Optimization of Alpha-Beta Log-Det Divergences and their Application in the Spatial Filtering of Two Class Motor Imagery Movements

Learning Log-Determinant Divergences for Positive Definite Matrices

Representations in the form of Symmetric Positive Definite (SPD) matrices have been popularized in a variety of visual learning applications due to their demonstrated ability to capture rich second-order statistics of visual data. There exist several similarity measures for comparing SPD matrices with documented benefits. However, selecting an appropriate measure for a given problem remains a challenge and in most cases, is the result of a trial-and-error process. In this paper, we propose to learn similarity measures in a data-driven manner. To this end, we capitalize on the αβ-log-det divergence, which is a meta-divergence parametrized by scalars α and β, subsuming a wide family of popular information divergences on SPD matrices for distinct and discrete values of these parameters. Our key idea is to cast these parameters in a continuum and learn them from data. We systematically extend this idea to learn vector-valued parameters, thereby increasing the expressiveness of the underlying non-linear measure. We conjoin the divergence learning problem with several standard tasks in machine learning, including supervised discriminative dictionary learning and unsupervised SPD matrix clustering. We present Riemannian gradient descent schemes for optimizing our formulations efficiently, and show the usefulness of our method on eight standard computer vision tasks.

A Robust Distance Measure for Similarity-Based Classification on the SPD Manifold

The symmetric positive definite (SPD) matrices, forming a Riemannian manifold, are commonly used as visual representations. The non-Euclidean geometry of the manifold often makes developing learning algorithms (e.g., classifiers) difficult and complicated. The concept of similarity-based learning has been shown to be effective to address various problems on SPD manifolds. This is mainly because the similarity-based algorithms are agnostic to the geometry and purely work based on the notion of similarities/distances. However, existing similarity-based models on SPD manifolds opt for holistic representations, ignoring characteristics of information captured by SPD matrices. To circumvent this limitation, we propose a novel SPD distance measure for the similarity-based algorithm. Specifically, we introduce the concept of point-to-set transformation, which enables us to learn multiple lower dimensional and discriminative SPD manifolds from a higher dimensional one. For lower dimensional SPD manifolds obtained by the point-to-set transformation, we propose a tailored set-to-set distance measure by making use of the family of alpha-beta divergences. We further propose to learn the point-to-set transformation and the set-to-set distance measure jointly, yielding a powerful similarity-based algorithm on SPD manifolds. Our thorough evaluations on several visual recognition tasks (e.g., action classification and face recognition) suggest that our algorithm comfortably outperforms various state-of-the-art algorithms.

An Optimized Channel Selection Method Based on Multifrequency CSP-Rank for Motor Imagery-Based BCI System

BACKGROUND

Due to the redundant information contained in multichannel electroencephalogram (EEG) signals, the classification accuracy of brain-computer interface (BCI) systems may deteriorate to a large extent. Channel selection methods can help to remove task-independent electroencephalogram (EEG) signals and hence improve the performance of BCI systems. However, in different frequency bands, brain areas associated with motor imagery are not exactly the same, which will result in the inability of traditional channel selection methods to extract effective EEG features.

NEW METHOD

To address the above problem, this paper proposes a novel method based on common spatial pattern- (CSP-) rank channel selection for multifrequency band EEG (CSP-R-MF). It combines the multiband signal decomposition filtering and the CSP-rank channel selection methods to select significant channels, and then linear discriminant analysis (LDA) was used to calculate the classification accuracy.

RESULTS

The results showed that our proposed CSP-R-MF method could significantly improve the average classification accuracy compared with the CSP-rank channel selection method.

EEG Signal Processing in MI-BCI Applications With Improved Covariance Matrix Estimators

In brain-computer interfaces (BCIs), the typical models of the EEG observations usually lead to a poor estimation of the trial covariance matrices, given the high non-stationarity of the EEG sources. We propose the application of two techniques that significantly improve the accuracy of these estimations and can be combined with a wide range of motor imagery BCI (MI-BCI) methods. The first one scales the observations in such a way that implicitly normalizes the common temporal strength of the source activities. When the scaling applies independently to the trials of the observations, the procedure justifies and improves the classical preprocessing for the EEG data. In addition, when the scaling is instantaneous and independent for each sample, the procedure particularizes to Tyler's method in statistics for obtaining a distribution-free estimate of scattering. In this case, the proposal provides an original interpretation of this existing method as a technique that pursuits an implicit instantaneous power-normalization of the underlying source processes. The second technique applies to the classifier and improves its performance through a convenient regularization of the features covariance matrix. Experimental tests reveal that a combination of the proposed techniques with the state-of-the-art algorithms for motor-imagery classification provides a significant improvement in the classification results.

Towards correlation-based time window selection method for motor imagery BCIs

The start of the cue is often used to initiate the feature window used to control motor imagery (MI)-based brain-computer interface (BCI) systems. However, the time latency during an MI period varies between trials for each participant. Fixing the starting time point of MI features can lead to decreased system performance in MI-based BCI systems. To address this issue, we propose a novel correlation-based time window selection (CTWS) algorithm for MI-based BCIs. Specifically, the optimized reference signals for each class were selected based on correlation analysis and performance evaluation. Furthermore, the starting points of time windows for both training and testing samples were adjusted using correlation analysis. Finally, the feature extraction and classification algorithms were used to calculate the classification accuracy. With two datasets, the results demonstrate that the CTWS algorithm significantly improved the system performance when compared to directly using feature extraction approaches. Importantly, the average improvement in accuracy of the CTWS algorithm on the datasets of healthy participants and stroke patients was 16.72% and 5.24%, respectively when compared to traditional common spatial pattern (CSP) algorithm. In addition, the average accuracy increased 7.36% and 9.29%, respectively when the CTWS was used in conjunction with Sub-Alpha-Beta Log-Det Divergences (Sub-ABLD) algorithm. These findings suggest that the proposed CTWS algorithm holds promise as a general feature extraction approach for MI-based BCIs.

Information Theoretic Approaches for Motor-Imagery BCI Systems: Review and Experimental Comparison

Brain computer interfaces (BCIs) have been attracting a great interest in recent years. The common spatial patterns (CSP) technique is a well-established approach to the spatial filtering of the electroencephalogram (EEG) data in BCI applications. Even though CSP was originally proposed from a heuristic viewpoint, it can be also built on very strong foundations using information theory. This paper reviews the relationship between CSP and several information-theoretic approaches, including the Kullback-Leibler divergence, the Beta divergence and the Alpha-Beta log-det (AB-LD)divergence. We also revise other approaches based on the idea of selecting those features that are maximally informative about the class labels. The performance of all the methods will be also compared via experiments.