Taking advantage of the S4 class system of the programming environment R, which facilitates the creation and maintenance of reusable and modular components, an objectoriented framework for robust multivariate analysis was developed. The framework resides in the packages robustbase and rrcov and includes an almost complete set of algorithms for computing robust multivariate location and scatter, various robust methods for principal component analysis as well as robust linear and quadratic discriminant analysis. The design of these methods follows common patterns which we call statistical design patterns in analogy to the design patterns widely used in software engineering. The application of the framework to data analysis as well as possible extensions by the development of new methods is demonstrated on examples which themselves are part of the package rrcov.
High-dimensional data often contain many variables that are irrelevant for predicting a response or for an accurate group assignment. The inclusion of such variables in a regression or classification model leads to a loss in performance, even if the contribution of the variables to the model is small. Sparse methods for regression and classification are able to suppress these variables. This is possible by adding an appropriate penalty term to the objective function of the method.An overview of recent sparse methods for regression and classification is provided. The methods are applied to several high-dimensional data sets from chemometrics. A comparison with the non-sparse counterparts allows us to acquire an insight into their performance.
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