Multiclass Linear Dimension Reduction by Weighted Pairwise Fisher Criteria

By Marco Loog, Robert P. W. Duin, Reinhold Häb-Umbach. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2001

483 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Statistics and Probability, Signal Processing

View Paper: https://www.semanticscholar.org/paper/75f14ff900ea5bfc11d601109298c6977f941483

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Citations in the corpus

Machine Learning and Radiology (2012, background): “For multiple classes problems, the above scatter matrices can be extended to the following form: SB ¼ PK i¼1piðmi mÞðmi mÞ T ; Sw ¼ PK k¼1piSi, where K is the number of classes, mi is the mean vector of class i, pi is the priori probability, m is the overall mean (Loog et al., 2001).”
A new ranking method for principal components analysis and its application to face image analysis (2010, methodology): “[8] introduced a weighted pairwise variant of the well-known multi-class Fisher criterion to improve the classification accuracy of the standard LDA.”
Approximative Bayes optimality linear discriminant analysis for Chinese handwriting character recognition (2016, methodology): “[10] proposed another weighting function using the approximation of pairwise Bayes function.”
Efficient and robust feature extraction by maximum margin criterion (2003, methodology): “Like the weighted pairwise Fisher’s criteria in [ 2 ], one may also define a weighted maximum margin criterion.”
Linear dimensionality reduction via a heteroscedastic extension of LDA: the Chernoff criterion (2004, methodology): “An improvement of the method may be possible by using some form of penalization [11], by weighting the relative contributions of the pairwise term [ 17 ] confining the influence of otherwise dominant terms on the final criterion, orbyreweightingalleigenvaluesoftheindividualterms[15].”
A Survey of Face Recognition Techniques (2009, methodology): “…recent LDA-based algorithms include Direct LDA [100, 101], Direct-weighted LDA [102], Nullspace LDA [103, 104], Dual-space LDA [105], Pair-wise LDA [106], Regularized Discriminant Analysis [107], Generalized Singular Value Decomposition [108, 109], Direct Fractional-Step LDA [110], Boosting LDA…”
Using discriminant analysis for multi-class classification: an experimental investigation (2006, unknown): “It has been shown that , however , for multi - class problem , the fisher ' s criterion is actually maximizing the mean squared distance between the classes in the lower - dimensional space and is clearly different from minimizing classification error ( Loog , et al .”
Copy Number Analysis Indicates Monoclonal Origin of Lethal Metastatic Prostate Cancer (2009, unknown): “D Euclidean space extracted by weighted Fisher criterion-based discriminatory component analysis (wFC-DCA)15, where the overall intrasubject copy number pattern similarity of both clustering cases (for example case 17, the cyan circles) and nonclustering cases (for example case 33, the magenta…”
Geometric Mean for Subspace Selection (2009, background): “Three criteria are analyzed: 1) maximization of the geometric mean of the KL divergences, 2) maximization of the geometric mean of the normalized KL divergences, and 3) the combination of 1 and 2.”
Subclass discriminant analysis (2006, methodology): “Index Terms—Feature extraction, discriminant analysis, pattern recognition, classification, eigenvalue decomposition, stability criterion, mixture of Gaussians.”
Nonparametric weighted feature extraction for classification (2004, background): “There are one simulated and one real data experiments in [18].”