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Worst-Case Linear Discriminant Analysis
2010
Neural Information Processing Systems
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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]
2014
arXiv
pre-print
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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
2008
SIAM Journal on Optimization
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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
2007
2007 46th IEEE Conference on Decision and Control
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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
2005
Neural Information Processing Systems
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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
2004
Journal of Multivariate Analysis
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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
2011
European Food Research and Technology
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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
2010
International Journal of Machine Learning and Cybernetics
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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
2011
International Journal of Computational Intelligence Systems
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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
2016
Communications in statistics. Simulation and computation
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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
2010
2010 20th International Conference on Pattern Recognition
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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]
1995
Lecture Notes in Computer Science
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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]
2021
arXiv
pre-print
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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
2014
International Conference on Grammatical Inference
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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?
2018
RSC Advances
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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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