Bidirectional discrimination with application to data visualization

Huang, Hanwen; Liu, Yufeng; Marron, J. S.

doi:10.1093/biomet/ass029

Cited by 11 publications

(13 citation statements)

References 15 publications

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“…(). Interpretability is generally difficult with SVMs, except for the linear kernel SVM and its linear extensions (Huang et al., ). The restriction in interpretability and the need to transfer data for nearest neighbor approaches could easily lead to the decision that only logreg and RF are used for an application.…”

Section: Discussionmentioning

confidence: 99%

Probability estimation with machine learning methods for dichotomous and multicategory outcome: Applications

et al. 2014

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Machine learning methods are applied to three different large datasets, all dealing with probability estimation problems for dichotomous or multicategory data. Specifically, we investigate k-nearest neighbors, bagged nearest neighbors, random forests for probability estimation trees, and support vector machines with the kernels of Bessel, linear, Laplacian, and radial basis type. Comparisons are made with logistic regression. The dataset from the German Stroke Study Collaboration with dichotomous and three-category outcome variables allows, in particular, for temporal and external validation. The other two datasets are freely available from the UCI learning repository and provide dichotomous outcome variables. One of them, the Cleveland Clinic Foundation Heart Disease dataset, uses data from one clinic for training and from three clinics for external validation, while the other, the thyroid disease dataset, allows for temporal validation by separating data into training and test data by date of recruitment into study. For dichotomous outcome variables, we use receiver operating characteristics, areas under the curve values with bootstrapped 95% confidence intervals, and Hosmer-Lemeshow-type figures as comparison criteria. For dichotomous and multicategory outcomes, we calculated bootstrap Brier scores with 95% confidence intervals and also compared them through bootstrapping. In a supplement, we provide R code for performing the analyses and for random forest analyses in Random Jungle, version 2.1.0. The learning machines show promising performance over all constructed models. They are simple to apply and serve as an alternative approach to logistic or multinomial logistic regression analysis.

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Section: Discussionmentioning

confidence: 99%

Probability estimation with machine learning methods for dichotomous and multicategory outcome: Applications

et al. 2014

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“…However, the combinations of the two variables obtained with multidirectional classifiers provide a better result. This is somehow natural because one group has clusters and it has already been observed in Huang et al (2012) that products of two hyperplanes might produce good results in this situation. When the dimension of the classification problem increases, the multidirectional classifier (based on QSVM) still manages to find the best two directions to look at the data.…”

Section: Discussionmentioning

confidence: 99%

“…The ideas in this paper are related to those in Huang et al (2012), where the authors look for two discriminative directions by solving an optimization problem subject to certain restrictions to deal with distinct subpopulations in the groups. Though the present approach is completely different, the methodology proposed in this paper can also work under the presence of different clusters within the groups (see the example in Section 4).…”

Section: Figurementioning

confidence: 99%

“…, 0) , Observe that under M1 and M3 the Bayes rule is actually LDA, whereas under M2 and M4 the Bayes rule is QDA. Notice that the design of the simulation study does not particularly favor multidirectional rules, whose behavior tends to be better when there are clusters within the populations as illustrated by the toy example in Section 4 and pointed out in Huang et al (2012).…”

Section: M32mentioning

confidence: 99%

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Linear components of quadratic classifiers

Berrendero

Cárcamo

2018

Adv Data Anal Classif

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Esta es la versión de autor del artículo publicado en: This is an author produced version of a paper published in:Advances in Data Analysis and Classification, 07 April (2018) DOI: https://doi.org/10.1007/s11634-018-0321-6Copyright: © Springer-Verlag GmbH Germany, part of Springer Nature 2018El acceso a la versión del editor puede requerir la suscripción del recurso Access to the published version may require subscription Abstract We obtain a decomposition of any quadratic classifier in terms of products of hyperplanes. These hyperplanes can be viewed as relevant linear components of the quadratic rule (with respect to the underlying classification problem). As an application, we introduce the associated multidirectional classifier; a piecewise linear classification rule induced by the approximating products. Such a classifier is useful to determine linear combinations of the predictor variables with ability to discriminate. We also show that this classifier can be used as a tool to reduce the dimension of the data and helps identify the most important variables to classify new elements. Finally, we illustrate with a real data set the use of these linear components to construct oblique classification trees.

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“…Among various classification tools, linear classifiers are popular especially for high dimensional problems, due to their simplicity and good interpretability. While widely used, linear classifiers can be suboptimal for many practical problems [7]. One main practical problem we are interested in this paper is classification in the presence of latent subgroups.…”

Section: Introductionmentioning

confidence: 99%

Composite large margin classifiers with latent subclasses for heterogeneous biomedical data

Chen

Liu

Shen

et al. 2016

Statistical Analysis

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High dimensional classification problems are prevalent in a wide range of modern scientific applications. Despite a large number of candidate classification techniques available to use, practitioners often face a dilemma of choosing between linear and general nonlinear classifiers. Specifically, simple linear classifiers have good interpretability, but may have limitations in handling data with complex structures. In contrast, general nonlinear classifiers are more flexible, but may lose interpretability and have higher tendency for overfitting. In this paper, we consider data with potential latent subgroups in the classes of interest. We propose a new method, namely the Composite Large Margin Classifier (CLM), to address the issue of classification with latent subclasses. The CLM aims to find three linear functions simultaneously: one linear function to split the data into two parts, with each part being classified by a different linear classifier. Our method has comparable prediction accuracy to a general nonlinear classifier, and it maintains the interpretability of traditional linear classifiers. We demonstrate the competitive performance of the CLM through comparisons with several existing linear and nonlinear classifiers by Monte Carlo experiments. Analysis of the Alzheimer’s disease classification problem using CLM not only provides a lower classification error in discriminating cases and controls, but also identifies subclasses in controls that are more likely to develop the disease in the future.

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Bidirectional discrimination with application to data visualization

Cited by 11 publications

References 15 publications

Probability estimation with machine learning methods for dichotomous and multicategory outcome: Applications

Probability estimation with machine learning methods for dichotomous and multicategory outcome: Applications

Linear components of quadratic classifiers

Composite large margin classifiers with latent subclasses for heterogeneous biomedical data

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