Learning Interpretable Features of Graphs and Time Series Data

Graphs and time series are two of the most ubiquitous representations of data of modern time. Representation learning of real-world graphs and time-series data is a key component for the downstream supervised and unsupervised machine learning tasks such as classification, clustering, and visualization. Because of the inherent high dimensionality, representation learning, i.e., low dimensional vector-based embedding of graphs and time-series data is very challenging. Learning interpretable features incorporates transparency of the feature roles, and facilitates downstream analytics tasks in addition to maximizing the performance of the downstream machine learning models. In this thesis, we leveraged tensor (multidimensional array) decomposition for generating interpretable and low dimensional feature space of graphs and time-series data found from three domains: social networks, neuroscience, and heliophysics. We present the theoretical models and empirical results on node embedding of social networks, biomarker embedding on fMRI-based brain networks, and prediction and visualization of multivariate time-series-based flaring and non-flaring solar events

Detecting the community structure and activity patterns of temporal networks: a non-negative tensor factorization approach

The increasing availability of temporal network data is calling for more research on extracting and characterizing mesoscopic structures in temporal networks and on relating such structure to specific functions or properties of the system. An outstanding challenge is the extension of the results achieved for static networks to time-varying networks, where the topological structure of the system and the temporal activity patterns of its components are intertwined. Here we investigate the use of a latent factor decomposition technique, non-negative tensor factorization, to extract the community-activity structure of temporal networks. The method is intrinsically temporal and allows to simultaneously identify communities and to track their activity over time. We represent the time-varying adjacency matrix of a temporal network as a three-way tensor and approximate this tensor as a sum of terms that can be interpreted as communities of nodes with an associated activity time series. We summarize known computational techniques for tensor decomposition and discuss some quality metrics that can be used to tune the complexity of the factorized representation. We subsequently apply tensor factorization to a temporal network for which a ground truth is available for both the community structure and the temporal activity patterns. The data we use describe the social interactions of students in a school, the associations between students and school classes, and the spatio-temporal trajectories of students over time. We show that non-negative tensor factorization is capable of recovering the class structure with high accuracy. In particular, the extracted tensor components can be validated either as known school classes, or in terms of correlated activity patterns, i.e., of spatial and temporal coincidences that are determined by the known school activity schedule

Enhancing Deep Learning Models through Tensorization: A Comprehensive Survey and Framework

The burgeoning growth of public domain data and the increasing complexity of deep learning model architectures have underscored the need for more efficient data representation and analysis techniques. This paper is motivated by the work of (Helal, 2023) and aims to present a comprehensive overview of tensorization. This transformative approach bridges the gap between the inherently multidimensional nature of data and the simplified 2-dimensional matrices commonly used in linear algebra-based machine learning algorithms. This paper explores the steps involved in tensorization, multidimensional data sources, various multiway analysis methods employed, and the benefits of these approaches. A small example of Blind Source Separation (BSS) is presented comparing 2-dimensional algorithms and a multiway algorithm in Python. Results indicate that multiway analysis is more expressive. Contrary to the intuition of the dimensionality curse, utilising multidimensional datasets in their native form and applying multiway analysis methods grounded in multilinear algebra reveal a profound capacity to capture intricate interrelationships among various dimensions while, surprisingly, reducing the number of model parameters and accelerating processing. A survey of the multi-away analysis methods and integration with various Deep Neural Networks models is presented using case studies in different application domains.Comment: 34 pages, 8 figures, 4 table