Parsimonious Mahalanobis Kernel for the Classification of High Dimensional Data

The classification of high dimensional data with kernel methods is considered in this article. Exploit- ing the emptiness property of high dimensional spaces, a kernel based on the Mahalanobis distance is proposed. The computation of the Mahalanobis distance requires the inversion of a covariance matrix. In high dimensional spaces, the estimated covariance matrix is ill-conditioned and its inversion is unstable or impossible. Using a parsimonious statistical model, namely the High Dimensional Discriminant Analysis model, the specific signal and noise subspaces are estimated for each considered class making the inverse of the class specific covariance matrix explicit and stable, leading to the definition of a parsimonious Mahalanobis kernel. A SVM based framework is used for selecting the hyperparameters of the parsimonious Mahalanobis kernel by optimizing the so-called radius-margin bound. Experimental results on three high dimensional data sets show that the proposed kernel is suitable for classifying high dimensional data, providing better classification accuracies than the conventional Gaussian kernel

Fault classification in dynamic processes using multiclass relevance vector machine and slow feature analysis

This paper proposes a modifed relevance vector machine with slow feature analysis fault classification for industrial processes. Traditional support vector machine classification does not work well when there are insufficient training samples. A relevance vector machine, which is a Bayesian learning-based probabilistic sparse model, is developed to determine the probabilistic prediction and sparse solutions for the fault category. This approach has the benefits of good generalization ability and robustness to small training samples. To maximize the dynamic separability between classes and reduce the computational complexity, slow feature analysis is used to extract the inner dynamic features and reduce the dimension. Experiments comparing the proposed method, relevance vector machine and support vector machine classification are performed using the Tennessee Eastman process. For all faults, relevance vector machine has a classification rate of 39%, while the proposed algorithm has an overall classification rate of 76.1%. This shows the efficiency and advantages of the proposed method

Convex Optimization for Binary Classifier Aggregation in Multiclass Problems

Multiclass problems are often decomposed into multiple binary problems that are solved by individual binary classifiers whose results are integrated into a final answer. Various methods, including all-pairs (APs), one-versus-all (OVA), and error correcting output code (ECOC), have been studied, to decompose multiclass problems into binary problems. However, little study has been made to optimally aggregate binary problems to determine a final answer to the multiclass problem. In this paper we present a convex optimization method for an optimal aggregation of binary classifiers to estimate class membership probabilities in multiclass problems. We model the class membership probability as a softmax function which takes a conic combination of discrepancies induced by individual binary classifiers, as an input. With this model, we formulate the regularized maximum likelihood estimation as a convex optimization problem, which is solved by the primal-dual interior point method. Connections of our method to large margin classifiers are presented, showing that the large margin formulation can be considered as a limiting case of our convex formulation. Numerical experiments on synthetic and real-world data sets demonstrate that our method outperforms existing aggregation methods as well as direct methods, in terms of the classification accuracy and the quality of class membership probability estimates.Comment: Appeared in Proceedings of the 2014 SIAM International Conference on Data Mining (SDM 2014

Projection based ensemble learning for ordinal regression

The classification of patterns into naturally ordered labels is referred to as ordinal regression. This paper proposes an ensemble methodology specifically adapted to this type of problems, which is based on computing different classification tasks through the formulation of different order hypotheses. Every single model is trained in order to distinguish between one given class (k) and all the remaining ones, but grouping them in those classes with a rank lower than k, and those with a rank higher than k. Therefore, it can be considered as a reformulation of the well-known one-versus-all scheme. The base algorithm for the ensemble could be any threshold (or even probabilistic) method, such as the ones selected in this paper: kernel discriminant analysis, support vector machines and logistic regression (all reformulated to deal with ordinal regression problems). The method is seen to be competitive when compared with other state-of-the-art methodologies (both ordinal and nominal), by using six measures and a total of fifteen ordinal datasets. Furthermore, an additional set of experiments is used to study the potential scalability and interpretability of the proposed method when using logistic regression as base methodology for the ensemble