Among all adaptive filtering algorithms, Widrow and Hoff's least mean square (LMS) has probably become the most popular because of its robustness, good tracking properties and simplicity. A drawback of LMS is that the step size implies a compromise between speed of convergence and final misadjustment. To combine different speed LMS filters serves to alleviate this compromise, as it was demonstrated by our studies on a two filter combination that we call combination of LMS filters (CLMS). Here, we extend this scheme in two directions. First, we propose a generalization to combine multiple LMS filters with different steps that provides the combination with better tracking capabilities. Second, we use a different mixing parameter for each weight of the filter in order to make independent their adaption speeds. Some simulation examples in plant identification and noise cancellation applications show the validity of the new schemes when compared to the CLMS filter and to other previous variable step approaches.

In this correspondence, we derive an online adaptive one-class support vector machine. The machine structure is updated via growing and pruning mechanisms and the weights are updated using structural risk minimization principles underlying support vector machines. Our approach leads to very compact machines compared to other online kernel methods whose size, unless truncated, grows almost linearly with the number of observed patterns. The proposed method is online in the sense that every pattern is only presented once to the machine and there is no need to store past samples and adaptive in the sense that it can forget past input patterns and adapt to the new characteristics of the incoming data. Thus, the characterizing properties of our algorithm are compactness, adaptiveness and real-time processing capabilities, making it especially well-suited to solve online novelty detection problems. Regarding algorithm performance, we have carried out experiments in a time series segmentation problem, obtaining favorable results in both accuracy and model complexity with respect to two existing state-of-the-art methods.

An important problem that hinders the use of supervised classification algorithms for brain imaging is that the number of variables per single subject far exceeds the number of training subjects available. Deriving multivariate measures of variable importance becomes a challenge in such scenarios. This paper proposes a new measure of variable importance termed sign-consistency bagging (SCB). The SCB captures variable importance by analyzing the sign consistency of the corresponding weights in an ensemble of linear support vector machine (SVM) classifiers. Further, the SCB variable importances are enhanced by means of transductive conformal analysis. This extra step is important when the data can be assumed to be heterogeneous. Finally, the proposal of these SCB variable importance measures is completed with the derivation of a parametric hypothesis test of variable importance. The new importance measures were compared with a t-test based univariate and an SVM-based multivariate variable importances using anatomical and functional magnetic resonance imaging data. The obtained results demonstrated that the new SCB based importance measures were superior to the compared methods in terms of reproducibility and classification accuracy.