Related papers: Cluster Magnification, Root Capacity, Unique Chain…
The proliferation of high-dimensional data from sources such as social media, sensor networks, and online platforms has created new challenges for clustering algorithms. Multi-view clustering, which integrates complementary information from…
We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant…
A differential version of the classical Weil descent is established in all characteristics. It yields a theory of differential restriction of scalars for differential varieties over finite differential field extensions. This theory is then…
After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…
We develop a network in which the natural numbers are the vertices. We use the decomposition of natural numbers by prime numbers to establish the connections. We perform data collapse and show that the degree distribution of these networks…
Graph clustering is a fundamental problem in unsupervised learning, with numerous applications in computer science and in analysing real-world data. In many real-world applications, we find that the clusters have a significant high-level…
Let a cluster be a term with a number of patterns occurring in it. We give two accounts of clusters, a geometric one as sets of (node and edge) positions, and an inductive one as pairs of terms with gaps (2nd order variables) and…
We consider the model of random trees introduced by Devroye (1999), the so-called random split trees. The model encompasses many important randomized algorithms and data structures. We then perform supercritical Bernoulli bond-percolation…
We propose a model for growing networks based on a finite memory of the nodes. The model shows stylized features of real-world networks: power law distribution of degree, linear preferential attachment of new links and a negative…
The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…
We study a percolation model on the square lattice, where clusters "freeze" (stop growing) as soon as their volume (i.e. the number of sites they contain) gets larger than N, the parameter of the model. A model where clusters freeze when…
We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text…
The description of complex configuration is a difficult issue. We present a powerful technique for cluster identification and characterization. The scheme is designed to treat with and analyze the experimental and/or simulation data from…
Height functions of growing random surfaces are often conjectured to be superconcentrated, meaning that their variances grow sublinearly in time. This article introduces a new concept, called subroughness, meaning that there exist two…
We consider the task of detecting a salient cluster in a sensor network, that is, an undirected graph with a random variable attached to each node. Motivated by recent research in environmental statistics and the drive to compete with the…
This paper presents a clustering algorithm that is an extension of the Category Trees algorithm. Category Trees is a clustering method that creates tree structures that branch on category type and not feature. The development in this paper…
The notion of key polynomials was first introduced in 1936 by S. Maclane in the case of discrete rank 1 valuations. . Let K -> L be a field extension and {\nu} a valuation of K. The original motivation for introducing key polynomials was…
Robustness in response to unexpected events is always desirable for real-world networks. To improve the robustness of any networked system, it is important to analyze vulnerability to external perturbation such as random failures or…
A hierarchical scheme for clustering data is presented which applies to spaces with a high number of dimension ($N_{_{D}}>3$). The data set is first reduced to a smaller set of partitions (multi-dimensional bins). Multiple clustering…
Let $F(z)$ be an arbitrary complex polynomial. We introduce the local root clustering problem, to compute a set of natural $\varepsilon$-clusters of roots of $F(z)$ in some box region $B_0$ in the complex plane. This may be viewed as an…