Related papers: Algebraic Conditions for Generating Accurate Adjac…
Visualization of the adjacency matrix enables us to capture macroscopic features of a network when the matrix elements are aligned properly. Community structure, a network consisting of several densely connected components, is a…
Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not…
Generation of realistic topologies plays an important role in determining the accuracy and validity of simulation studies. This study presents a discussion to justify why, and how often randomly generated adjacency matrices may not not…
Most existing semi-supervised graph-based clustering methods exploit the supervisory information by either refining the affinity matrix or directly constraining the low-dimensional representations of data points. The affinity matrix…
Causal learning is a beneficial approach to analyze the cause and effect relationships among variables in a dataset. A causal graph can be generated from a dataset using a particular causal algorithm, for instance, the PC algorithm or Fast…
In graphs, the concept of adjacency is clearly defined: it is a pairwise relationship between vertices. Adjacency in hypergraphs has to integrate hyperedge multi-adicity: the concept of adjacency needs to be defined properly by introducing…
Finding a new mathematical representations for graph, which allows direct comparison between different graph structures, is an open-ended research direction. Having such a representation is the first prerequisite for a variety of machine…
In the theory of line graphs of undirected graphs there exists an important theorem linking the incidence matrix of the root graph to the adjacency matrix of its line graph. For directed or mixed graphs, however, the exists no analogous…
For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomorphism problems. However, in some classification problems,…
Detecting tampered text in document images is a challenging task due to data scarcity. To address this, previous work has attempted to generate tampered documents using rule-based methods. However, the resulting documents often suffer from…
Symmetry plays a major role in subgraph matching both in the description of the graphs in question and in how it confounds the search process. This work addresses how to quantify these effects and how to use symmetries to increase the…
The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an…
In this work we target the problem of provably computing the equivalence between two programs represented as dataflow graphs. To this end, we formalize the problem of equivalence between two programs as finding a set of semantics-preserving…
Similarity graphs are an active research direction for the nearest neighbor search (NNS) problem. New algorithms for similarity graph construction are continuously being proposed and analyzed by both theoreticians and practitioners.…
We discuss the problem of extending data mining approaches to cases in which data points arise in the form of individual graphs. Being able to find the intrinsic low-dimensionality in ensembles of graphs can be useful in a variety of…
This is a proposal of an algebra which aims at distributed array processing. The focus lies on re-arranging and distributing array data, which may be multi-dimensional. The context of the work is scientific processing; thus, the core…
Many degree sequences can only be realised in graphs that contain a `ds-completable card', defined as a vertex-deleted subgraph in which the erstwhile neighbours of the deleted vertex can be identified from their degrees, if one knows the…
In this study, a pairwise comparison matrix is generalized to the case when coefficients create Lie group $G$, non necessarily abelian. A necessary and sufficient criterion for pairwise comparisons matrices to be consistent is provided.…
Causal graphs are commonly used to understand and model complex systems. Researchers often construct these graphs from different perspectives, leading to significant variations for the same problem. Comparing causal graphs is, therefore,…
Graph algorithms are central to large-scale applications such as navigation systems, social networks, and data analysis platforms. This thesis studies two important challenges in such systems: robustness to failures and fairness in…