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Understanding non-linear relationships among financial instruments has various applications in investment processes ranging from risk management, portfolio construction and trading strategies. Here, we focus on interconnectedness among…

While most network embedding techniques model the relative positions of nodes in a network, recently there has been significant interest in structural embeddings that model node role equivalences, irrespective of their distances to any…

A main challenge in mining network-based data is finding effective ways to represent or encode graph structures so that it can be efficiently exploited by machine learning algorithms. Several methods have focused in network representation…

spectral-based subspace learning is a common data preprocessing step in many machine learning pipelines. The main aim is to learn a meaningful low dimensional embedding of the data. However, most subspace learning methods do not take into…

Graph embeddings, wherein the nodes of the graph are represented by points in a continuous space, are used in a broad range of Graph ML applications. The quality of such embeddings crucially depends on whether the geometry of the space…

Large datasets with interactions between objects are common to numerous scientific fields (i.e. social science, internet, biology...). The interactions naturally define a graph and a common way to explore or summarize such dataset is graph…

We present a graph-theoretic modeling approach for hierarchical optimization that leverages the OptiGraph abstraction implemented in the Julia package Plasmo.jl. We show that the abstraction is flexible and can effectively capture complex…

Active area of research in AI is the theory of manifold learning and finding lower-dimensional manifold representation on how we can learn geometry from data for providing better quality curated datasets. There are however various issues…

A drawing in the plane ($\mathbb{R}^2$) of a graph $G=(V,E)$ equipped with a function $\gamma: V \rightarrow \mathbb{N}$ is \emph{$x$-bounded} if (i) $x(u) <x(v)$ whenever $\gamma(u)<\gamma(v)$ and (ii) $\gamma(u)\leq\gamma(w)\leq…

Neural embedding approaches have become a staple in the fields of computer vision, natural language processing, and more recently, graph analytics. Given the pervasive nature of these algorithms, the natural question becomes how to exploit…

A graph drawing in the plane is called an almost embedding if the images of any two non-adjacent simplices (i.e. vertices or edges) are disjoint. Almost embeddings (more precisely, their higher-dimensional analogues) naturally appear in…

This paper presents primarily two Euclidean embeddings of the quotient space generated by matrices that are identified modulo arbitrary row permutations. The original application is in deep learning on graphs where the learning task is…

Graph learning plays a central role in many data mining and machine learning tasks, such as manifold learning, data representation and analysis, dimensionality reduction, clustering, and visualization. In this work, we propose a highly…

Accurate localization is a fundamental requirement for autonomous robots operating in indoor environments. Scene graphs encode the spatial structure of an environment as a hierarchy of semantic entities and their relationships, and can be…

Theory of graphical models has matured over more than three decades to provide the backbone for several classes of models that are used in a myriad of applications such as genetic mapping of diseases, credit risk evaluation, reliability and…

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…

Graph Neural Networks usually rely on the assumption that the graph topology is available to the network as well as optimal for the downstream task. Latent graph inference allows models to dynamically learn the intrinsic graph structure of…

Revealing hidden geometry and topology in noisy data sets is a challenging task. Elastic principal graph is a computationally efficient and flexible data approximator based on embedding a graph into the data space and minimizing the energy…

Datasets encountered in scientific and engineering applications appear in complex formats (e.g., images, multivariate time series, molecules, video, text strings, networks). Graph theory provides a unifying framework to model such datasets…

The null space of the $k$-th order Laplacian $\mathbf{\mathcal L}_k$, known as the {\em $k$-th homology vector space}, encodes the non-trivial topology of a manifold or a network. Understanding the structure of the homology embedding can…