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Worst-Case Linear Discriminant Analysis

Yu Zhang, Dit-Yan Yeung
2010 Neural Information Processing Systems  
Based on this analysis, we then propose a new dimensionality reduction method called worst-case linear discriminant analysis (WLDA) by defining new between-class and within-class scatter measures.  ...  In this paper, we first analyze the scatter measures used in the conventional linear discriminant analysis (LDA) model and note that the formulation is based on the average-case view.  ...  Worst-Case Linear Discriminant Analysis We are given a training set of data points, = {x 1 , . . . , x } ⊂ ℝ .  ... 
dblp:conf/nips/ZhangY10 fatcat:eeh7at3qcbdzfjcfg55ibffsoy

Worst-Case Linear Discriminant Analysis as Scalable Semidefinite Feasibility Problems [article]

Hui Li, Chunhua Shen, Anton van den Hengel, Qinfeng Shi
2014 arXiv   pre-print
In this paper, we propose an efficient semidefinite programming (SDP) approach to worst-case linear discriminant analysis (WLDA).  ...  Compared with the traditional LDA, WLDA considers the dimensionality reduction problem from the worst-case viewpoint, which is in general more robust for classification.  ...  WORST-CASE LINEAR DISCRIMINANT ANALYSIS We briefly review WLDA problem proposed by [5] firstly.  ... 
arXiv:1411.7450v1 fatcat:2gnyqk3gyncgzodeqfqfhzwwpm

A Minimax Theorem with Applications to Machine Learning, Signal Processing, and Finance

Seung-Jean Kim, Stephen Boyd
2008 SIAM Journal on Optimization  
We describe applications in machine learning (robust Fisher linear discriminant analysis), signal processing (robust beamforming, robust matched filtering), and finance (robust portfolio selection).  ...  Fisher linear discriminant analysis In linear discriminant analysis (LDA), we want to separate two classes which can be identified with two random variables in R n .  ...  The worst-case analysis problem of finding the worst-case means and covariances for a given discriminant w can be written as minimize f (w, µ + − µ − , Σ + + Σ − ) subject to (µ + , µ − , Σ + , Σ − ) ∈  ... 
doi:10.1137/060677586 fatcat:jpgiczkmiffn7l2ekcvc66xtrq

A minimax theorem with applications to machine learning, signal processing, and finance

Seung-Jean Kim, Stephen Boyd
2007 2007 46th IEEE Conference on Decision and Control  
We describe applications in machine learning (robust Fisher linear discriminant analysis), signal processing (robust beamforming, robust matched filtering), and finance (robust portfolio selection).  ...  Fisher linear discriminant analysis In linear discriminant analysis (LDA), we want to separate two classes which can be identified with two random variables in R n .  ...  The worst-case analysis problem of finding the worst-case means and covariances for a given discriminant w can be written as minimize f (w, µ + − µ − , Σ + + Σ − ) subject to (µ + , µ − , Σ + , Σ − ) ∈  ... 
doi:10.1109/cdc.2007.4434853 dblp:conf/cdc/KimB07 fatcat:ywkhez3cdnd6np6vjj5nfcotj4

Robust Fisher Discriminant Analysis

Seung-Jean Kim, Alessandro Magnani, Stephen P. Boyd
2005 Neural Information Processing Systems  
Fisher linear discriminant analysis (LDA) can be sensitive to the problem data.  ...  Robust Fisher LDA can systematically alleviate the sensitivity problem by explicitly incorporating a model of data uncertainty in a classification problem and optimizing for the worst-case scenario under  ...  Robust Fisher LDA We first consider the worst-case analysis problem (1).  ... 
dblp:conf/nips/KimMB05 fatcat:klupsrhisva6fj5vjuh2xcgupe

A lower bound on the performance of the quadratic discriminant function

Tristrom Cooke
2004 Journal of Multivariate Analysis  
In some cases however, the assumption of normality is a poor one and the classification error is increased.  ...  The bound is strict when the class means and covariances and the quadratic discriminant surface satisfy certain specified symmetry conditions. Crown  ...  The bound is strict when the problem satisfies the symmetry requirements of Section 2, and for this case, the quadratic discriminant which minimises the worst possible classification error is the linear  ... 
doi:10.1016/j.jmva.2003.11.005 fatcat:3toifahkmrblflv3e4aoxkntfa

Discrimination of wheat grain varieties using image analysis: morphological features

Piotr Zapotoczny
2011 European Food Research and Technology  
The final discriminant analysis was performed with the use of stepwise progressive analysis and Meta MultiClass Classifier.  ...  Variables calculated from linear dimensions had the greatest share in the group of discriminating variables, with shape-related indexes being of lesser importance.  ...  In the case of the latter, the maximum accuracy of Table 3 The results of discriminant analysis for the raw data Training set 1840, test set 785, method of selection Ranker Discrimination by the stepwise  ... 
doi:10.1007/s00217-011-1573-y fatcat:wkjcnhzcg5cyzfevgublqudoja

