPCA) plus Fisher linear discriminant analysis (LDA). This framework provides novel insights into the nature of KFD. Base ..."
Abstract - Cited by 139 (7 self) - Add to MetaCart
. Based on this framework, the authors propose a complete kernel Fisher discriminant analysis (CKFD) algorithm. CKFD can be used to carry out discriminant analysis in “double discriminant subspaces.” The fact that, it can make full use of two kinds of discriminant information, regular and irregular, makes

Fisher Discriminant Analysis With Kernels

by Sebastian Mika, Gunnar Rätsch, Jason Weston, Bernhard Schölkopf, Klaus-Robert Müller , 1999
"... A non-linear classification technique based on Fisher's discriminant is proposed. The main ingredient is the kernel trick which allows the efficient computation of Fisher discriminant in feature space. The linear classification in feature space corresponds to a (powerful) non-linear decision f ..."
Abstract - Cited by 503 (18 self) - Add to MetaCart
A non-linear classification technique based on Fisher's discriminant is proposed. The main ingredient is the kernel trick which allows the efficient computation of Fisher discriminant in feature space. The linear classification in feature space corresponds to a (powerful) non-linear decision

An introduction to kernel-based learning algorithms

by Klaus-Robert Müller, Sebastian Mika, Gunnar Rätsch, Koji Tsuda, Bernhard Schölkopf - IEEE TRANSACTIONS ON NEURAL NETWORKS , 2001
"... This paper provides an introduction to support vector machines (SVMs), kernel Fisher discriminant analysis, and ..."
Abstract - Cited by 598 (55 self) - Add to MetaCart
This paper provides an introduction to support vector machines (SVMs), kernel Fisher discriminant analysis, and

Improving the Fisher kernel for large-scale image classification.

by Florent Perronnin , Jorge Sánchez , Thomas Mensink - In ECCV, , 2010
"... Abstract. The Fisher kernel (FK) is a generic framework which combines the benefits of generative and discriminative approaches. In the context of image classification the FK was shown to extend the popular bag-of-visual-words (BOV) by going beyond count statistics. However, in practice, this enric ..."
Abstract - Cited by 362 (20 self) - Add to MetaCart
Abstract. The Fisher kernel (FK) is a generic framework which combines the benefits of generative and discriminative approaches. In the context of image classification the FK was shown to extend the popular bag-of-visual-words (BOV) by going beyond count statistics. However, in practice

Benchmarking Least Squares Support Vector Machine Classifiers

by Tony Van Gestel, Johan A. K. Suykens, Bart Baesens, Stijn Viaene, Jan Vanthienen, Guido Dedene, Bart De Moor, Joos Vandewalle - NEURAL PROCESSING LETTERS , 2001
"... In Support Vector Machines (SVMs), the solution of the classification problem is characterized by a (convex) quadratic programming (QP) problem. In a modified version of SVMs, called Least Squares SVM classifiers (LS-SVMs), a least squares cost function is proposed so as to obtain a linear set of eq ..."
Abstract - Cited by 476 (46 self) - Add to MetaCart
of equations in the dual space. While the SVM classifier has a large margin interpretation, the LS-SVM formulation is related in this paper to a ridge regression approach for classification with binary targets and to Fisher's linear discriminant analysis in the feature space. Multiclass categorization

Hierarchical Modelling and Analysis for Spatial Data. Chapman and Hall/CRC,

by S Banerjee , B P Carlin , A E Gelfand , Chapman , / Hall , New Crc , N York; Cressie , P J Diggle , P J Ribeiro Jr , B D Ripley , 2004
"... Abstract Often, there are two streams in statistical research -one developed by practitioners and other by main stream statisticians. Development of geostatistics is a very good example where pioneering work under realistic assumptions came from mining engineers whereas it is only now that statisti ..."
Abstract - Cited by 442 (45 self) - Add to MetaCart
that statistical framework is getting more transparent. The subject with statistical emphasis has been evolving, as seen by various excellent books from statistical sides (Banerjee, S., Introduction It is well known that the maximum likelihood (ML) method is a powerful statistical tool in estimation

Fisher Kernels on Visual Vocabularies for Image Categorization

by Florent Perronnin, et al.
"... Within the field of pattern classification, the Fisher kernel is a powerful framework which combines the strengths of generative and discriminative approaches. The idea is to characterize a signal with a gradient vector derived from a generative probability model and to subsequently feed this repres ..."
Abstract - Cited by 214 (21 self) - Add to MetaCart
Within the field of pattern classification, the Fisher kernel is a powerful framework which combines the strengths of generative and discriminative approaches. The idea is to characterize a signal with a gradient vector derived from a generative probability model and to subsequently feed

Graph embedding and extension: A general framework for dimensionality reduction

by Shuicheng Yan, Dong Xu, Benyu Zhang, Hong-jiang Zhang, Qiang Yang, Stephen Lin - IEEE TRANS. PATTERN ANAL. MACH. INTELL , 2007
"... Over the past few decades, a large family of algorithms—supervised or unsupervised; stemming from statistics or geometry theory—has been designed to provide different solutions to the problem of dimensionality reduction. Despite the different motivations of these algorithms, we present in this paper ..."
Abstract - Cited by 271 (29 self) - Add to MetaCart
in this paper a general formulation known as graph embedding to unify them within a common framework. In graph embedding, each algorithm can be considered as the direct graph embedding or its linear/kernel/tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric

Using the Fisher kernel method to detect remote protein homologies

by Tommi Jaakkola, Mark Diekhans, David Haussler - In Proceedings of the Seventh International Conference on Intelligent Systems for Molecular Biology , 1999
"... A new method, called the Fisher kernel method, for detecting remote protein homologies is introduced and shown to perform well in classifying protein domains by SCOP superfamily. The method is a variant of support vector machines using a new kernel function. The kernel function is derived from a hid ..."
Abstract - Cited by 208 (4 self) - Add to MetaCart
A new method, called the Fisher kernel method, for detecting remote protein homologies is introduced and shown to perform well in classifying protein domains by SCOP superfamily. The method is a variant of support vector machines using a new kernel function. The kernel function is derived from a

port Vector Machines, Kernel Fisher Discriminant analysis

by Sebastian Mika, Koji Tsuda
"... Abstract | This review provides an introduction to Sup- ..."
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Abstract | This review provides an introduction to Sup-
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