Related papers: Weighted total variation based convex clustering
Convex clustering, a convex relaxation of k-means clustering and hierarchical clustering, has drawn recent attentions since it nicely addresses the instability issue of traditional nonconvex clustering methods. Although its computational…
In this manuscript, we study the statistical properties of convex clustering. We establish that convex clustering is closely related to single linkage hierarchical clustering and $k$-means clustering. In addition, we derive the range of…
Convex clustering is a well-regarded clustering method, resembling the similar centroid-based approach of Lloyd's $k$-means, without requiring a predefined cluster count. It starts with each data point as its centroid and iteratively merges…
Clustering, like covariate selection for classification, is an important step to compress and interpret the data. However, clustering of covariates is often performed independently of the classification step, which can lead to undesirable…
Convex clustering is an attractive clustering algorithm with favorable properties such as efficiency and optimality owing to its convex formulation. It is thought to generalize both k-means clustering and agglomerative clustering. However,…
Convex clustering has recently garnered increasing interest due to its attractive theoretical and computational properties, but its merits become limited in the face of high-dimensional data. In such settings, pairwise affinity terms that…
This survey reviews a clustering method based on solving a convex optimization problem. Despite the plethora of existing clustering methods, convex clustering has several uncommon features that distinguish it from prior art. The…
Matrix valued data has become increasingly prevalent in many applications. Most of the existing clustering methods for this type of data are tailored to the mean model and do not account for the dependence structure of the features, which…
Clustering approaches that utilize convex loss functions have recently attracted growing interest in the formation of compact data clusters. Although classical methods like k-means and its wide family of variants are still widely used, all…
Common clustering methods, such as $k$-means and convex clustering, group similar vector-valued observations into clusters. However, with the increasing prevalence of matrix-valued observations, which often exhibit low rank characteristics,…
In a clustered observational study, a treatment is assigned to groups and all units within the group are exposed to the treatment. We develop a new method for statistical adjustment in clustered observational studies using approximate…
Clustering ensemble, or consensus clustering, has emerged as a powerful tool for improving both the robustness and the stability of results from individual clustering methods. Weighted clustering ensemble arises naturally from clustering…
Convex clustering is a recent stable alternative to hierarchical clustering. It formulates the recovery of progressively coalescing clusters as a regularized convex problem. While convex clustering was originally designed for handling…
We prove polynomial-time solvability of a large class of clustering problems where a weighted set of items has to be partitioned into clusters with respect to some balancing constraints. The data points are weighted with respect to…
Sum-of-norms clustering is a convex optimization problem whose solution can be used for the clustering of multivariate data. We propose and study a localized version of this method, and show in particular that it can separate arbitrarily…
A main task in data analysis is to organize data points into coherent groups or clusters. The stochastic block model is a probabilistic model for the cluster structure. This model prescribes different probabilities for the presence of edges…
We study the large sample behavior of a convex clustering framework, which minimizes the sample within cluster sum of squares under an~$\ell_1$ fusion constraint on the cluster centroids. This recently proposed approach has been gaining in…
Variable selection in cluster analysis is important yet challenging. It can be achieved by regularization methods, which realize a trade-off between the clustering accuracy and the number of selected variables by using a lasso-type penalty.…
Finite mixtures of regressions with fixed covariates are a commonly used model-based clustering methodology to deal with regression data. However, they assume assignment independence, i.e. the allocation of data points to the clusters is…
We generalize finite-sample bounds for convex clustering to the setting where affinity weights appearing in the objective correspond to a general connected graph. These bounds and their analysis lead to a better understanding of clustering…