Regularized linear discriminant analysis and its application in microarrays
TL;DR: Through both simulated data and real life data, it is shown that this method performs very well in multivariate classification problems, often outperforms the PAM method and can be as competitive as the support vector machines classifiers.
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Abstract: In this paper, we introduce a modified version of linear discriminant analysis, called the "shrunken centroids regularized discriminant analysis" (SCRDA). This method generalizes the idea of the "nearest shrunken centroids" (NSC) (Tibshirani and others, 2003) into the classical discriminant analysis. The SCRDA method is specially designed for classification problems in high dimension low sample size situations, for example, microarray data. Through both simulated data and real life data, it is shown that this method performs very well in multivariate classification problems, often outperforms the PAM method (using the NSC algorithm) and can be as competitive as the support vector machines classifiers. It is also suitable for feature elimination purpose and can be used as gene selection method. The open source R package for this method (named "rda") is available on CRAN (http://www.r-project.org) for download and testing.
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References
Regression Shrinkage and Selection via the Lasso
TL;DR: A new method for estimation in linear models called the lasso, which minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant, is proposed.
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The Elements of Statistical Learning
Trevor Hastie,Robert Tibshirani,Jerome H. Friedman +2 more
- 01 Jan 2001
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Regularization and variable selection via the elastic net
Hui Zou,Trevor Hastie +1 more
TL;DR: It is shown that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation, and an algorithm called LARS‐EN is proposed for computing elastic net regularization paths efficiently, much like algorithm LARS does for the lamba.
The Elements of Statistical Learning
TL;DR: Chapter 11 includes more case studies in other areas, ranging from manufacturing to marketing research, and a detailed comparison with other diagnostic tools, such as logistic regression and tree-based methods.
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Molecular classification of cancer: class discovery and class prediction by gene expression monitoring.
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TL;DR: A generic approach to cancer classification based on gene expression monitoring by DNA microarrays is described and applied to human acute leukemias as a test case and suggests a general strategy for discovering and predicting cancer classes for other types of cancer, independent of previous biological knowledge.