相关论文: A Strongly Consistent Sparse $k$-means Clustering …

Context. K-means is a clustering algorithm that has been used to classify large datasets in astronomical databases. It is an unsupervised method, able to cope very different types of problems. Aims. We check whether a variant of the…

Sparse convex clustering is to cluster observations and conduct variable selection simultaneously in the framework of convex clustering. Although a weighted $L_1$ norm is usually employed for the regularization term in sparse convex…

We propose the \emph{weighted K-harmonic means} (WKHM) clustering algorithm, a regularized variant of K-harmonic means designed to ensure numerical stability while enabling soft assignments through inverse-distance weighting. Unlike…

Large language models (LLMs) have spurred development in multiple industries. However, the growing number of their parameters brings substantial storage and computing burdens, making it essential to explore model compression techniques for…

This paper deals with unsupervised clustering with feature selection. The problem is to estimate both labels and a sparse projection matrix of weights. To address this combinatorial non-convex problem maintaining a strict control on the…

The $k$-means algorithm (Lloyd's algorithm) is a widely used method for clustering unlabeled data. A key bottleneck of the $k$-means algorithm is that each iteration requires time linear in the number of data points, which can be expensive…

Due to its low computational cost, Lasso is an attractive regularization method for high-dimensional statistical settings. In this paper, we consider multivariate counting processes depending on an unknown function parameter to be estimated…

We study feature selection for $k$-means clustering. Although the literature contains many methods with good empirical performance, algorithms with provable theoretical behavior have only recently been developed. Unfortunately, these…

In Compressed Sensing and high dimensional estimation, signal recovery often relies on sparsity assumptions and estimation is performed via $\ell_1$-penalized least-squares optimization, a.k.a. LASSO. The $\ell_1$ penalisation is usually…

Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…

In statistical machine learning, kernel methods allow to consider infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done by solving an optimization problem…

The $k$-means algorithm is arguably the most popular nonparametric clustering method but cannot generally be applied to datasets with incomplete records. The usual practice then is to either impute missing values under an assumed…

The classical $k$-means algorithm for partitioning $n$ points in $\mathbb{R}^d$ into $k$ clusters is one of the most popular and widely spread clustering methods. The need to respect prescribed lower bounds on the cluster sizes has been…

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.…

The classical k-means clustering, based on distances computed from all data features, cannot be directly applied to incomplete data with missing values. A natural extension of k-means to missing data, namely k-POD, uses only the observed…

Recent work has proposed Wasserstein k-means (Wk-means) clustering as a powerful method to classify regimes in time series data, and one-dimensional asset returns in particular. In this paper, we begin by studying in detail the behaviour of…

The $\ell_1$-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of…

For some or all of the data instances a number of independent-world clustering issues suffer from incomplete data characterization due to losing or absent attributes. Typical clustering approaches cannot be applied directly to such data…

We describe a fast method to eliminate features (variables) in l1 -penalized least-square regression (or LASSO) problems. The elimination of features leads to a potentially substantial reduction in running time, specially for large values…

Clustering is a fundamental technique in data analysis, with the $k$-means being one of the widely studied objectives due to its simplicity and broad applicability. In many practical scenarios, data points come with associated weights that…