相关论文: Point sets and functions inducing tangles of set s…

Clustering is an unsupervised learning problem that aims to partition unlabelled data points into groups with similar features. Traditional clustering algorithms provide limited insight into the groups they find as their main focus is…

A new class of graphical models capturing the dependence structure of events that occur in time is proposed. The graphs represent so-called local independences, meaning that the intensities of certain types of events are independent of some…

Knowledge graphs have emerged as a widely adopted medium for storing relational data, making methods for automatically reasoning with them highly desirable. In this paper, we present a novel approach for inducing a hierarchy of subject…

Gated networks are networks that contain gating connections, in which the outputs of at least two neurons are multiplied. Initially, gated networks were used to learn relationships between two input sources, such as pixels from two images.…

Carmesin has extended Robertson and Seymour's tree-of-tangles theorem to the infinite tangles of locally finite infinite graphs. We extend it further to the infinite tangles of all infinite graphs. Our result has a number of applications…

We introduce a novel criterion in clustering that seeks clusters with limited range of values associated with each cluster's elements. In clustering or classification the objective is to partition a set of objects into subsets, called…

The concept of $typed$ $topology$ is introduced. In a typed topological space, some open sets are assigned "types", and topological concepts such as closure, connectedness can be defined using types. A finite data set in $R^2$ is a…

Many empirical networks display an inherent tendency to cluster, i.e. to form circles of connected nodes. This feature is typically measured by the clustering coefficient (CC). The CC, originally introduced for binary, undirected graphs,…

Motivated by the application problem of sensor fusion the author introduced the concept of graded set. It is reasoned that in classification problem arising in an information system (represented by information table), a novel set called…

We demonstrate the versatility of the tangle-tree duality theorem for abstract separation systems by using it to prove tree-of-tangles theorems. This approach allows us to strengthen some of the existing tree-of-tangles theorems by bounding…

We prove canonical and non-canonical tree-of-tangles theorems for abstract separation systems that are merely structurally submodular. Our results imply all known tree-of-tangles theorems for graphs, matroids and abstract separation systems…

Following Penrose, we introduce a family of graph functions defined in terms of contractions of certain products of symmetric tensors along the edges of a graph. Special cases of these functions enumerate edge colorings and cycles of…

We present a structural clustering algorithm for large-scale datasets of small labeled graphs, utilizing a frequent subgraph sampling strategy. A set of representatives provides an intuitive description of each cluster, supports the…

In this paper, we introduce complex functional maps, which extend the functional map framework to conformal maps between tangent vector fields on surfaces. A key property of these maps is their orientation awareness. More specifically, we…

Graphs are commonly used in mathematics to represent some relationships between items. However, as simple objects, they sometimes fail to capture all relevant aspects of real-world data. To address this problem, we generalize them and model…

A new and extensive formalism is developed for monads and galaxies in non-standard enlargements. It is shown that monads and galaxies can be manipulated using order-preserving and order-reversing set-to-set maps, and that set properties…

The objective functions used in spectral clustering are usually composed of two terms: i) a term that minimizes the local quadratic variation of the cluster assignments on the graph and; ii) a term that balances the clustering partition and…

Graphs are commonly used to represent and visualize causal relations. For a small number of variables, this approach provides a succinct and clear view of the scenario at hand. As the number of variables under study increases, the graphical…

Formation of a molecular network from multifunctional precursors is modelled with a random graph process. The random graph model favours reactivity for monomers that are positioned close in the network topology, and disfavours reactivity…

Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of…