Clustering is a fundamental problem in many scientific applications. Standard methods such as k-means, Gaussian mixture models, and hierarchical clustering, however, are beset by local minima, which are sometimes drastically suboptimal. Recently introduced convex relaxations of k-means and hierarchical clustering shrink cluster centroids toward one another and ensure a unique global minimizer. ...

Abstract Convex clustering has received recently an increased interest as a valuable method for unsupervised learning. Unlike conventional methods such k-means, its formulation corresponds to solving convex optimization problem and hence, alleviates initialization local minima problems. However, while several algorithms have been proposed solve formulations, including those based on the alterna...

We propose a new method for clustering based on finding maximum margin hyperplanes through data. By reformulating the problem in terms of the implied equivalence relation matrix, we can pose the problem as a convex integer program. Although this still yields a difficult computational problem, the hard-clustering constraints can be relaxed to a soft-clustering formulation which can be feasibly s...

0957-4174/$ see front matter 2009 Elsevier Ltd. A doi:10.1016/j.eswa.2009.10.019 * Corresponding author. Tel.: +98 2177240487; fax E-mail addresses: [email protected] (F. Bayat), eade [email protected] (A.A. Jalali), [email protected] In this paper, using the concepts of field theory and potential functions a sub-optimal non-parametric algorithm for clustering of convex and non-convex da...

Multi-way partitioning of an undirected weighted graph where pairwise similarities are assigned as edge weights, provides an important tool for data clustering, but is an NP-hard problem. Spectral relaxation is a popular way of relaxation, leading to spectral clustering where the clustering is performed by the eigen-decomposition of the (normalized) graph Laplacian. On the other hand, semidefin...

In this paper, we consider the l1-clustering problem for a finite data-point set which should be partitioned into k disjoint nonempty subsets. In that case, the objective function does not have to be either convex or differentiable, and generally it may have many local or global minima. Therefore, it becomes a complex global optimization problem. A method of searching for a locally optimal solu...

Representative-based clustering algorithms are quite popular due to their relative high speed and because of their sound theoretical foundation. On the other hand, the clusters they can obtain are limited to convex shapes and clustering results are also highly sensitive to initializations. In this paper, a novel agglomerative clustering algorithm called MOSAIC is proposed which greedily merges ...

assigning a set of objects to groups such that objects in one group or cluster are more similar to each other than the other clusters’ objects is the main task of clustering analysis. sspco optimization algorithm is anew optimization algorithm that is inspired by the behavior of a type of bird called see-see partridge. one of the things that smart algorithms are applied to solve is the problem ...

Clustering is one of the most fundamental and important tasks in data mining. Traditional clustering algorithms, such as K-means, assign every data point to exactly one cluster. However, in real-world datasets, the clusters may overlap with each other. Furthermore, often, there are outliers that should not belong to any cluster. We recently proposed the NEO-K-Means (Non-Exhaustive, Overlapping ...

We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial optimization problems and convex integer programming problems in variable dimension. We discuss some of the many applications of this theory including to quadratic prog...