(185e) A Graph-Based Software Framework for Data Science

Graphs are mathematical representations that that can be used to model a wide range of systems arising in science and engineering. Simply stated, graphs are models that capture connectivity in systems by using sets of nodes and edges (links between nodes) and data embedded in such nodes and edges. For example, graphs have been used to represent chemical processes (collections of interconnected unit operations) [1] and molecules (collections of interconnected atoms) [2,3]. By creating graph representations for systems of interest, researchers have also enabled a variety of descriptors that are useful for analysis and graph quantification such as spanning trees, number of nodes or edges, number of connected components, and topological descriptors (e.g., Euler Characteristic) [4,5,6,7,8]. These and other tools have been applied in analyzing networks in different fields, including chemical processes [6], biological systems [9], brain networks [10], or geomorphology [11].

Many datasets encountered in science and engineering can also be represented as graphs, and doing so can unravel unique insights. For example, a data matrix can be represented as a graph where each entry is a weighted node with weight corresponding to the entry value and with edges that capture adjacency between matrix entries (form a perfect mesh). Furthermore, any symmetric matrix (e.g., a covariance matrix or a Euclidean distance matrix) can be represented an edge weighted graph where the rows and columns of the matrix correspond to nodes and each matrix entry corresponds to a weighted edge between the row node and the column node corresponding to that entry. Graph data representations can be manipulated through operations such as filtration, aggregation, or partitioning and analyzed using topological descriptors [6]. This approach differs from standard matrix analysis techniques (e.g., eigenvalue analysis). Graph analysis tools can also be applied to high-dimensional representations; for example, molecules contain large amounts of data within each atom node (multiple attributes) [2,3].

In this work, we present a Julia-based software framework for the modeling analysis of graph-based data representations. The framework provides user-friendly capabilities to automatically manipulate diverse raw data types (e.g., matrices and time-series) to obtain different graph representations. The graph representations can then be analyzed using filtration and aggregation functions and summarized using a wide range of graph descriptors. Moreover, our framework facilitates the partitioning and visualization of graph objects to gain deeper analysis. We also present examples of applications for these tools and show how these tools simplify some data analysis.

References

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