A Semiparametric Bayesian Approach to Heterogeneous Spatial Autoregressive Models.

Many semiparametric spatial autoregressive (SSAR) models have been used to analyze spatial data in a variety of applications; however, it is a common phenomenon that heteroscedasticity often occurs in spatial data analysis. Therefore, when considering SSAR models in this paper, it is allowed that the variance parameters of the models can depend on the explanatory variable, and these are called heterogeneous semiparametric spatial autoregressive models. In order to estimate the model parameters, a Bayesian estimation method is proposed for heterogeneous SSAR models based on B-spline approximations of the nonparametric function. Then, we develop an efficient Markov chain Monte Carlo sampling algorithm on the basis of the Gibbs sampler and Metropolis-Hastings algorithm that can be used to generate posterior samples from posterior distributions and perform posterior inference. Finally, some simulation studies and real data analysis of Boston housing data have demonstrated the excellent performance of the proposed Bayesian method.

A Tensor-Based Frequency Features Combination Method for Brain-Computer Interfaces.

With the development of the brain-computer interface (BCI) community, motor imagery-based BCI system using electroencephalogram (EEG) has attracted increasing attention because of its portability and low cost. Concerning the multi-channel EEG, the frequency component is one of the most critical features. However, insufficient extraction hinders the development and application of MI-BCIs. To deeply mine the frequency information, we proposed a method called tensor-based frequency feature combination (TFFC). It combined tensor-to-vector projection (TVP), fast fourier transform (FFT), common spatial pattern (CSP) and feature fusion to construct a new feature set. With two datasets, we used different classifiers to compare TFFC with the state-of-the-art feature extraction methods. The experimental results showed that our proposed TFFC could robustly improve the classification accuracy of about 5% ( ). Moreover, visualization analysis implied that the TFFC was a generalization of CSP and Filter Bank CSP (FBCSP). Also, a complementarity between weighted narrowband features (wNBFs) and broadband features (BBFs) was observed from the averaged fusion ratio. This article certificates the importance of frequency information in the MI-BCI system and provides a new direction for designing a feature set of MI-EEG.