Related papers: Tree-Guided $L_1$-Convex Clustering

Clustering temporal and dynamically changing multivariate time series from real-world fields, called temporal clustering for short, has been a major challenge due to inherent complexities. Although several deep temporal clustering…

This paper proposes a new decentralized conjugate gradient (NDCG) method and a decentralized memoryless BFGS (DMBFGS) method for the nonconvex and strongly convex decentralized optimization problem, respectively, of minimizing a finite sum…

Here, we propose a clustering technique for general clustering problems including those that have non-convex clusters. For a given desired number of clusters $K$, we use three stages to find a clustering. The first stage uses a hybrid…

Convex clustering refers, for given $\left\{x_1, \dots, x_n\right\} \subset \mathbb{R}^p$, to the minimization of \begin{eqnarray*} u(\gamma) & = & \underset{u_1, \dots, u_n }{\arg\min}\;\sum_{i=1}^{n}{\lVert x_i - u_i \rVert^2} + \gamma…

Graph clustering aims to divide the graph into different clusters. The recently emerging deep graph clustering approaches are largely built on graph neural networks (GNN). However, GNN is designed for general graph encoding and there is a…

Clustering and prediction are two primary tasks in the fields of unsupervised and supervised learning, respectively. Although much of the recent advances in machine learning have been centered around those two tasks, the interdependent,…

Constrained clustering leverages limited domain knowledge to improve clustering performance and interpretability, but incorporating pairwise must-link and cannot-link constraints is an NP-hard challenge, making global optimization…

Originally, tangles were invented as an abstract tool in mathematical graph theory to prove the famous graph minor theorem. In this paper, we showcase the practical potential of tangles in machine learning applications. Given a collection…

Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex optimization solvers do not scale well, and…

Data clustering is a fundamental problem with a wide range of applications. Standard methods, eg the $k$-means method, usually require solving a non-convex optimization problem. Recently, total variation based convex relaxation to the…

Co-Clustering, the problem of simultaneously identifying clusters across multiple aspects of a data set, is a natural generalization of clustering to higher-order structured data. Recent convex formulations of bi-clustering and tensor…

Clustering is a fundamental task in data analysis, and spectral clustering has been recognized as a promising approach to it. Given a graph describing the relationship between data, spectral clustering explores the underlying cluster…

High-order clustering aims to identify heterogeneous substructures in multiway datasets that arise commonly in neuroimaging, genomics, social network studies, etc. The non-convex and discontinuous nature of this problem pose significant…

Biclustering, also known as co-clustering or two-way clustering, simultaneously partitions the rows and columns of a data matrix to reveal submatrices with coherent patterns. Incorporating background knowledge into clustering to enhance…

Image clustering is one of the most important computer vision applications, which has been extensively studied in literature. However, current clustering methods mostly suffer from lack of efficiency and scalability when dealing with…

We propose a distributed solution for a constrained convex optimization problem over a network of clustered agents each consisted of a set of subagents. The communication range of the clustered agents is such that they can form a connected…

Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…

This paper explores the problem of clustering ensemble, which aims to combine multiple base clusterings to produce better performance than that of the individual one. The existing clustering ensemble methods generally construct a…

We present a new method for clustering based on compression. The method doesn't use subject-specific features or background knowledge, and works as follows: First, we determine a universal similarity distance, the normalized compression…

This letter presents a new spectral-clustering-based approach to the subspace clustering problem. Underpinning the proposed method is a convex program for optimal direction search, which for each data point d finds an optimal direction in…