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Principal component analysis (PCA) is widely used in data processing and dimensionality reduction. However, PCA suffers from the fact that each principal component is a linear combination of all the original variables, thus it is often difficult to interpret the results. We introduce a new method called sparse principal component analysis (SPCA) using the lasso (elastic net) to produce modified principal components with sparse loadings. We first show that PCA can be formulated as a regression-type optimization problem; sparse loadings are then obtained by imposing the lasso (elastic net) constraint on the regression coefficients. Efficient algorithms are proposed to fit our SPCA models for both regular multivariate data and gene expression arrays. We also give a new formula to compute the total variance of modified principal components. As illustrations, SPCA is applied to real and simulated data with encouraging results. [ABSTRACT FROM AUTHOR]

The support vector machine (SVM) is known for its good performance in two-class classification, but its extension to multiclass classification is still an ongoing research is- sue. In this article, we propose a new approach for classification, called the import vector machine (IVM), which is built on kernel logistic regression (KLR). We show that the IVM not only performs as well as the SVM in two-class classification, but also can naturally be generalized to the multiclass case. Furthermore, the IVM provides an estimate of the underlying probability. Similar to the support points of the SVM, the IVM model uses only a fraction of the training data to index kernel basis functions, typically a much smaller fraction than the SVM. This gives the IVM a potential computational advantage over the SVM. [ABSTRACT FROM AUTHOR]

Develops a general method for finding important discriminant directions without assuming the class densities belong to any particular parametric family using a likelihood-based interpretation of linear discriminant analysis criterion. Importance of discriminant directions; Existence of local maxima; Misclassification errors for different one-dimensional Bayes rules.

We propose statistical measures for finding masses in mammograms. The measures are based on fitting broken line regressions to local intensity plots of the images. The method is illustrated on a small database of mammograms that have been read by a radiologist and confirmed by operative data. This work illustrates some of the statistical challenges in working with large diagnostic images, [ABSTRACT FROM AUTHOR]

Provides information on plug-in classification technique (PICT), a method that takes a standard classifier and plugs it into an algorithm to produce a new classifier. Suggested PICT for solving class classification problems using binary classifiers; Discussion on coding matrix; Functions of ECOC PICT.

Discusses an alternative algorithm in which the smooth functions are estimated using smoothing spline. The generalized cross-validation (GSV) based techniques used to select the smoothing parameters and number of terms; Structure of the automatic smoothing spline projection pursuit (ASP) algorithm; Examples comparing ASP with the standard supersmoother-based PPR algorithm of Friedman.