Related papers: Kernel Biclustering algorithm in Hilbert Spaces
Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…
A novel nonparametric clustering algorithm is proposed using the interpoint distances between the members of the data to reveal the inherent clustering structure existing in the given set of data, where we apply the classical nonparametric…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…
Kernel techniques are among the most popular and flexible approaches in data science allowing to represent probability measures without loss of information under mild conditions. The resulting mapping called mean embedding gives rise to a…
The field of quantum machine learning is a promising way to lead to a revolution in intelligent data processing methods. In this way, a hybrid learning method based on classic kernel methods is proposed. This proposal also requires the…
Modern large-scale kernel-based tests such as maximum mean discrepancy (MMD) and kernelized Stein discrepancy (KSD) optimize kernel hyperparameters on a held-out sample via data splitting to obtain the most powerful test statistics. While…
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…
We develop novel clustering algorithms for functional data when the number of clusters $K$ is unknown and also when it is prefixed. These algorithms are developed based on the Maximum Mean Discrepancy (MMD) measure between two sets of…
Clustering algorithms partition a dataset into groups of similar points. The clustering problem is very general, and different partitions of the same dataset could be considered correct and useful. To fully understand such data, it must be…
Distances between probability distributions that take into account the geometry of their sample space,like the Wasserstein or the Maximum Mean Discrepancy (MMD) distances have received a lot of attention in machine learning as they can, for…
The kernel mean embedding of probability distributions is commonly used in machine learning as an injective mapping from distributions to functions in an infinite dimensional Hilbert space. It allows us, for example, to define a distance…
Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings,…
Distance-based clustering and classification are widely used in various fields to group mixed numeric and categorical data. In many algorithms, a predefined distance measurement is used to cluster data points based on their dissimilarity.…
The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely-many multivariate samples. When the distributions are locally low-dimensional, the proposed…
In this paper we present a family of algorithms that can simultaneously align and cluster sets of multidimensional curves measured on a discrete time grid. Our approach is based on a generative mixture model that allows non-linear time…
Embedding probability distributions into reproducing kernel Hilbert spaces (RKHS) has enabled powerful nonparametric methods such as the maximum mean discrepancy (MMD), a statistical distance with strong theoretical and computational…
We propose a deep learning approach for discovering kernels tailored to identifying clusters over sample data. Our neural network produces sample embeddings that are motivated by--and are at least as expressive as--spectral clustering. Our…
We present a new method for multiclass thresholding of a histogram which is based on the nonparametric Kernel Density (KD) estimation, where the unknown parameters of the KD estimate are defined using the Expectation-Maximization (EM)…
Modern data-driven and distributed learning frameworks deal with diverse massive data generated by clients spread across heterogeneous environments. Indeed, data heterogeneity is a major bottleneck in scaling up many distributed learning…