Similarities and Representations of Graph Structures

TSITSULIN, Anton, 2021. Similarities and Representations of Graph Structures. PhD Thesis. Universitäts-und Landesbibliothek Bonn. page . pdf

Knowledge discovery in databases (K D D) process [HPK01]

Jiawei Han, Jian Pei, and Micheline Kamber. Data mining: concepts and techniques. Elsevier, 2001. pdf

manual feature engineering

data-driven representation learning, which leverages the hidden symmetries and similarities in data

approaches to Feature Creation

having the data as a graph […] for example, we can quickly access the local neighborhood of each point. Local graph algorithms provide major e›ciency improvements over their global counterparts [Lin87].

LINIAL, Nathan, 1987. Distributive graph algorithms global solutions from local data. In: 28th Annual Symposium on Foundations of Computer Science (sfcs 1987). IEEE. 1987. p. 331–335. ieee .

This paper deals with distributed graph algorithms. Processors reside in the vertices of a graph G and communicate only with their Neighbors. The system is synchronous and reliable, there is no limit on message lengths and local computation is instantaneous. The results: A maximal independent set in an n-cycle cannot be found faster than Ω(log* n) and this is optimal by [CV]. The d-regular tree of radius r cannot be colored with fewer than √d colors in time 2r / 3. If Δ is the largest degree in G which has order n, then in time O(log*n) it can be colored with O(Δ2) colors.

The local graph modeling paradigm is one of the few that allows building algorithms that process billions of data points. In contrast, it is notably hard to develop local algorithms for dealing with tabular data, as there is no natural definition of points’ local neighborhood.

Graphs also provide us with a natural way of thinking about their multiscale structure ranging from the microscopic ego-network structure of nodes to mesoscopic clustersì to the overall macroscopic connectivity patterns.

Clusters in graphs are also called communities.

Diverse applications require analyzing graphs on different structural scales. While a sociologist classifies friends of a person into social circles—a purely local task, a biologist studies global activity patterns in brain networks. Therefore, scale-adaptive methods—ones that can focus the analysis on various structural scales—are oftentimes desirable for real-world applications. It is crucial to distinguish effcient local methods from the myopic single-scale local graph analysis. The very best local algorithms can provide a global view of the graph.