Related papers: Exponentially Consistent Nonparametric Linkage-Bas…
In this paper, we study the strong consistency of the sparse K-means clustering for high dimensional data. We prove the consistency in both risk and clustering for the Euclidean distance. We discuss the characterization of the limit of the…
We consider the problem of estimating the number of clusters (k) in a dataset. We propose a non-parametric approach to the problem that utilizes similarity graphs to construct a robust statistic that effectively captures similarity…
In this paper, we first propose a new iterative algorithm, called the K-sets+ algorithm for clustering data points in a semi-metric space, where the distance measure does not necessarily satisfy the triangular inequality. We show that the…
Clustering is a fundamental unsupervised learning approach. Many clustering algorithms -- such as $k$-means -- rely on the euclidean distance as a similarity measure, which is often not the most relevant metric for high dimensional data…
Clustering high-dimensional datasets is hard because interpoint distances become less informative in high-dimensional spaces. We present a clustering algorithm that performs nonlinear dimensionality reduction and clustering jointly. The…
We present a new fast online clustering algorithm that reliably recovers arbitrary-shaped data clusters in high throughout data streams. Unlike the existing state-of-the-art online clustering methods based on k-means or k-medoid, it does…
Distance-based hierarchical clustering (HC) methods are widely used in unsupervised data analysis but few authors take account of uncertainty in the distance data. We incorporate a statistical model of the uncertainty through corruption or…
In this study, we address the problem of clustering string data in an unsupervised manner by developing a theory of a mixture model and an EM algorithm for string data based on probability theory on a topological monoid of strings developed…
Clustering is an important part of many modern data analysis pipelines, including network analysis and data retrieval. There are many different clustering algorithms developed by various communities, and it is often not clear which…
We consider the problem of clustering noisy finite-length observations of stationary ergodic random processes according to their nonparametric generative models without prior knowledge of the model statistics and the number of generative…
In the era of Big Data, scalable and accurate clustering algorithms for high-dimensional data are essential. We present new Bayesian Distance Clustering (BDC) models and inference algorithms with improved scalability while maintaining the…
Clustering is a widely deployed unsupervised learning tool. Model-based clustering is a flexible framework to tackle data heterogeneity when the clusters have different shapes. Likelihood-based inference for mixture distributions often…
We consider the problem of identifying tandem scattered subsequences within a string. Our algorithm identifies a longest subsequence which occurs twice without overlap in a string. This algorithm is based on the Hunt-Szymanski algorithm,…
Unsupervised clustering algorithm can effectively reduce the dimension of high-dimensional unlabeled data, thus reducing the time and space complexity of data processing. However, the traditional clustering algorithm needs to set the upper…
k-medoids algorithm is a partitional, centroid-based clustering algorithm which uses pairwise distances of data points and tries to directly decompose the dataset with $n$ points into a set of $k$ disjoint clusters. However, k-medoids…
A limitation of many clustering algorithms is the requirement to tune adjustable parameters for each application or even for each dataset. Some techniques require an \emph{a priori} estimate of the number of clusters while density-based…
We present massively parallel (MPC) algorithms and hardness of approximation results for computing Single-Linkage Clustering of $n$ input $d$-dimensional vectors under Hamming, $\ell_1, \ell_2$ and $\ell_\infty$ distances. All our…
In online clustering problems, there is often a large amount of uncertainty over possible cluster assignments that cannot be resolved until more data are observed. This difficulty is compounded when clusters follow complex distributions, as…
The consistency of the maximum likelihood estimator for mixtures of elliptically-symmetric distributions for estimating its population version is shown, where the underlying distribution $P$ is nonparametric and does not necessarily belong…
We consider the problem of clustering noisy finite-length observations of stationary ergodic random processes according to their generative models without prior knowledge of the model statistics and the number of generative models. Two…