Related papers: Guaranteed clustering and biclustering via semidef…
In this work we consider a straightforward linear programming formulation of the recently introduced $\{k\}$-packing function problem in graphs, for each fixed value of the positive integer number $k$. We analyse a special relation between…
A $k$-defective clique of an undirected graph $G$ is a subset of its vertices that induces a nearly complete graph with a maximum of $k$ missing edges. The maximum $k$-defective clique problem, which asks for the largest $k$-defective…
Given an undirected graph $G$, the Densest $k$-subgraph problem (DkS) asks to compute a set $S \subset V$ of cardinality $\left\lvert S\right\rvert \leq k$ such that the weight of edges inside $S$ is maximized. This is a fundamental NP-hard…
Many graph mining applications rely on detecting subgraphs which are near-cliques. There exists a dichotomy between the results in the existing work related to this problem: on the one hand the densest subgraph problem (DSP) which maximizes…
Community-based graph clustering is one of the most popular topics in the analysis of complex social networks. This type of clustering involves grouping vertices that are considered to share more connections, whereas vertices in different…
Semidefinite programming is an important tool to tackle several problems in data science and signal processing, including clustering and community detection. However, semidefinite programs are often slow in practice, so speed up techniques…
In this article, we develop a clique-based method for social network clustering. We introduce a new index to evaluate the quality of clustering results, and propose an efficient algorithm based on recursive bipartition to maximize an…
We study the cluster recovery problem in the semi-supervised active clustering framework. Given a finite set of input points, and an oracle revealing whether any two points lie in the same cluster, our goal is to recover all clusters…
Spectral Clustering as a relaxation of the normalized/ratio cut has become one of the standard graph-based clustering methods. Existing methods for the computation of multiple clusters, corresponding to a balanced $k$-cut of the graph, are…
Disentangled distributed representations of data are desirable for machine learning, since they are more expressive and can generalize from fewer examples. However, for complex data, the distributed representations of multiple objects…
Clustering is a critical component of decision-making in todays data-driven environments. It has been widely used in a variety of fields such as bioinformatics, social network analysis, and image processing. However, clustering accuracy…
Motivated by a geometric problem, we introduce a new non-convex graph partitioning objective where the optimality criterion is given by the sum of the Dirichlet eigenvalues of the partition components. A relaxed formulation is identified…
Listing k-cliques plays a fundamental role in various data mining tasks, such as community detection and mining of cohesive substructures. Existing algorithms for the k-clique listing problem are built upon a general framework, which finds…
Dense subgraph discovery methods are routinely used in a variety of applications including the identification of a team of skilled individuals for collaboration from a social network. However, when the network's node set is associated with…
Cluster deletion is an NP-hard graph clustering objective with applications in computational biology and social network analysis, where the goal is to delete a minimum number of edges to partition a graph into cliques. We first provide a…
A graph is $k$-degenerate if any induced subgraph has a vertex of degree at most $k$. In this paper we prove new algorithms for cliques and similar structures for these graphs. We design linear time Fixed-Parameter Tractable algorithms for…
Subspace clustering is the unsupervised grouping of points lying near a union of low-dimensional linear subspaces. Algorithms based directly on geometric properties of such data tend to either provide poor empirical performance, lack…
In the Dominated Cluster Deletion problem, we are given an undirected graph $G$ and integers $k$ and $d$ and the question is to decide whether there exists a set of at most $k$ vertices whose removal results in a graph in which each…
Spectral clustering and its extensions usually consist of two steps: (1) constructing a graph and computing the relaxed solution; (2) discretizing relaxed solutions. Although the former has been extensively investigated, the discretization…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…