A method for the empirical mode decomposition (EMD) of complex-valued data is proposed. This is achieved based on the filter bank interpretation of the EMD mapping and by making use of the relationship between the positive and negative frequency component of the Fourier spectrum. The so-generated intrinsic mode functions (IMFs) are complex-valued, which facilitates the extension of the standard EMD to the complex domain. The analysis is supported by simulations on both synthetic and real-world complex-valued signals

The spatial weights for electrodes called common spatial pattern (CSP) are known to be effective in EEG signal classification for motor imagery-based brain-computer interface (MI-BCI). To achieve accurate classification in CSP, it is necessary to find frequency bands that relate to brain activities associated with BCI tasks. Several methods that determine such a set of frequency bands have been proposed. However, the existing methods cannot find the multiple frequency bands by using only learning data. To address this problem, we propose discriminative filter bank CSP (DFBCSP) that designs finite impulse response filters and the associated spatial weights by optimizing an objective function which is a natural extension of that of CSP. The optimization is conducted by sequentially and alternatively solving subproblems into which the original problem is divided. By experiments, it is shown that DFBCSP can effectively extract discriminative features for MI-BCI. Moreover, experimental results exhibit that DFBCSP can detect and extract the bands related to brain activities of motor imagery.

Big data analysis has become a crucial part of new emerging technologies such as the internet of things, cyber-physical analysis, deep learning, anomaly detection, etc. Among many other techniques, dimensionality reduction plays a key role in such analyses and facilitates feature selection and feature extraction. Randomized algorithms are efficient tools for handling big data tensors. They accelerate decomposing large-scale data tensors by reducing the computational complexity of deterministic algorithms and the communication among different levels of memory hierarchy, which is the main bottleneck in modern computing environments and architectures. In this article, we review recent advances in randomization for computation of Tucker decomposition and Higher Order SVD (HOSVD). We discuss random projection and sampling approaches, single-pass and multi-pass randomized algorithms and how to utilize them in the computation of the Tucker decomposition and the HOSVD. Simulations on synthetic and real datasets are provided to compare the performance of some of best and most promising algorithms.

Goal: A new method for steady-state visual evoked potentials (SSVEPs) frequency recognition is proposed to enhance the performance of SSVEP-based brain-computer interface (BCI). Methods: Correlated component analysis (CORCA) is introduced, which originally was designed to find linear combinations of electrodes that are consistent across subjects and maximally correlated between them. We propose a CORCA algorithm to learn spatial filters with multiple blocks of individual training data for SSVEP-based BCI scenario. The spatial filters are used to remove background noises by combining the multichannel EEG signals. We conduct a comparison between the proposed CORCA-based and the task-related component analysis (TRCA) based methods using a 40-class SSVEP benchmark dataset recorded from 35 subjects. Results: Our experimental study validates the efficiency of the CORCA-based method, and the extensive comparison results indicate that the CORCAbased method significantly outperforms the TRCA-based method. Conclusion and Significance: Superior performance demonstrates that the proposed method holds the promising potential to achieve satisfactory performance for SSVEP-based BCI with a large number of targets.