Variable selection for discrimination of more than two classes where data are sparse

In classification, with an increasing number of variables, the required number of observations grows drastically. In this paper we present an approach to put into effect the maximal possible variable selection, by splitting a K class classification problem into pairwise problems. The principle makes use of the possibility that a variable that discriminates two classes will not necessarily do so for all such class pairs. We further present the construction of a classification rule based on the pairwise solutions by the Pairwise Coupling algorithm according to Hastie and Tibshirani (1998). The suggested proceedure can be applied to any classification method. Finally, situations with lack of data in multidimensional spaces are investigated on different simulated data sets to illustrate the problem and the possible gain. The principle is compared to the classical approach of linear and quadratic discriminant analysis. --

Variable selection for discrimination of more than two classes where data are sparse

In classification, with an increasing number of variables, the required number of observations grows drastically. In this paper we present an approach to put into effect the maximal possible variable selection, by splitting a K class classification problem into pairwise problems. The principle makes use of the possibility that a variable that discriminates two classes will not necessarily do so for all such class pairs. We further present the construction of a classification rule based on the pairwise solutions by the Pairwise Coupling algorithm according to Hastie and Tibshirani (1998). The suggested proceedure can be applied to any classification method. Finally, situations with lack of data in multidimensional spaces are investigated on different simulated data sets to illustrate the problem and the possible gain. The principle is compared to the classical approach of linear and quadratic discriminant analysis

Learning Discriminative Bayesian Networks from High-dimensional Continuous Neuroimaging Data

Due to its causal semantics, Bayesian networks (BN) have been widely employed to discover the underlying data relationship in exploratory studies, such as brain research. Despite its success in modeling the probability distribution of variables, BN is naturally a generative model, which is not necessarily discriminative. This may cause the ignorance of subtle but critical network changes that are of investigation values across populations. In this paper, we propose to improve the discriminative power of BN models for continuous variables from two different perspectives. This brings two general discriminative learning frameworks for Gaussian Bayesian networks (GBN). In the first framework, we employ Fisher kernel to bridge the generative models of GBN and the discriminative classifiers of SVMs, and convert the GBN parameter learning to Fisher kernel learning via minimizing a generalization error bound of SVMs. In the second framework, we employ the max-margin criterion and build it directly upon GBN models to explicitly optimize the classification performance of the GBNs. The advantages and disadvantages of the two frameworks are discussed and experimentally compared. Both of them demonstrate strong power in learning discriminative parameters of GBNs for neuroimaging based brain network analysis, as well as maintaining reasonable representation capacity. The contributions of this paper also include a new Directed Acyclic Graph (DAG) constraint with theoretical guarantee to ensure the graph validity of GBN.Comment: 16 pages and 5 figures for the article (excluding appendix

Parsimonious Kernel Fisher Discrimination

By applying recent results in optimization transfer, a new algorithm for kernel Fisher Discriminant Analysis is provided that makes use of a non-smooth penalty on the coefficients to provide a parsimonious solution. The algorithm is simple, easily programmed and is shown to perform as well as or better than a number of leading machine learning algorithms on a substantial benchmark. It is then applied to a set of extreme small-sample-size problems in virtual screening where it is found to be less accurate than a currently leading approach but is still comparable in a number of cases