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

Communities in C. elegans connectome through the prism of non-backtracking walks

Abstract The fundamental relationship between the mesoscopic structure of neuronal circuits and organismic functions they subserve is one of the major challenges in contemporary neuroscience. Formation of structurally connected modules of neurons enacts the conversion from single-cell firing to large-scale behaviour of an organism, highlighting the importance of their accurate profiling in the data. While connectomes are typically characterized by significant sparsity of neuronal connections, recent advances in network theory and machine learning have revealed fundamental limitations of traditionally used community detection approaches in cases where the network is sparse. Here we studied the optimal community structure in the structural connectome of Caenorhabditis elegans, for which we exploited a non-conventional approach that is based on non-backtracking random walks, virtually eliminating the sparsity issue. In full agreement with the previous asymptotic results, we demonstrated that non-backtracking walks resolve the ground truth annotation into clusters on stochastic block models (SBM) with the size and density of the connectome better than the spectral methods related to simple random walks. Based on the cluster detectability threshold, we determined that the optimal number of modules in a recently mapped connectome of C. elegans is 10, which precisely corresponds to the number of isolated eigenvalues in the spectrum of the non-backtracking flow matrix. The discovered communities have a clear interpretation in terms of their functional role, which allows one to discern three structural compartments in the worm: the Worm Brain (WB), the Worm Movement Controller (WMC), and the Worm Information Flow Connector (WIFC). Broadly, our work provides a robust network-based framework to reveal mesoscopic structures in sparse connectomic datasets, paving way to further investigation of connectome mechanisms for different functions