Related papers: Discretize Relaxed Solution of Spectral Clustering…
Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…
Clustering is the problem of separating a set of objects into groups (called clusters) so that objects within the same cluster are more similar to each other than to those in different clusters. Spectral clustering is a now well-known…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…
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…
We use sensitivity analysis to design bounding-focused discretization (cutting-surface) methods for the global optimization of nonconvex semi-infinite programs (SIPs). We begin by formulating the optimal bounding-focused discretization of…
We propose an efficient linear-time graph-based divisive cluster analysis approach called Reductive Clustering. The approach tries to reveal the hierarchical structural information through reducing the graph into a more concise one…
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…
The applicability of agglomerative clustering, for inferring both hierarchical and flat clustering, is limited by its scalability. Existing scalable hierarchical clustering methods sacrifice quality for speed and often lead to over-merging…
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…
Spectral clustering, as a popular tool for data clustering, requires an eigen-decomposition step on a given affinity to obtain the spectral embedding. Nevertheless, such a step suffers from the lack of generalizability and scalability.…
Clustering is a fundamental tool for analyzing large data sets. A rich body of work has been devoted to designing data-stream algorithms for the relevant optimization problems such as $k$-center, $k$-median, and $k$-means. Such algorithms…
Clustering is a fundamental task in data mining and machine learning, particularly for analyzing large-scale data. In this paper, we introduce Clust-Splitter, an efficient algorithm based on nonsmooth optimization, designed to solve the…
We revisit the theoretical performances of Spectral Clustering, a classical algorithm for graph partitioning that relies on the eigenvectors of a matrix representation of the graph. Informally, we show that Spectral Clustering works well as…
When designing clustering algorithms, the choice of initial centers is crucial for the quality of the learned clusters. In this paper, we develop a new initialization scheme, called HST initialization, for the $k$-median problem in the…
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…
We study the problem of clustering sequences of unlabeled point sets taken from a common metric space. Such scenarios arise naturally in applications where a system or process is observed in distinct time intervals, such as biological…
In this paper we propose an heuristic to improve the performances of the recently proposed derivative-free method for nonsmooth optimization CS-DFN. The heuristic is based on a clustering-type technique to compute a direction { which relies…
There are existing standard solvers for tackling discrete optimization problems. However, in practice, it is uncommon to apply them directly to the large input space typical of this class of problems. Rather, the input is preprocessed to…
Finding a set of nested partitions of a dataset is useful to uncover relevant structure at different scales, and is often dealt with a data-dependent methodology. In this paper, we introduce a general two-step methodology for model-based…
We study the complexity of finding an optimal hierarchical clustering of an unweighted similarity graph under the recently introduced Dasgupta objective function. We introduce a proof technique, called the normalization procedure, that…