Multi-View Multi-Graph Embedding for Brain Network Clustering Analysis

Network analysis of human brain connectivity is critically important for understanding brain function and disease states. Embedding a brain network as a whole graph instance into a meaningful low-dimensional representation can be used to investigate disease mechanisms and inform therapeutic interventions. Moreover, by exploiting information from multiple neuroimaging modalities or views, we are able to obtain an embedding that is more useful than the embedding learned from an individual view. Therefore, multi-view multi-graph embedding becomes a crucial task. Currently, only a few studies have been devoted to this topic, and most of them focus on the vector-based strategy which will cause structural information contained in the original graphs lost. As a novel attempt to tackle this problem, we propose Multi-view Multi-graph Embedding (M2E) by stacking multi-graphs into multiple partially-symmetric tensors and using tensor techniques to simultaneously leverage the dependencies and correlations among multi-view and multi-graph brain networks. Extensive experiments on real HIV and bipolar disorder brain network datasets demonstrate the superior performance of M2E on clustering brain networks by leveraging the multi-view multi-graph interactions

Multilayer Networks

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure

Spectrum: Fast density-aware spectral clustering for single and multi-omic data

Abstract Clustering of single or multi-omic data is key to developing personalised medicine and identifying new cell types. We present Spectrum, a fast spectral clustering method for single and multi-omic expression data. Spectrum is flexible and performs well on single-cell RNA-seq data. The method uses a new density-aware kernel that adapts to data scale and density. It uses a tensor product graph data integration and diffusion technique to reveal underlying structures and reduce noise. We developed a powerful method of eigenvector analysis to determine the number of clusters. Benchmarking Spectrum on 21 datasets demonstrated improvements in runtime and performance relative to other state-of-the-art methods. Contact: [email protected]

Learning Product Graphs from Spectral Templates

Graph Learning (GL) is at the core of inference and analysis of connections in data mining and machine learning (ML). By observing a dataset of graph signals, and considering specific assumptions, Graph Signal Processing (GSP) tools can provide practical constraints in the GL approach. One applicable constraint can infer a graph with desired frequency signatures, i.e., spectral templates. However, a severe computational burden is a challenging barrier, especially for inference from high-dimensional graph signals. To address this issue and in the case of the underlying graph having graph product structure, we propose learning product (high dimensional) graphs from product spectral templates with significantly reduced complexity rather than learning them directly from high-dimensional graph signals, which, to the best of our knowledge, has not been addressed in the related areas. In contrast to the rare current approaches, our approach can learn all types of product graphs (with more than two graphs) without knowing the type of graph products and has fewer parameters. Experimental results on both the synthetic and real-world data, i.e., brain signal analysis and multi-view object images, illustrate explainable and meaningful factor graphs supported by expert-related research, as well as outperforming the rare current restricted approaches.Comment: 10 figures, 12 pages, Submitted to IEEE Transactions on Signal and Information Processing over Networks on 10-Oct-202

Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks

Tensor-variate machine learning on graphs

Traditional machine learning algorithms are facing significant challenges as the world enters the era of big data, with a dramatic expansion in volume and range of applications and an increase in the variety of data sources. The large- and multi-dimensional nature of data often increases the computational costs associated with their processing and raises the risks of model over-fitting - a phenomenon known as the curse of dimensionality. To this end, tensors have become a subject of great interest in the data analytics community, owing to their remarkable ability to super-compress high-dimensional data into a low-rank format, while retaining the original data structure and interpretability. This leads to a significant reduction in computational costs, from an exponential complexity to a linear one in the data dimensions. An additional challenge when processing modern big data is that they often reside on irregular domains and exhibit relational structures, which violates the regular grid assumptions of traditional machine learning models. To this end, there has been an increasing amount of research in generalizing traditional learning algorithms to graph data. This allows for the processing of graph signals while accounting for the underlying relational structure, such as user interactions in social networks, vehicle flows in traffic networks, transactions in supply chains, chemical bonds in proteins, and trading data in financial networks, to name a few. Although promising results have been achieved in these fields, there is a void in literature when it comes to the conjoint treatment of tensors and graphs for data analytics. Solutions in this area are increasingly urgent, as modern big data is both large-dimensional and irregular in structure. To this end, the goal of this thesis is to explore machine learning methods that can fully exploit the advantages of both tensors and graphs. In particular, the following approaches are introduced: (i) Graph-regularized tensor regression framework for modelling high-dimensional data while accounting for the underlying graph structure; (ii) Tensor-algebraic approach for computing efficient convolution on graphs; (iii) Graph tensor network framework for designing neural learning systems which is both general enough to describe most existing neural network architectures and flexible enough to model large-dimensional data on any and many irregular domains. The considered frameworks were employed in several real-world applications, including air quality forecasting, protein classification, and financial modelling. Experimental results validate the advantages of the proposed methods, which achieved better or comparable performance against state-of-the-art models. Additionally, these methods benefit from increased interpretability and reduced computational costs, which are crucial for tackling the challenges posed by the era of big data.Open Acces