Multivariate Wasserstein Functional Connectivity for Autism Screening

Most approaches to the estimation of brain functional connectivity from the functional magnetic resonance imaging (fMRI) data rely on computing some measure of statistical dependence, or more generally, a distance between univariate representative time series of regions of interest (ROIs) consisting of multiple voxels. However, summarizing a ROI's multiple time series with its mean or the first principal component (1PC) may result to the loss of information as, for example, 1PC explains only a small fraction of variance of the multivariate signal of the neuronal activity. We propose to compare ROIs directly, without the use of representative time series, defining a new measure of multivariate connectivity between ROIs, not necessarily consisting of the same number of voxels, based on the Wasserstein distance. We assess the proposed Wasserstein functional connectivity measure on the autism screening task, demonstrating its superiority over commonly used univariate and multivariate functional connectivity measures.

Individual Topology Structure of Eye Movement Trajectories

Traditionally, extracting patterns from eye movement data relies on statistics of different macro-events such as fixations and saccades. This requires an additional preprocessing step to separate the eye movement subtypes, often with a number of parameters on which the classification results depend. Besides that, definitions of such macro events are formulated in different ways by different researchers. We propose an application of a new class of features to the quantitative analysis of personal eye movement trajectories structure. This new class of features based on algebraic topology allows extracting patterns from different modalities of gaze such as time series of coordinates and amplitudes, heatmaps, and point clouds in a unified way at all scales from micro to macro. We experimentally demonstrate the competitiveness of the new class of features with the traditional ones and their significant synergy while being used together for the person authentication task on the recently published eye movement trajectories dataset.

Data Augmentation with Manifold Barycenters

The training of Generative Adversarial Networks (GANs) requires a large amount of data, stimulating the development of new data augmentation methods to alleviate the challenge. Oftentimes, these methods either fail to produce enough new data or expand the dataset beyond the original knowledge domain. In this paper, we propose a new way of representing the available knowledge in the manifold of data barycenters. Such a representation allows performing data augmentation based on interpolation between the nearest data elements using Wasserstein distance. The proposed method finds cliques in the nearest-neighbors graph and, at each sampling iteration, randomly draws one clique to compute the Wasserstein barycenter with random uniform weights. These barycenters then become the new natural-looking elements that one could add to the dataset. We apply this approach to the problem of landmarks detection and augment the available landmarks data within the dataset. Additionally, the idea is validated on cardiac data for the task of medical segmentation. Our approach reduces the overfitting and improves the quality metrics both beyond the original data outcome and beyond the result obtained with classical augmentation methods.