Related papers: Constrained variable clustering and the best basis…

The area of constrained clustering has been extensively explored by researchers and used by practitioners. Constrained clustering formulations exist for popular algorithms such as k-means, mixture models, and spectral clustering but have…

Clustering is a core task in machine learning with wide-ranging applications in data mining and pattern recognition. However, its unsupervised nature makes it inherently challenging. Many existing clustering algorithms suffer from critical…

We study constrained clustering, where constraints guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the…

In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a…

Despite its popularity, it is widely recognized that the investigation of some theoretical aspects of clustering has been relatively sparse. One of the main reasons for this lack of theoretical results is surely the fact that, whereas for…

Clustering under pairwise constraints is an important knowledge discovery tool that enables the learning of appropriate kernels or distance metrics to improve clustering performance. These pairwise constraints, which come in the form of…

Common clustering algorithms require multiple scans of all the data to achieve convergence, and this is prohibitive when large databases, with data arriving in streams, must be processed. Some algorithms to extend the popular K-means method…

We review clustering as an analysis tool and the underlying concepts from an introductory perspective. What is clustering and how can clusterings be realised programmatically? How can data be represented and prepared for a clustering task?…

Nowadays, more and more problems are dealing with data with one infinite continuous dimension: functional data. In this paper, we introduce the funLOCI algorithm which allows to identify functional local clusters or functional loci, i.e.,…

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…

Image segmentation has come a long way since the early days of computer vision, and still remains a challenging task. Modern variations of the classical (purely bottom-up) approach, involve, e.g., some form of user assistance (interactive…

Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…

Data clustering, including problems such as finding network communities, can be put into a systematic framework by means of a Bayesian approach. The application of Bayesian approaches to real problems can be, however, quite challenging. In…

Factor analysis has been extensively used to reveal the dependence structures among multivariate variables, offering valuable insight in various fields. However, it cannot incorporate the spatial heterogeneity that is typically present in…

A natural approach to analyze interaction data of form "what-connects-to-what-when" is to create a time-series (or rather a sequence) of graphs through temporal discretization (bandwidth selection) and spatial discretization (vertex…

Cluster analysis methods seek to partition a data set into homogeneous subgroups. It is useful in a wide variety of applications, including document processing and modern genetics. Conventional clustering methods are unsupervised, meaning…

Compared to supervised variable selection, the research on unsupervised variable selection is far behind. A forward partial-variable clustering full-variable loss (FPCFL) method is proposed for the corresponding challenges. An advantage is…

We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…

In many applications, data cluster. Failing to take the cluster structure into consideration generally leads to underestimated variances of point estimators and inflated type I errors in hypothesis tests. Many circumstance-dependent…

We present a new theoretical and numerical assessment methodology for a one-dimensional process chain with general applicability to management problems such as the optimization of decision chains or production chains. The process is thereby…