Related papers: DBGSA: A Novel Data Adaptive Bregman Clustering Al…

In the past few years powerful generalizations to the Euclidean k-means problem have been made, such as Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9,18], and tensor…

The K-means algorithm is one of the most widely studied clustering algorithms in machine learning. While extensive research has focused on its ability to achieve a globally optimal solution, there still lacks a rigorous analysis of its…

Using a trimming approach, we investigate a k-means type method based on Bregman divergences for clustering data possibly corrupted with clutter noise. The main interest of Bregman divergences is that the standard Lloyd algorithm adapts to…

Recent progress in center-based clustering algorithms combats poor local minima by implicit annealing, using a family of generalized means. These methods are variations of Lloyd's celebrated $k$-means algorithm, and are most appropriate for…

In this paper we introduce the Boosted Double-proximal Subgradient Algorithm (BDSA), a novel splitting algorithm designed to address general structured nonsmooth and nonconvex mathematical programs expressed as sums and differences of…

Clustering large, mixed data is a central problem in data mining. Many approaches adopt the idea of k-means, and hence are sensitive to initialisation, detect only spherical clusters, and require a priori the unknown number of clusters. We…

Cluster analysis plays a crucial role in database mining, and one of the most widely used algorithms in this field is DBSCAN. However, DBSCAN has several limitations, such as difficulty in handling high-dimensional large-scale data,…

The $k$-Means clustering problem on $n$ points is NP-Hard for any dimension $d\ge 2$, however, for the 1D case there exists exact polynomial time algorithms. Previous literature reported an $O(kn^2)$ time dynamic programming algorithm that…

Coresets are compact representations of data sets such that models trained on a coreset are provably competitive with models trained on the full data set. As such, they have been successfully used to scale up clustering models to massive…

Clustering algorithms start with a fixed divergence, which captures the possibly asymmetric distance between a sample and a centroid. In the mixture model setting, the sample distribution plays the same role. When all attributes have the…

Clustering analysis, a classical issue in data mining, is widely used in various research areas. This article aims at proposing a self-adaption grey DBSCAN clustering (SAG-DBSCAN) algorithm. First, the grey relational matrix is used to…

Bregman divergences play a central role in the design and analysis of a range of machine learning algorithms. This paper explores the use of Bregman divergences to establish reductions between such algorithms and their analyses. We present…

Clustering mixed data presents numerous challenges inherent to the very heterogeneous nature of the variables. A clustering algorithm should be able, despite of this heterogeneity, to extract discriminant pieces of information from the…

Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key…

Most of existing clustering algorithms are proposed without considering the selection bias in data. In many real applications, however, one cannot guarantee the data is unbiased. Selection bias might bring the unexpected correlation between…

Coresets are efficient representations of data sets such that models trained on the coreset are provably competitive with models trained on the original data set. As such, they have been successfully used to scale up clustering models such…

Clustering algorithms are fundamental tools across many fields, with density-based methods offering particular advantages in identifying arbitrarily shaped clusters and handling noise. However, their effectiveness is often limited by the…

We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…

Although many convex relaxations of clustering have been proposed in the past decade, current formulations remain restricted to spherical Gaussian or discriminative models and are susceptible to imbalanced clusters. To address these…

As the complexity of learning tasks surges, modern machine learning encounters a new constrained learning paradigm characterized by more intricate and data-driven function constraints. Prominent applications include Neyman-Pearson…