Multiple classifier systems for robust classifier design in adversarial environments

Battista Biggio, Giorgio Fumera, Fabio Roli
2010 International Journal of Machine Learning and Cybernetics  
In this paper we focus on a strategy recently proposed in the literature to improve the robustness of linear classifiers to adversarial data manipulation, and experimentally investigate whether it can  ...  In the case of linear classifiers, it is of interest to evaluate robustness in a worst-case scenario.  ...  Worst-case attack.  ... 
doi:10.1007/s13042-010-0007-7 fatcat:mlfrbkm2pbfhxpk5fykddvbjom

A Modified Super-Efficiency DEA Approach for Solving Multi-Groups Classification Problems

Jie Wu, Qingxian An, Liang Liang
2011 International Journal of Computational Intelligence Systems  
Therefore, it can be applied to the discriminant analysis in various real-life cases.  ...  In this paper, we propose a new discriminant approach based upon the relative distance measured by super-efficiency data envelopment analysis (DEA).  ...  In previous studies on nonparametric DA, Sueyoshi (2006) and Cooper et al. (1999) had proven that the piecewise linear discriminant function was more flexible than conventional linear discriminant  ... 
doi:10.2991/ijcis.2011.4.4.17 fatcat:cis2vrvkxzd6db4hcgmwvr3esa

Discriminant analysis under the common principal components model

P. T. Pepler, D. W. Uys, D. G. Nel
2016 Communications in statistics. Simulation and computation  
and linear discriminant analysis.  ...  Monte Carlo simulation results show that CPC discriminant analysis offers significant improvements in misclassification error rates in certain situations, and at worst performs similar to ordinary quadratic  ...  The multivariate normality assumption is thus not necessary for linear discriminant analysis (LDA), and the method can also be applied to multivariate non-normal data.  ... 
doi:10.1080/03610918.2015.1134568 fatcat:oxiociohsveyzelsy2ykusifjy

Dimensionality Reduction by Minimal Distance Maximization

Bo Xu, Kaizhu Huang, Cheng-Lin Liu
2010 2010 20th International Conference on Pattern Recognition  
In this paper, we propose a novel discriminant analysis method, called Minimal Distance Maximization (MDM).  ...  Furthermore, we elegantly formulate the worst-case problem as a convex problem, making the algorithm solvable for larger data sets.  ...  Introduction Linear discriminant analysis (LDA) [2] , one of the most popularly used discriminant analysis algorithms, has been widely used in various fields including economics, psychology, neuroscience  ... 
doi:10.1109/icpr.2010.144 dblp:conf/icpr/XuHL10 fatcat:xqi3qrnrkbb57ddud73rsvrcdy

The effect of numeric features on the scalability of inductive learning programs [chapter]

Georgios Paliouras, David S. Brée
1995 Lecture Notes in Computer Science  
The theoretical part of the work involved a detailed worst-case computational complexity anMysis of the algorithms.  ...  The artificial data set introduces a near-worst-case situation for the examined algorithms, while the real data sets provide an indication of their average-case behaviour.  ...  Using a computational complexity analysis, it has been shown that., in the worst case, the behaviour of the algorithms is not linear, as previously reported, but higher than quadratic.  ... 
doi:10.1007/3-540-59286-5_60 fatcat:qupbcpq7qrh6tgenfabfmag43q

Target Robust Discriminant Analysis [article]

Wouter M. Kouw, Marco Loog
2021 arXiv   pre-print
We construct robust parameter estimators for discriminant analysis that guarantee performance improvements of the adaptive classifier over the non-adaptive source classifier.  ...  function of the feature values and hence is termed linear discriminant analysis (LDA).  ...  Furthermore, for the discriminant analysis case, its risk is always strictly smaller.  ... 
arXiv:1806.09463v2 fatcat:iivrruu3xraxzku7wzpvhqsbde

An Abstract Framework for Counterexample Analysis in Active Automata Learning

Malte Isberner, Bernhard Steffen
2014 International Conference on Grammatical Inference  
We demonstrate the conciseness and simplicity of our framework by using it to present new counterexample analysis algorithms, which, while maintaining the worst-case complexity of O(log m), perform significantly  ...  Counterexample analysis has emerged as one of the key challenges in Angluin-style active automata learning.  ...  Rivest&Schapire's Method: Binary Search A linear worst-case query complexity might at first not seem bad.  ... 
dblp:conf/icgi/IsbernerS14 fatcat:kawzhatoozhzbbegwtuumen32m

Is soft independent modeling of class analogies a reasonable choice for supervised pattern recognition?

Anita Rácz, Attila Gere, Dávid Bajusz, Károly Héberger
2018 RSC Advances  
discriminant analysis (LDA).  ...  Regularized discriminant analyses use a meta-parameter to develop a better estimate of the covariance matrix of the data than linear or quadratic discriminant analysis without ignoring the differences  ... 
doi:10.1039/c7ra08901e fatcat:5bznybd5ynacdguax3c7txnbua
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