# Fisher discriminant analysis with kernels

@article{Mika1999FisherDA, title={Fisher discriminant analysis with kernels}, author={Sebastian Mika and Gunnar R{\"a}tsch and Jason Weston and Bernhard Scholkopf and K.R. Mullers}, journal={Neural Networks for Signal Processing IX: Proceedings of the 1999 IEEE Signal Processing Society Workshop (Cat. No.98TH8468)}, year={1999}, pages={41-48} }

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 function in input space. Large scale simulations demonstrate the competitiveness of our approach.

## 2,912 Citations

Kernel Fisher Discriminant Analysis Embedded with Feature Selection

- Computer Science2007 International Conference on Machine Learning and Cybernetics
- 2007

Experimental results clearly show that the new kernel Fisher discriminant analysis embedded with feature selection can greatly reduce the dimensions of the inputs, without harm to the classification results.

Invariant Feature Extraction and Classification in Kernel Spaces

- Computer Science, MathematicsNIPS
- 1999

Employing a unified framework in terms of a nonlinear variant of the Rayleigh coefficient, this work proposes non-linear generalizations of Fisher's discriminant and oriented PCA using Support Vector kernel functions.

Two Variations on Fisher's Linear Discriminant for Pattern Recognition

- Computer ScienceIEEE Trans. Pattern Anal. Mach. Intell.
- 2002

This paper provides two fast and simple techniques for improving on the classification performance provided by Fisher's linear discriminant for two classes by extended to nonlinear decision surfaces through the use of Mercer kernels.

Discriminant kernels based support vector machine

- Computer ScienceThe First Asian Conference on Pattern Recognition
- 2011

KDA is one of the nonlinear extensions of Linear Discriminant Analysis and the kernel function is usually defined a priori and it is not known what the optimum kernel function for nonlinear discriminant analysis is.

Non-parametric Fisher's discriminant analysis with kernels for data classification

- Computer SciencePattern Recognit. Lett.
- 2013

A sequential approach for multi-class discriminant analysis with kernels

- Computer Science2004 IEEE International Conference on Acoustics, Speech, and Signal Processing
- 2004

This work presents a sequential algorithm for GDA avoiding problems when one deals with large numbers of datapoints when dealing with nonlinear discriminant analysis using kernel functions.

Kernel Discriminant Analysis Based Face Recognition

- Computer Science
- 2014

The kernel trick is used to represent the complicated nonlinear relationships of input data to develop kernel discriminant analysis (KDA) algorithm, a traditional dimensionality reduction technique for feature extraction.

An improved training algorithm for kernel Fisher discriminants

- Computer ScienceAISTATS
- 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…

Nonlinear Discriminant Analysis Using Kernel Functions

- Computer ScienceNIPS
- 1999

The presented algorithm allows a simple formulation of the EM-algorithm in terms of kernel functions which leads to a unique concept for unsupervised mixture analysis, supervised discriminant analysis and semi-supervised discriminantAnalysis with partially unlabelled observations in feature spaces.

Weighted maximum margin discriminant analysis with kernels

- Computer Science, EngineeringNeurocomputing
- 2005

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