Approximate joint diagonalization and geometric mean of symmetric positive definite matrices

Transfer Learning for P300 Brain-Computer Interfaces by Joint Alignment of Feature Vectors

This article presents a new transfer learning method named group learning, that jointly aligns multiple domains (many-to-many) and an extension named fast alignment that aligns any further domain to previously aligned group of domains (many-to-one). The proposed group alignment algorithm (GALIA) is evaluated on brain-computer interface (BCI) data and optimal hyper-parameter values of the algorithm are studied for classification performance and computational cost. Six publicly available P300 databases comprising 333 sessions from 177 subjects are used. As compared to the conventional subject-specific train/test pipeline, both group learning and fast alignment significantly improve the classification accuracy except for the database with clinical subjects (average improvement: 2.12±1.88%). GALIA utilizes cyclic approximate joint diagonalization (AJD) to find a set of linear transformations, one for each domain, jointly aligning the feature vectors of all domains. Group learning achieves a many-to-many transfer learning without compromising the classification performance on non-clinical BCI data. Fast alignment further extends the group learning for any unseen domains, allowing a many-to-one transfer learning with the same properties. The former method creates a single machine learning model using data from previous subjects and/or sessions, whereas the latter exploits the trained model for an unseen domain requiring no further training of the classifier.

mSPD-NN: A Geometrically Aware Neural Framework for Biomarker Discovery from Functional Connectomics Manifolds

Connectomics has emerged as a powerful tool in neuroimaging and has spurred recent advancements in statistical and machine learning methods for connectivity data. Despite connectomes inhabiting a matrix manifold, most analytical frameworks ignore the underlying data geometry. This is largely because simple operations, such as mean estimation, do not have easily computable closed-form solutions. We propose a geometrically aware neural framework for connectomes, i.e., the mSPD-NN, designed to estimate the geodesic mean of a collections of symmetric positive definite (SPD) matrices. The mSPD-NN is comprised of bilinear fully connected layers with tied weights and utilizes a novel loss function to optimize the matrix-normal equation arising from Fréchet mean estimation. Via experiments on synthetic data, we demonstrate the efficacy of our mSPD-NN against common alternatives for SPD mean estimation, providing competitive performance in terms of scalability and robustness to noise. We illustrate the real-world flexibility of the mSPD-NN in multiple experiments on rs-fMRI data and demonstrate that it uncovers stable biomarkers associated with subtle network differences among patients with ADHD-ASD comorbidities and healthy controls.

Revisiting Riemannian geometry-based EEG decoding through approximate joint diagonalization

Objective.The wider adoption of Riemannian geometry in electroencephalography (EEG) processing is hindered by two factors: (a) it involves the manipulation of complex mathematical formulations and, (b) it leads to computationally demanding tasks. The main scope of this work is to simplify particular notions of Riemannian geometry and provide an efficient and comprehensible scheme for neuroscientific explorations.Approach.To overcome the aforementioned shortcomings, we exploit the concept of approximate joint diagonalization in order to reconstruct the spatial covariance matrices assuming the existence of (and identifying) a common eigenspace in which the application of Riemannian geometry is significantly simplified.Main results.The employed reconstruction process abides to physiologically plausible assumptions, reduces the computational complexity in Riemannian geometry schemes and bridges the gap between rigorous mathematical procedures and computational neuroscience. Our approach is both formally established and experimentally validated by employing real and synthetic EEG data.Significance.The implications of the introduced reconstruction process are highlighted by reformulating and re-introducing two signal processing methodologies, namely the 'Symmetric Positive Definite (SPD) Matrix Quantization' and the 'Coding over SPD Atoms'. The presented approach paves the way for robust and efficient neuroscientific explorations that exploit Riemannian geometry schemes.

