Finding appropriate low dimensional representations of high-dimensional multimodal data can be challenging, since each modality embodies unique deformations and interferences. In this paper, we address the problem using manifold learning, where the data from each modality is assumed to lie on some manifold. In this context, the goal is to characterize the relations between the different modalities by studying their underlying manifolds. We propose two new diffusion operators that allow to isolate, enhance and attenuate the hidden components of multi-modal data in a data-driven manner. Based on these new operators, efficient low-dimensional representations can be constructed for such data, which characterize the common structures and the differences between the manifolds underlying the different modalities. The capabilities of the proposed operators are demonstrated on 3D shapes and on a fetal heart rate monitoring application.

Analyzing signals arising from dynamical systems typically requires many modeling assumptions and parameter estimation. In high dimensions, this modeling is particularly difficult due to the "curse of dimensionality". In this paper, we propose a method for building an intrinsic representation of such signals in a purely data-driven manner. First, we apply a manifold learning technique, diffusion maps, to learn the intrinsic model of the latent variables of the dynamical system, solely from the measurements. Second, we use concepts and tools from control theory and build a linear contracting observer to estimate the latent variables in a sequential manner from new incoming measurements. The effectiveness of the presented framework is demonstrated by applying it to a toy problem and to a music analysis application. In these examples we show that our method reveals the intrinsic variables of the analyzed dynamical systems.

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Objective To investigate the network dynamics mechanisms underlying differential initiation of epileptic interictal spikes and seizures. Methods We performed combined in vivo 2‐photon calcium imaging from different targeted neuronal subpopulations and extracellular electrophysiological recordings during 4‐aminopyridine–induced neocortical spikes and seizures. Results Both spikes and seizures were associated with intense synchronized activation of excitatory layer 2/3 pyramidal neurons (PNs) and to a lesser degree layer 4 neurons, as well as inhibitory parvalbumin‐expressing interneurons (INs). In sharp contrast, layer 5 PNs and somatostatin‐expressing INs were gradually and asynchronously recruited into the ictal activity during the course of seizures. Within layer 2/3, the main difference between onset of spikes and seizures lay in the relative recruitment dynamics of excitatory PNs compared to parvalbumin‐ and somatostatin‐expressing inhibitory INs. Whereas spikes exhibited balanced recruitment of PNs and parvalbumin‐expressing INs, during seizures IN responses were reduced and less synchronized than in layer 2/3 PNs. Similar imbalance was not observed in layers 4 or 5 of the neocortex. Machine learning–based algorithms we developed were able to distinguish spikes from seizures based solely on activation dynamics of layer 2/3 PNs at discharge onset. Interpretation During onset of seizures, the recruitment dynamics markedly differed between neuronal subpopulations, with rapid synchronous recruitment of layer 2/3 PNs, layer 4 neurons, and parvalbumin‐expressing INs and gradual asynchronous recruitment of layer 5 PNs and somatostatin‐expressing INs. Seizures initiated in layer 2/3 due to a dynamic mismatch between local PNs and inhibitory INs, and only later spread to layer 5 by gradually and asynchronously recruiting PNs in this layer. ANN NEUROL 2020;87:97–115

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