Learning Representations from EEG with Deep Recurrent-Convolutional Neural Networks

One of the challenges in modeling cognitive events from electroencephalogram (EEG) data is finding representations that are invariant to inter- and intra-subject differences, as well as to inherent noise associated with such data. Herein, we propose a novel approach for learning such representations from multi-channel EEG time-series, and demonstrate its advantages in the context of mental load classification task. First, we transform EEG activities into a sequence of topology-preserving multi-spectral images, as opposed to standard EEG analysis techniques that ignore such spatial information. Next, we train a deep recurrent-convolutional network inspired by state-of-the-art video classification to learn robust representations from the sequence of images. The proposed approach is designed to preserve the spatial, spectral, and temporal structure of EEG which leads to finding features that are less sensitive to variations and distortions within each dimension. Empirical evaluation on the cognitive load classification task demonstrated significant improvements in classification accuracy over current state-of-the-art approaches in this field.Comment: To be published as a conference paper at ICLR 201

Positive Alexander Duality for Pursuit and Evasion

Considered is a class of pursuit-evasion games, in which an evader tries to avoid detection. Such games can be formulated as the search for sections to the complement of a coverage region in a Euclidean space over a timeline. Prior results give homological criteria for evasion in the general case that are not necessary and sufficient. This paper provides a necessary and sufficient positive cohomological criterion for evasion in a general case. The principal tools are (1) a refinement of the Cech cohomology of a coverage region with a positive cone encoding spatial orientation, (2) a refinement of the Borel-Moore homology of the coverage gaps with a positive cone encoding time orientation, and (3) a positive variant of Alexander Duality. Positive cohomology decomposes as the global sections of a sheaf of local positive cohomology over the time axis; we show how this decomposition makes positive cohomology computable as a linear program.Comment: 19 pages, 6 figures; improvements made throughout: e.g. positive (co)homology generalized to arbitrary degrees; Positive Alexander Duality generalized from homological degrees 0,1; Morse and smoothness conditions generalized; illustrations of positive homology added. minor corrections in proofs, notation, organization, and language made throughout. variant of Borel-Moore homology now use

Joint segmentation and classification of retinal arteries/veins from fundus images

Objective Automatic artery/vein (A/V) segmentation from fundus images is required to track blood vessel changes occurring with many pathologies including retinopathy and cardiovascular pathologies. One of the clinical measures that quantifies vessel changes is the arterio-venous ratio (AVR) which represents the ratio between artery and vein diameters. This measure significantly depends on the accuracy of vessel segmentation and classification into arteries and veins. This paper proposes a fast, novel method for semantic A/V segmentation combining deep learning and graph propagation. Methods A convolutional neural network (CNN) is proposed to jointly segment and classify vessels into arteries and veins. The initial CNN labeling is propagated through a graph representation of the retinal vasculature, whose nodes are defined as the vessel branches and edges are weighted by the cost of linking pairs of branches. To efficiently propagate the labels, the graph is simplified into its minimum spanning tree. Results The method achieves an accuracy of 94.8% for vessels segmentation. The A/V classification achieves a specificity of 92.9% with a sensitivity of 93.7% on the CT-DRIVE database compared to the state-of-the-art-specificity and sensitivity, both of 91.7%. Conclusion The results show that our method outperforms the leading previous works on a public dataset for A/V classification and is by far the fastest. Significance The proposed global AVR calculated on the whole fundus image using our automatic A/V segmentation method can better track vessel changes associated to diabetic retinopathy than the standard local AVR calculated only around the optic disc.Comment: Preprint accepted in Artificial Intelligence in Medicin

Topological Schemas of Memory Spaces

Hippocampal cognitive map---a neuronal representation of the spatial environment---is broadly discussed in the computational neuroscience literature for decades. More recent studies point out that hippocampus plays a major role in producing yet another cognitive framework that incorporates not only spatial, but also nonspatial memories---the memory space. However, unlike cognitive maps, memory spaces have been barely studied from a theoretical perspective. Here we propose an approach for modeling hippocampal memory spaces as an epiphenomenon of neuronal spiking activity. First, we suggest that the memory space may be viewed as a finite topological space---a hypothesis that allows treating both spatial and nonspatial aspects of hippocampal function on equal footing. We then model the topological properties of the memory space to demonstrate that this concept naturally incorporates the notion of a cognitive map. Lastly, we suggest a formal description of the memory consolidation process and point out a connection between the proposed model of the memory spaces to the so-called Morris' schemas, which emerge as the most compact representation of the memory structure.Comment: 24 pages, 8 Figures, 1 Suppl. Figur