Probabilistic Fisher discriminant analysis: A robust and flexible alternative to Fisher discriminant analysis

International audienceFisher discriminant analysis (FDA) is a popular and powerful method for dimensionality reduction and classification. Unfortunately, the optimality of the dimension reduction provided by FDA is only proved in the homoscedastic case. In addition, FDA is known to have poor performances in the cases of label noise and sparse labeled data. To overcome these limitations, this work proposes a probabilistic framework for FDA which relaxes the homoscedastic assumption on the class covariance matrices and adds a term to explicitly model the non-discriminative information. This allows the proposed method to be robust to label noise and to be used in the semi-supervised context. Experiments on real-world datasets show that the proposed approach works at least as well as FDA in standard situations and outperforms it in the label noise and sparse label cases

Robust linear discriminant analysis for multiple groups: influence and classification efficiencies.

Linear discriminant analysis for multiple groups is typically carried out using Fisher's method. This method relies on the sample averages and covariance ma- trices computed from the different groups constituting the training sample. Since sample averages and covariance matrices are not robust, it is proposed to use robust estimators of location and covariance instead, yielding a robust version of Fisher's method. In this paper expressions are derived for the influence that an observation in the training set has on the error rate of the Fisher method for multiple linear discriminant analysis. These influence functions on the error rate turn out to be unbounded for the classical rule, but bounded when using a robust approach. Using these influence functions, we compute relative classification efficiencies of the robust procedures with respect to the classical method. It is shown that, by using an appropriate robust estimator, the loss in classification efficiency at the normal model remains limited. These findings are confirmed by finite sample simulations.Classification; Covariance; Discriminant analysis; Efficiency; Error rate; Estimator; Fisher rule; Functions; Influence function; Model; Multiple groups; Research; Robustness; Simulation; Training;

Classification efficiencies for robust linear discriminant analysis.

Linear discriminant analysis is typically carried out using Fisher’s method. This method relies on the sample averages and covariance matrices computed from the different groups constituting the training sample. Since sample averages and covariance matrices are not robust, it has been proposed to use robust estimators of location and covariance instead, yielding a robust version of Fisher’s method. In this paper relative classification efficiencies of the robust procedures with respect to the classical method are computed. Second order influence functions appear to be useful for computing these classification efficiencies. It turns out that, when using an appropriate robust estimator, the loss in classification efficiency at the normal model remains limited. These findings are confirmed by finite sample simulations.Classification efficiency; Discriminant analysis; Error rate; Fisher rule; Influence function; Robustness;

Fisher and Kernel Fisher Discriminant Analysis: Tutorial

This is a detailed tutorial paper which explains the Fisher discriminant Analysis (FDA) and kernel FDA. We start with projection and reconstruction. Then, one- and multi-dimensional FDA subspaces are covered. Scatters in two- and then multi-classes are explained in FDA. Then, we discuss on the rank of the scatters and the dimensionality of the subspace. A real-life example is also provided for interpreting FDA. Then, possible singularity of the scatter is discussed to introduce robust FDA. PCA and FDA directions are also compared. We also prove that FDA and linear discriminant analysis are equivalent. Fisher forest is also introduced as an ensemble of fisher subspaces useful for handling data with different features and dimensionality. Afterwards, kernel FDA is explained for both one- and multi-dimensional subspaces with both two- and multi-classes. Finally, some simulations are performed on AT&T face dataset to illustrate FDA and compare it with PCA

A robust adaptive wavelet-based method for classification of meningioma histology images

Intra-class variability in the texture of samples is an important problem in the domain of histological image classification. This issue is inherent to the field due to the high complexity of histology image data. A technique that provides good results in one trial may fail in another when the test and training data are changed and therefore, the technique needs to be adapted for intra-class texture variation. In this paper, we present a novel wavelet based multiresolution analysis approach to meningioma subtype classification in response to the challenge of data variation.We analyze the stability of Adaptive Discriminant Wavelet Packet Transform (ADWPT) and present a solution to the issue of variation in the ADWPT decomposition when texture in data changes. A feature selection approach is proposed that provides high classification accuracy

Person Re-identification by Local Maximal Occurrence Representation and Metric Learning

Person re-identification is an important technique towards automatic search of a person's presence in a surveillance video. Two fundamental problems are critical for person re-identification, feature representation and metric learning. An effective feature representation should be robust to illumination and viewpoint changes, and a discriminant metric should be learned to match various person images. In this paper, we propose an effective feature representation called Local Maximal Occurrence (LOMO), and a subspace and metric learning method called Cross-view Quadratic Discriminant Analysis (XQDA). The LOMO feature analyzes the horizontal occurrence of local features, and maximizes the occurrence to make a stable representation against viewpoint changes. Besides, to handle illumination variations, we apply the Retinex transform and a scale invariant texture operator. To learn a discriminant metric, we propose to learn a discriminant low dimensional subspace by cross-view quadratic discriminant analysis, and simultaneously, a QDA metric is learned on the derived subspace. We also present a practical computation method for XQDA, as well as its regularization. Experiments on four challenging person re-identification databases, VIPeR, QMUL GRID, CUHK Campus, and CUHK03, show that the proposed method improves the state-of-the-art rank-1 identification rates by 2.2%, 4.88%, 28.91%, and 31.55% on the four databases, respectively.Comment: This paper has been accepted by CVPR 2015. For source codes and extracted features please visit http://www.cbsr.ia.ac.cn/users/scliao/projects/lomo_xqda