Related papers: Convex clustering via $\ell_1$ fusion penalization
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…
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…
A data filtering method for cluster analysis is proposed, based on minimizing a least squares function with a weighted $\ell_0$-norm penalty. To overcome the discontinuity of the objective function, smooth non-convex functions are employed…
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…
We propose a novel methodology for feature screening in clustering massive datasets, in which both the number of features and the number of observations can potentially be very large. Taking advantage of a fusion penalization based convex…
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…
Clustering is a ubiquitous problem in data science and signal processing. In many applications where we observe noisy signals, it is common practice to first denoise the data, perhaps using wavelet denoising, and then to apply a clustering…
Convex clustering is a modern method with both hierarchical and $k$-means clustering characteristics. Although convex clustering can capture complex clustering structures hidden in data, the existing convex clustering algorithms are not…
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…
The presence of missing entries in data often creates challenges for pattern recognition algorithms. Traditional algorithms for clustering data assume that all the feature values are known for every data point. We propose a method to…
Classical inference methods notoriously fail when applied to data-driven test hypotheses or inference targets. Instead, dedicated methodologies are required to obtain statistical guarantees for these selective inference problems. Selective…
We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text…
Fast accumulation of large amounts of complex data has created a need for more sophisticated statistical methodologies to discover interesting patterns and better extract information from these data. The large scale of the data often…
Background: When planning a cluster randomized trial, evaluators often have access to an enumerated cohort representing the target population of clusters. Practicalities of conducting the trial, such as the need to oversample clusters with…
In many applications of X-ray computed tomography, an unsupervised segmentation of the reconstructed 3D volumes forms an important step in the image processing chain for further investigation of the digitized object. Therefore, the goal is…
Clustering analysis is one of the most widely used statistical tools in many emerging areas such as microarray data analysis. For microarray and other high-dimensional data, the presence of many noise variables may mask underlying…
Convex clustering is a convex relaxation of the $k$-means and hierarchical clustering. It involves solving a convex optimization problem with the objective function being a squared error loss plus a fusion penalty that encourages the…
The analysis of large datasets is often complicated by the presence of missing entries, mainly because most of the current machine learning algorithms are designed to work with full data. The main focus of this work is to introduce a…
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…
This paper considers the problem of clustering a partially observed unweighted graph---i.e., one where for some node pairs we know there is an edge between them, for some others we know there is no edge, and for the remaining we do not know…