Related papers: Risk Bounds For Mode Clustering

Mode clustering is a nonparametric method for clustering that defines clusters using the basins of attraction of a density estimator's modes. We provide several enhancements to mode clustering: (i) a soft variant of cluster assignment, (ii)…

The two most extended density-based approaches to clustering are surely mixture model clustering and modal clustering. In the mixture model approach, the density is represented as a mixture and clusters are associated to the different…

We present a nonparametric method for selecting informative features in high-dimensional clustering problems. We start with a screening step that uses a test for multimodality. Then we apply kernel density estimation and mode clustering to…

Mode-based clustering methods define clusters to be the basins of attraction of the modes of a density estimate. The most common version is mean shift clus- tering which uses a gradient ascent algorithm to find the basins. Rodriguez and…

Density-based clustering relies on the idea of linking groups to some specific features of the probability distribution underlying the data. The reference to a true, yet unknown, population structure allows to frame the clustering problem…

The idea underlying the modal formulation of density-based clustering is to associate groups with the regions around the modes of the probability density function underlying the data. This correspondence between clusters and dense regions…

We study potential biases of popular cluster quality metrics, such as conductance or modularity. We propose a method that uses both stochastic and preferential attachment block models construction to generate networks with preset community…

A natural way to characterize the cluster structure of a dataset is by finding regions containing a high density of data. This can be done in a nonparametric way with a kernel density estimate, whose modes and hence clusters can be found…

This paper deals with nonparametric estimation of conditional den-sities in mixture models in the case when additional covariates are available. The proposed approach consists of performing a prelim-inary clustering algorithm on the…

In this paper, we propose a new fuzzy clustering algorithm based on the mode-seeking framework. Given a dataset in $\mathbb{R}^d$, we define regions of high density that we call cluster cores. We then consider a random walk on a…

The nonparametric formulation of density-based clustering, known as modal clustering, draws a correspondence between groups and the attraction domains of the modes of the density function underlying the data. Its probabilistic foundation…

We conduct an in-depth analysis of the Bayes risk of clustering in the context of Hidden Markov and i.i.d. models. In both settings, we identify the situations where this risk is comparable to the Bayes risk of classification and those…

We study generalized density-based clustering in which sharply defined clusters such as clusters on lower-dimensional manifolds are allowed. We show that accurate clustering is possible even in high dimensions. We propose two data-based…

Modes and ridges of the probability density function behind observed data are useful geometric features. Mode-seeking clustering assigns cluster labels by associating data samples with the nearest modes, and estimation of density ridges…

We present a first procedure that can estimate -- with statistical consistency guarantees -- any local-maxima of a density, under benign distributional conditions. The procedure estimates all such local maxima, or $\textit{modal-sets}$, of…

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…

Mean shift clustering finds the modes of the data probability density by identifying the zero points of the density gradient. Since it does not require to fix the number of clusters in advance, the mean shift has been a popular clustering…

Face clustering is a promising way to scale up face recognition systems using large-scale unlabeled face images. It remains challenging to identify small or sparse face image clusters that we call hard clusters, which is caused by the…

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…

With the recent growth in data availability and complexity, and the associated outburst of elaborate modelling approaches, model selection tools have become a lifeline, providing objective criteria to deal with this increasingly challenging…