Related papers: Characteristic Length and Clustering
Graph-based clustering has shown promising performance in many tasks. A key step of graph-based approach is the similarity graph construction. In general, learning graph in kernel space can enhance clustering accuracy due to the…
These are notes on the method of normalized graph cuts and its applications to graph clustering. I provide a fairly thorough treatment of this deeply original method due to Shi and Malik, including complete proofs. I include the necessary…
We propose and study a novel graph clustering method for data with an intrinsic network structure. Similar to spectral clustering, we exploit an intrinsic network structure of data to construct Euclidean feature vectors. These feature…
Graph clustering becomes an important problem due to emerging applications involving the web, social networks and bio-informatics. Recently, many such applications generate data in the form of streams. Clustering massive, dynamic graph…
For every connected graph $G$ and surface $S$, we consider the well-known string of inequalities $\delta_S(G) \leq \mu_S(G) \leq \nu_S(G)$, where $\mu$ and $\nu$ denote skewness and crossing number and $\delta$ is the Euler-formula lower…
Graph clustering is an important unsupervised learning technique for partitioning graphs with attributes and detecting communities. However, current methods struggle to accurately capture true community structures and intra-cluster…
High dimensional Gaussian graphical models provide a rigorous framework to describe a network of statistical dependencies between entities, such as genes in genomic regulation studies or species in ecology. Penalized methods, including the…
We study clustering properties of networks of single integrator nodes over a directed graph, in which the nodes converge to steady-state values. These values define clustering groups of nodes, which depend on interaction topology, edge…
We make calculations in graph homology which further understanding of the topology of spaces of string links, in particular calculating the Euler characteristics of finite-dimensional summands in their homology and homotopy. In doing so, we…
This is the second paper in a series of papers adressing the characteristic gluing problem for the Einstein vacuum equations. We solve the codimension-$10$ characteristic gluing problem for characteristic data which are close to the…
This paper studies the problem of graph-level clustering, which is a novel yet challenging task. This problem is critical in a variety of real-world applications such as protein clustering and genome analysis in bioinformatics. Recent years…
The evolution of random undirected graphs by the clustering attachment (CA) both without node and edge deletion and with uniform node or edge deletion is investigated. Theoretical results are obtained for the CA without node and edge…
A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square [0,1]^2. The topological properties of the…
One iteration of standard $k$-means (i.e., Lloyd's algorithm) or standard EM for Gaussian mixture models (GMMs) scales linearly with the number of clusters $C$, data points $N$, and data dimensionality $D$. In this study, we explore whether…
Graph clustering aims to partition nodes into distinct clusters based on their similarity, thereby revealing relationships among nodes. Nevertheless, most existing methods do not fully utilize these edge weights. Leveraging edge weights in…
Clustering algorithms for large networks typically use modularity values to test which partitions of the vertex set better represent structure in the data. The modularity of a graph is the maximum modularity of a partition. We consider the…
Graph clustering has many important applications in computing, but due to the increasing sizes of graphs, even traditionally fast clustering methods can be computationally expensive for real-world graphs of interest. Scalability problems…
The cosmological dynamics of gravitational clustering satisfies an approximate invariance with respect to the cosmological parameters that is often used to simplify analytical computations. We describe how this approximate symmetry gives…
In an increasingly interconnected world, understanding and summarizing the structure of these networks becomes increasingly relevant. However, this task is nontrivial; proposed summary statistics are as diverse as the networks they…
High density clusters can be characterized by the connected components of a level set $L(\lambda) = \{x:\ p(x)>\lambda\}$ of the underlying probability density function $p$ generating the data, at some appropriate level $\lambda\geq 0$. The…