Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Automorphic Distance Metric and its Application to Node Embedding for
  Role Mining   Role is a fundamental concept in the analysis of the behavior and function of
interacting entities represented by network data. Role discovery is the task of
uncovering hidden roles. Node roles are commonly defined in terms of
equivalence classes, where two nodes have the same role if they fall within the
same equivalence class. Automorphic equivalence, where two nodes are equivalent
when they can swap their labels to form an isomorphic graph, captures this
common notion of role. The binary concept of equivalence is too restrictive and
nodes in real-world networks rarely belong to the same equivalence class.
Instead, a relaxed definition in terms of similarity or distance is commonly
used to compute the degree to which two nodes are equivalent. In this paper, we
propose a novel distance metric called automorphic distance, which measures how
far two nodes are of being automorphically equivalent. We also study its
application to node embedding, showing how our metric can be used to generate
vector representations of nodes preserving their roles for data visualization
and machine learning. Our experiments confirm that the proposed metric
outperforms the RoleSim automorphic equivalence-based metric in the generation
of node embeddings for different networks.

31
The categories of this paper are: ao-sci
2
The categories of this paper are: math
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph