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Linear discriminant analysis (LDA) is a well-known technique for linear classification, feature extraction, and dimension reduction. To improve the accuracy of LDA under the high dimension low sample size (HDLSS) settings, shrunken estimators, such as Graphical Lasso, can be used to strike a balance between biases and variances. Although the estimator with induced sparsity obtains a faster convergence rate, however, the introduced bias may also degrade the performance. In this paper, we theoretically analyze how the sparsity and the convergence rate of the precision matrix (also known as inverse covariance matrix) estimator would affect the classification accuracy by proposing an analytic model on the upper bound of an LDA misclassification rate. Guided by the model, we propose a novel classifier, $\mathcal {DBSDA}$ , which improves classification accuracy through debiasing. Theoretical analysis shows that $\mathcal {DBSDA}$ possesses a reduced upper bound of misclassification rate and better asymptotic properties than sparse LDA (SDA). We conduct experiments on both synthetic datasets and real application datasets to confirm the correctness of our theoretical analysis and demonstrate the superiority of $\mathcal {DBSDA}$ over LDA, SDA, and other downstream competitors under HDLSS settings. [ABSTRACT FROM AUTHOR]

Recently, Dufrenois and Noyer proposed a one class Fisher’s linear discriminant to isolate normal data from outliers. In this paper, a kernelized version of their criterion is presented. Originally on the basis of an iterative optimization process, alternating between subspace selection and clustering, I show here that their criterion has an upper bound making these two problems independent. In particular, the estimation of the label vector is formulated as an unconstrained binary linear problem (UBLP) which can be solved using an iterative perturbation method. Once the label vector is estimated, an optimal projection subspace is obtained by solving a generalized eigenvalue problem. Like many other kernel methods, the performance of the proposed approach depends on the choice of the kernel. Constructed with a Gaussian kernel, I show that the proposed contrast measure is an efficient indicator for selecting an optimal kernel width. This property simplifies the model selection problem which is typically solved by costly (generalized) cross-validation procedures. Initialization, convergence analysis, and computational complexity are also discussed. Lastly, the proposed algorithm is compared with recent novelty detectors on synthetic and real data sets. [ABSTRACT FROM PUBLISHER]

This paper presents a Gaussian classifier-based evolutionary strategy (GCES) to solve multimodal optimization problems. An evolutionary technique for them must answer two crucial questions to guarantee its success: how to distinguish among the different basins of attraction and how to safeguard the already discovered good-quality solutions including both global and local optima. In GCES, multimodal optimization problems are regarded as classification ones, and Gaussian mixture models are employed to save the locations and basins of already and presently identified local or global optima. A sequential estimation technique for the covariance of a Gaussian model is introduced into GCES. To best adjust the global step size, a strategy named top-ranked sample selection is introduced, and a classification method instead of a common but problematic radius-triggered manner is proposed. Experiments are performed on a series of benchmark test functions to compare GCES with the state-of-the-art multimodal optimization approaches. The results show that GCES is not only simple to program and understand, but also provides better and consistent performance. [ABSTRACT FROM AUTHOR]