The purpose of this paper is to infer a dynamic graph as a global (collective) model of time-varying measurements at a set of network nodes. This model captures both pairwise as well as higher order interactions (i.e., more than two nodes) among the nodes. The motivation of this work lies in the search for a connectome model which properly captures brain functionality across all regions of the brain, and possibly at individual neurons. We formulate it as an optimization problem, a quadratic objective functional and tensor information of observed node signals over short time intervals. The proper regularization constraints reflect the graph smoothness and other dynamics involving the underlying graph’s Laplacian, as well as the time evolution smoothness of the underlying graph. The resulting joint optimization is solved by a continuous relaxation of the weight parameters and an introduced novel gradient-projection scheme. While the work may be applicable to any time-evolving data set (e.g., fMRI), we apply our algorithm to a real-world dataset comprising recorded activities of individual brain cells. The resulting model is shown to be not only viable but also efficiently computable.

In the era of big data, the sheer volume and complexity of datasets pose significant challenges in machine learning, particularly in image processing tasks. This paper introduces an innovative Autoencoder-based Dataset Condensation Model backed by Koopman operator theory that effectively packs large datasets into compact, information-rich representations. Inspired by the predictive coding mechanisms of the human brain, our model leverages a novel approach to encode and reconstruct data, maintaining essential features and label distributions. The condensation process utilizes an autoencoder neural network architecture, coupled with Optimal Transport theory and Wasserstein distance, to minimize the distributional discrepancies between the original and synthesized datasets. We present a two-stage implementation strategy: first, condensing the large dataset into a smaller synthesized subset; second, evaluating the synthesized data by training a classifier and comparing its performance with a classifier trained on an equivalent subset of the original data. Our experimental results demonstrate that the classifiers trained on condensed data exhibit comparable performance to those trained on the original datasets, thus affirming the efficacy of our condensation model. This work not only contributes to the reduction of computational resources but also paves the way for efficient data handling in constrained environments, marking a significant step forward in data-efficient machine learning.

The purpose of this paper is to infer a global (collective) model of time-varying responses of a set of nodes as a dynamic graph, where the individual time series are respectively observed at each of the nodes. The motivation of this work lies in the search for a connectome model which properly captures brain functionality upon observing activities in different regions of the brain and possibly of individual neurons. We formulate the problem as a quadratic objective functional of observed node signals over short time intervals, subjected to the proper regularization reflecting the graph smoothness and other dynamics involving the underlying graph's Laplacian, as well as the time evolution smoothness of the underlying graph. The resulting joint optimization is solved by a continuous relaxation and an introduced novel gradient-projection scheme. We apply our algorithm to a real-world dataset comprising recorded activities of individual brain cells. The resulting model is shown to not only be viable but also efficiently computable.