Related papers: Stability for layer points
We uncover the global organization of clustering in real complex networks. As it happens with other fundamental properties of networks such as the degree distribution, we find that real networks are neither completely random nor ordered…
Clustering partitions a dataset such that observations placed together in a group are similar but different from those in other groups. Hierarchical and $K$-means clustering are two approaches but have different strengths and weaknesses.…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…
We extend the observability model to multiplex networks. We present mathematical frameworks, valid under the treelike ansatz, able to describe the emergence of the macroscopic cluster of mutually observable nodes in both synthetic and…
In an earlier paper, we introduced and studied a system of hierarchically interacting measure-valued random processes which describes a large population of individuals carrying types and living in colonies labelled by the hierarchical group…
We continue the investigation of problems concerning correlation clustering or clustering with qualitative information, which is a clustering formulation that has been studied recently. The basic setup here is that we are given as input a…
Phase separation mechanisms can produce a variety of complicated and intricate microstructures, which often can be difficult to characterize in a quantitative way. In recent years, a number of novel topological metrics for microstructures…
Clustering, or transitivity has been observed in real networks and its effects on their structure and function has been discussed extensively. The focus of these studies has been on clustering of single networks while the effect of…
We introduce the Lennard-Jones layer (LJL) for the equalization of the density of 2D and 3D point clouds through systematically rearranging points without destroying their overall structure (distribution normalization). LJL simulates a…
The information that a pattern of firing in the output layer of a feedforward network of threshold-linear neurons conveys about the network's inputs is considered. A replica-symmetric solution is found to be stable for all but small amounts…
In the paper, multivariate probability distributions are considered that are representable as scale mixtures of multivariate elliptically contoured stable distributions. It is demonstrated that these distributions form a special subclass of…
Cluster synchronization is a phenomenon in which a network self-organizes into a pattern of synchronized sets. It has been shown that diverse patterns of stable cluster synchronization can be captured by symmetries of the network. Here we…
In this work, we introduce a novel methodology for divisive hierarchical clustering. Our divisive (``top-down'') approach is motivated by the fact that agglomerative hierarchical clustering (``bottom-up''), which is commonly used for…
Throughout this paper, a persistence diagram ${\cal P}$ is composed of a set $P$ of planar points (each corresponding to a topological feature) above the line $Y=X$, as well as the line $Y=X$ itself, i.e., ${\cal P}=P\cup\{(x,y)|y=x\}$.…
Clusters are the dense inner regions of a wide-spread hierarchy of young stellar structures. They often reveal a continuation of this hierarchy inside of them, to smaller scales, when they are young, but orbital mixing eventually erases…
Sequential lateration is a class of methods for multidimensional scaling where a suitable subset of nodes is first embedded by some method, e.g., a clique embedded by classical scaling, and then the remaining nodes are recursively embedded…
The new concept of multilevel network is introduced in order to embody some topological properties of complex systems with structures in the mesoscale which are not completely captured by the classical models. This new model, which…
A rank-invariant clustering of variables is introduced that is based on the predictive strength between groups of variables, i.e., two groups are assigned a high similarity if the variables in the first group contain high predictive…
Interpreting the prediction mechanism of complex models is currently one of the most important tasks in the machine learning field, especially with layered neural networks, which have achieved high predictive performance with various…
A new concept called multilevel contours is introduced through this article by the author. Theorems on contours constructed on a bundle of complex planes are stated and proved. Multilevel contours can transport information from one complex…