Multiclass Posterior Probability Twin SVM for Motor Imagery EEG Classification

Motor imagery electroencephalography is widely used in the brain-computer interface systems. Due to inherent characteristics of electroencephalography signals, accurate and real-time multiclass classification is always challenging. In order to solve this problem, a multiclass posterior probability solution for twin SVM is proposed by the ranking continuous output and pairwise coupling in this paper. First, two-class posterior probability model is constructed to approximate the posterior probability by the ranking continuous output techniques and Platt’s estimating method. Secondly, a solution of multiclass probabilistic outputs for twin SVM is provided by combining every pair of class probabilities according to the method of pairwise coupling. Finally, the proposed method is compared with multiclass SVM and twin SVM via voting, and multiclass posterior probability SVM using different coupling approaches. The efficacy on the classification accuracy and time complexity of the proposed method has been demonstrated by both the UCI benchmark datasets and real world EEG data from BCI Competition IV Dataset 2a, respectively.

Peripheral Members of M67

Despite enormous effort put into the membership determination of M67, we do not know very well its peripheral members. Since the Bonn double astrograph as well as Pulkovo normal astrograph plates cover nearly 1°.5 × 1°.5 on the sky we have combined newly derived astrometric data from both instruments. Nearly 2,000 stars were measured down to the plate limit B ≈ 16.5. The proper–motion standard error for well-measured stars is ±0.3 mas/yr. For the membership probability solution we selected only 1363 stars, all brighter than V ≈ 15.0, with good proper motions. The membership solution yielded 446 cluster members showing convincing discrimination between the cluster and field stars. The spatial distribution of peripheral cluster members seems to be asymmetric, although, it does not indicate that the tidal radius of the cluster has been reached.