A novel method to reduce the motor imagery BCI illiteracy

To reduce the motor imagery brain-computer interface (MI-BCI) illiteracy phenomenon and improve the classification accuracy, this paper proposed a novel method combining paradigm selection and Riemann distance classification. Firstly, a novel sensitivity-based paradigm selection (SPS) algorithm is designed for the optimization of classification to find the best classification pattern through a sensitive indicator. Then, a generalized Riemann minimum distance mean (GRMDM) classifier is proposed by introducing a weight factor to fuse the Log-Euclidean Metric classifier and the Riemannian Stein divergence classifier. The experimental results show that the proposed method achieves a better performance for multi-class motor imagery tasks. The average classification accuracy on the BCI competition IV dataset2a is 80.98%, which is 11.04% higher than Stein divergence classifier on the original two-class paradigm. Furthermore, the proposed method demonstrates its capacity on reducing MI-BCI illiteracy. Graphical abstract Here we investigate whether the BCI illiteracy phenomenon can be reduced through sensitivity-based paradigm selection (SPS) method and generalized Riemann minimum distance mean (GRMDM) classifier when performing motor imagery tasks.

Assignment Flow for Order-Constrained OCT Segmentation

At the present time optical coherence tomography (OCT) is among the most commonly used non-invasive imaging methods for the acquisition of large volumetric scans of human retinal tissues and vasculature. The substantial increase of accessible highly resolved 3D samples at the optic nerve head and the macula is directly linked to medical advancements in early detection of eye diseases. To resolve decisive information from extracted OCT volumes and to make it applicable for further diagnostic analysis, the exact measurement of retinal layer thicknesses serves as an essential task be done for each patient separately. However, manual examination of OCT scans is a demanding and time consuming task, which is typically made difficult by the presence of tissue-dependent speckle noise. Therefore, the elaboration of automated segmentation models has become an important task in the field of medical image processing. We propose a novel, purely data driven geometric approach to order-constrained 3D OCT retinal cell layer segmentation which takes as input data in any metric space and can be implemented using only simple, highly parallelizable operations. As opposed to many established retinal layer segmentation methods, we use only locally extracted features as input and do not employ any global shape prior. The physiological order of retinal cell layers and membranes is achieved through the introduction of a smoothed energy term. This is combined with additional regularization of local smoothness to yield highly accurate 3D segmentations. The approach thereby systematically avoid bias pertaining to global shape and is hence suited for the detection of anatomical changes of retinal tissue structure. To demonstrate its robustness, we compare two different choices of features on a data set of manually annotated 3D OCT volumes of healthy human retina. The quality of computed segmentations is compared to the state of the art in automatic retinal layer segmention as well as to manually annotated ground truth data in terms of mean absolute error and Dice similarity coefficient. Visualizations of segmented volumes are also provided.

Using data from the Microsoft Kinect 2 to determine postural stability in healthy subjects: A feasibility trial

The objective of this study was to determine whether kinematic data collected by the Microsoft Kinect 2 (MK2) could be used to quantify postural stability in healthy subjects. Twelve subjects were recruited for the project, and were instructed to perform a sequence of simple postural stability tasks. The movement sequence was performed as subjects were seated on top of a force platform, and the MK2 was positioned in front of them. This sequence of tasks was performed by each subject under three different postural conditions: "both feet on the ground" (1), "One foot off the ground" (2), and "both feet off the ground" (3). We compared force platform and MK2 data to quantify the degree to which the MK2 was returning reliable data across subjects. We then applied a novel machine-learning paradigm to the MK2 data in order to determine the extent to which data from the MK2 could be used to reliably classify different postural conditions. Our initial comparison of force plate and MK2 data showed a strong agreement between the two devices, with strong Pearson correlations between the trunk centroids "Spine_Mid" (0.85 ± 0.06), "Neck" (0.86 ± 0.07) and "Head" (0.87 ± 0.07), and the center of pressure centroid inferred by the force platform. Mean accuracy for the machine learning classifier from MK2 was 97.0%, with a specific classification accuracy breakdown of 90.9%, 100%, and 100% for conditions 1 through 3, respectively. Mean accuracy for the machine learning classifier derived from the force platform data was lower at 84.4%. We conclude that data from the MK2 has sufficient information content to allow us to classify sequences of tasks being performed under different levels of postural stability. Future studies will focus on validating this protocol on large populations of individuals with actual balance impairments in order to create a toolkit that is clinically validated and available to the medical community.