相关论文: Consistency and Inconsistency in $K$-Means Cluster…

We address the problem of validating the ouput of clustering algorithms. Given data $\mathcal{D}$ and a partition $\mathcal{C}$ of these data into $K$ clusters, when can we say that the clusters obtained are correct or meaningful for the…

The classical $k$-means clustering requires a complete data matrix without missing entries. As a natural extension of the $k$-means clustering for missing data, the $k$-POD clustering has been proposed, which ignores the missing entries in…

We consider panel data models with group structure. We study the asymptotic behavior of least-squares estimators and information criterion for the number of groups, allowing for the presence of small groups that have an asymptotically…

The $k$-center problem is a canonical and long-studied facility location and clustering problem with many applications in both its symmetric and asymmetric forms. Both versions of the problem have tight approximation factors on worst case…

Many clustering algorithms exist that estimate a cluster centroid, such as K-means, K-medoids or mean-shift, but no algorithm seems to exist that clusters data by returning exactly K meaningful modes. We propose a natural definition of a…

In this paper, we define and study a new notion of stability for the $k$-means clustering scheme building upon the notion of quantization of a probability measure. We connect this notion of stability to a geometric feature of the underlying…

Causal effects are often characterized with population summaries. These might provide an incomplete picture when there are heterogeneous treatment effects across subgroups. Since the subgroup structure is typically unknown, it is more…

The $k$-means method is an iterative clustering algorithm which associates each observation with one of $k$ clusters. It traditionally employs cluster centers in the same space as the observed data. By relaxing this requirement, it is…

We prove in this paper that the expected value of the objective function of the $k$-means++ algorithm for samples converges to population expected value. As $k$-means++, for samples, provides with constant factor approximation for $k$-means…

Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…

Centroid based clustering methods such as k-means, k-medoids and k-centers are heavily applied as a go-to tool in exploratory data analysis. In many cases, those methods are used to obtain representative centroids of the data manifold for…

The problem of constrained clustering has attracted significant attention in the past decades. In this paper, we study the balanced $k$-center, $k$-median, and $k$-means clustering problems where the size of each cluster is constrained by…

The problem of constrained $k$-center clustering has attracted significant attention in the past decades. In this paper, we study balanced $k$-center cluster where the size of each cluster is constrained by the given lower and upper bounds.…

There has been much progress on efficient algorithms for clustering data points generated by a mixture of $k$ probability distributions under the assumption that the means of the distributions are well-separated, i.e., the distance between…

Designing efficient, effective, and consistent metric clustering algorithms is a significant challenge attracting growing attention. Traditional approaches focus on the stability of cluster centers; unfortunately, this neglects the…

$k$-means clustering is a fundamental problem in unsupervised learning. The problem concerns finding a partition of the data points into $k$ clusters such that the within-cluster variation is minimized. Despite its importance and wide…

This paper investigates the validity of Kleinberg's axioms for clustering functions with respect to the quite popular clustering algorithm called $k$-means. While Kleinberg's axioms have been discussed heavily in the past, we concentrate…

We improve current instability-based methods for the selection of the number of clusters $k$ in cluster analysis by developing a normalized cluster instability measure that corrects for the distribution of cluster sizes, a previously…

The classical center based clustering problems such as $k$-means/median/center assume that the optimal clusters satisfy the locality property that the points in the same cluster are close to each other. A number of clustering problems arise…

This note introduces a novel clustering preserving transformation of cluster sets obtained from $k$-means algorithm. This transformation may be used to generate new labeled data{}sets from existent ones. It is more flexible that Kleinberg…