Related papers: Tight Continuous Relaxation of the Balanced $k$-Cu…
An important form of prior information in clustering comes in form of cannot-link and must-link constraints. We present a generalization of the popular spectral clustering technique which integrates such constraints. Motivated by the…
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…
Spectral clustering is sensitive to how graphs are constructed from data particularly when proximal and imbalanced clusters are present. We show that Ratio-Cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced data…
Unsupervised clustering of scattered, noisy and high-dimensional data points is an important and difficult problem. Tight continuous relaxations of balanced cut problems have recently been shown to provide excellent clustering results. In…
Spectral clustering has become one of the most widely used clustering techniques when the structure of the individual clusters is non-convex or highly anisotropic. Yet, despite its immense popularity, there exists fairly little theory about…
Clustering is an effective technique in data mining to generate groups that are the matter of interest. Among various clustering approaches, the family of k-means algorithms and min-cut algorithms gain most popularity due to their…
Spectral clustering is a popular and versatile clustering method based on a relaxation of the normalised graph cut objective. Despite its popularity, however, there is no single agreed upon method for tuning the important scaling parameter,…
A tight continuous relaxation is a crucial factor in solving mixed integer formulations of many NP-hard combinatorial optimization problems. The (weighted) max $k$-cut problem is a fundamental combinatorial optimization problem with…
Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or…
Coresets have become an invaluable tool for solving $k$-means and kernel $k$-means clustering problems on large datasets with small numbers of clusters. On the other hand, spectral clustering works well on sparse graphs and has recently…
Spectral Clustering is one of the most traditional methods to solve segmentation problems. Based on Normalized Cuts, it aims at partitioning an image using an objective function defined by a graph. Despite their mathematical attractiveness,…
We introduce a novel method for clustering using a semidefinite programming (SDP) relaxation of the Max k-Cut problem. The approach is based on a new methodology for rounding the solution of an SDP relaxation using iterated linear…
Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…
This paper proposes a variant of the normalized cut algorithm for spectral clustering. Although the normalized cut algorithm applies the K-means algorithm to the eigenvectors of a normalized graph Laplacian for finding clusters, our…
The well-known graph-based clustering methods, including spectral clustering, symmetric non-negative matrix factorization, and doubly stochastic normalization, can be viewed as relaxations of the kernel $k$-means approach. However, we posit…
We propose a Greedy strategy to solve the problem of Graph Cut, called GGC. It starts from the state where each data sample is regarded as a cluster and dynamically merges the two clusters which reduces the value of the global objective…
Fair graph clustering is crucial for ensuring equitable representation and treatment of diverse communities in network analysis. Traditional methods often ignore disparities among social, economic, and demographic groups, perpetuating…
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…
Spectral clustering is a broad class of clustering procedures in which an intractable combinatorial optimization formulation of clustering is "relaxed" into a tractable eigenvector problem, and in which the relaxed solution is subsequently…
The problem of constrained clustering has attracted significant attention in the past decades. In this paper, we study the balanced $k$-center, $k$-median, and $k$-means clustering problems where the size of each cluster is constrained by…