Related papers: Descriptive Proximities I: Properties and interpla…
Experimental evidence indicates that simple models outperform complex deep networks on many unsupervised similarity tasks. We provide a simple yet rigorous explanation for this behaviour by introducing the concept of an optimal…
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
Random intersection graphs model networks with communities, assuming an underlying bipartite structure of groups and individuals, where these groups may overlap. Group memberships are generated through the bipartite configuration model.…
The principle of similarity, or homophily, is often used to explain patterns observed in complex networks such as transitivity and the abundance of triangles (3-cycles). However, many phenomena from division of labor to protein-protein…
Hypergraph is a general way of representing high-order relations on a set of objects. It is a generalization of graph, in which only pairwise relations can be represented. It finds applications in various domains where relationships of more…
We study the structure of representations, defined as approximations of minimal sufficient statistics that are maximal invariants to nuisance factors, for visual data subject to scaling and occlusion of line-of-sight. We derive analytical…
The appearance of the world varies dramatically not only from place to place but also from hour to hour and month to month. Every day billions of images capture this complex relationship, many of which are associated with precise time and…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
The paper proposes a general notion of interaction between attributes, which can be applied to many fields in decision making and data analysis. It generalizes the notion of interaction defined for criteria modelled by capacities, by…
We investigate some aspects of relativistic classical theories with "relative locality", in which pairs of events established to be coincident by nearby observers may be described as non-coincident by distant observers. While previous…
In this paper, we use theory of rough set to study graphs using the concept of orbits. We investigate the indiscernibility partitions and approximations of graphs induced by orbits of graphs. We also study rough membership functions,…
We characterize the orderings of pairs of sets induced by several distances: Hamming, Jaccard, S\o rensen-Dice and Overlap. We also characterize these distances.
A simple field theory approach is developed to model the properties of charged, dielectric bodies and their associated counterions. This predictive theory is able to accurately describe the properties of systems (as compared to computer…
Structural roles define sets of structurally similar nodes that are more similar to nodes inside the set than outside, whereas communities define sets of nodes with more connections inside the set than outside. Roles based on structural…
Many learning algorithms such as kernel machines, nearest neighbors, clustering, or anomaly detection, are based on the concept of 'distance' or 'similarity'. Before similarities are used for training an actual machine learning model, we…
The perceived similarity between objects has often been attributed to their physical and conceptual features, such as appearance and animacy, and the theoretical framework of object space is accordingly conceived. Here, we extend this…
This article consists in two independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they…
Bibliographic and co-citation coupling are two analytical methods widely used to measure the degree of similarity between scientific papers. These approaches are intuitive, easy to put into practice, and computationally cheap. Moreover,…
To understand the computations of our visual system, it is important to understand also the natural environment it evolved to interpret. Unfortunately, existing models of the visual environment are either unrealistic or too complex for…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…