Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Crossing Minimization within Graph Embeddings   We propose a novel optimization-based approach to embedding heterogeneous
high-dimensional data characterized by a graph. The goal is to create a
two-dimensional visualization of the graph structure such that edge-crossings
are minimized while preserving proximity relations between nodes. This paper
provides a fundamentally new approach for addressing the crossing minimization
criteria that exploits Farkas' Lemma to re-express the condition for no
edge-crossings as a system of nonlinear inequality constraints. The approach
has an intuitive geometric interpretation closely related to support vector
machine classification. While the crossing minimization formulation can be
utilized in conjunction with any optimization-based embedding objective, here
we demonstrate the approach on multidimensional scaling by modifying the stress
majorization algorithm to include penalties for edge crossings. The proposed
method is used to (1) solve a visualization problem in tuberculosis molecular
epidemiology and (2) generate embeddings for a suite of randomly generated
graphs designed to challenge the algorithm. Experimental results demonstrate
the efficacy of the approach. The proposed edge-crossing constraints and
penalty algorithm can be readily adapted to other supervised and unsupervised
optimization-based embedding or dimensionality reduction methods. The
constraints can be generalized to remove overlaps between any graph components
represented as convex polyhedrons including node-edge and node-node
intersections.

9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs