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 exp...

A low-degree dual-cube was proposed as an alternative to the hypercubes. A dual-cube DC(m) has m + 1 links per node, where m is the degree of a cluster (m-cube) and one more link is used for connecting to a node in another cluster. There are 2 clusters and hence the total number of nodes in a DC(m) is 2 + . In this paper, by using Gray code, we show that there exists a fault-free cycle containi...

Graph-based representations are of broad use and applicability in pattern recognition. They exhibit, however, a major drawback with regards to the processing tools that are available in their domain. Graph embedding into vector spaces is a growing field among the structural pattern recognition community which aims at providing a feature vector representation for every graph, and thus enables cl...

Let fv denote the number of faulty vertices in an n-dimensional hypercube Qn. In this paper, we prove that every fault-free edge of Qn for n ≥ 4 and every fault-free vertex of Qn for n ≥ 3 lies on a fault-free cycle of every even length from 6 to 2 − 2fv inclusive if fv = n− 1, and all faulty vertices are not adjacent to the same vertex.

Graph embedding, representing local and global neighbourhood information by numerical vectors, is a crucial part of the mathematical modeling wide range real-world systems. Among embedding algorithms, random walk-based algorithms have proven to be very successful. These collect creating numerous walks with predefined number steps. Creating most demanding process. The computation demand increase...

Graph neural networks (GNNs) have demonstrated a significant success in various graph learning tasks, from classification to anomaly detection. There recently has emerged number of approaches adopting pooling operation within GNNs, with goal preserve attributive and structural features during the representation learning. However, most existing operations suffer limitations relying on node-wise ...

Recent work has attempted to identify structure in social and information graphs by using the following approach: first, use random walk methods to explore the neighborhood of a node; second, use ideas from natural language processing to use this neighborhood information to learn vector representations of these nodes reflecting properties of the graph. Informally, the idea is that if a node is ...

A low-degree dual-cube was proposed as an alternative to the hypercubes. A dual-cube DC(m) has m + 1 links per node where m is the degree of a cluster (m-cube) and one more link is used for connecting to a node in another cluster. There are 2m+1 clusters and hence the total number of nodes is 22m+1 in a DC(m). In this paper, by using Gray code, we show that there exists a faulty-free cycle cont...

Graph clustering (or community detection) has long drawn enormous aŠention from the research on web mining and information networks. Recent literature on this topic has reached a consensus that node contents and link structures should be integrated for reliable graph clustering, especially in an unsupervised setting. However, existing methods based on shallow models o‰en su‚er from content nois...