Related papers: Kernel Biclustering algorithm in Hilbert Spaces
Multi-manifold modeling is increasingly used in segmentation and data representation tasks in computer vision and related fields. While the general problem, modeling data by mixtures of manifolds, is very challenging, several approaches…
Measures of similarity (or dissimilarity) are a key ingredient to many machine learning algorithms. We introduce DID, a pairwise dissimilarity measure applicable to a wide range of data spaces, which leverages the data's internal structure…
Clustering samples according to an effective metric and/or vector space representation is a challenging unsupervised learning task with a wide spectrum of applications. Among several clustering algorithms, k-means and its kernelized version…
Divergence is not only an important mathematical concept in information theory, but also applied to machine learning problems such as low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection. We…
In order to help physicists to expand their knowledge of the climate in the Lesser Antilles, we aim to identify the spatio-temporal configurations using clustering analysis on wind speed and cumulative rainfall datasets. But we show that…
In this paper we combine the theory of reproducing kernel Hilbert spaces with the field of collocation methods to solve boundary value problems with special emphasis on reproducing property of kernels. From the reproducing property of…
We study the clustering problem for mixtures of bounded covariance distributions, under a fine-grained separation assumption. Specifically, given samples from a $k$-component mixture distribution $D = \sum_{i =1}^k w_i P_i$, where each $w_i…
Subsampling methods aim to select a subsample as a surrogate for the observed sample. Such methods have been used pervasively in large-scale data analytics, active learning, and privacy-preserving analysis in recent decades. Instead of…
Any clustering algorithm must synchronously learn to model the clusters and allocate data to those clusters in the absence of labels. Mixture model-based methods model clusters with pre-defined statistical distributions and allocate data to…
Depth measures have gained popularity in the statistical literature for defining level sets in complex data structures like multivariate data, functional data, and graphs. Despite their versatility, integrating depth measures into…
This paper introduces a novel mixture model-based approach for simultaneous clustering and optimal segmentation of functional data which are curves presenting regime changes. The proposed model consists in a finite mixture of piecewise…
This paper deals with the problem of clustering data returned by a radar sensor network that monitors a region where multiple moving targets are present. The network is formed by nodes with limited functionalities that transmit the…
Clustering algorithms are one of the main analytical methods to detect patterns in unlabeled data. Existing clustering methods typically treat samples in a dataset as points in a metric space and compute distances to group together similar…
The Wasserstein distance is a powerful metric based on the theory of optimal transport. It gives a natural measure of the distance between two distributions with a wide range of applications. In contrast to a number of the common…
Motivated by the increasing availability of low- and mixed-precision arithmetic on modern hardware, we develop mixed-precision variants of Lloyd's algorithm for k-means clustering. The main ingredient is a family of mixed-precision kernels…
We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…
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…
In a mixture of linear regression model, the regression coefficients are treated as random vectors that may follow either a continuous or discrete distribution. We propose two Expectation-Maximization (EM) algorithms to estimate this prior…
Bi-clustering is a technique that allows for the simultaneous clustering of observations and features in a dataset. This technique is often used in bioinformatics, text mining, and time series analysis. An important advantage of…
In this paper we present novel algorithms for several multidimensional data processing problems. We consider problems related to the computation of restricted clusters and of the diameter of a set of points using a new distance function. We…