Related papers: Kernel distance measures for time series, random f…
Clustering is spotting pattern in a group of objects and resultantly grouping the similar objects together. Objects have attributes which are not always numerical, sometimes attributes have domain or categories to which they could belong…
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…
Comparing differently sized data sets is one main task in model assessment and calibration. This is due to field data being generally sparse compared to simulated model results. We tackled this task by the application of a new…
This paper presents a kernelized version of the t-SNE algorithm, capable of mapping high-dimensional data to a low-dimensional space while preserving the pairwise distances between the data points in a non-Euclidean metric. This can be…
This paper studies the optimality of kernel methods in high-dimensional data clustering. Recent works have studied the large sample performance of kernel clustering in the high-dimensional regime, where Euclidean distance becomes less…
This paper considers metric spaces where distances between a pair of nodes are represented by distance intervals. The goal is to study methods for the determination of hierarchical clusters, i.e., a family of nested partitions indexed by a…
Nonlinear similarity measures defined in kernel space, such as correntropy, can extract higher-order statistics of data and offer potentially significant performance improvement over their linear counterparts especially in non-Gaussian…
Consider a setting with multiple units (e.g., individuals, cohorts, geographic locations) and outcomes (e.g., treatments, times, items), where the goal is to learn a multivariate distribution for each unit-outcome entry, such as the…
Kernel alignment measures the degree of similarity between two kernels. In this paper, inspired from kernel alignment, we propose a new Linear Discriminant Analysis (LDA) formulation, kernel alignment LDA (kaLDA). We first define two…
Due to the ever rising importance of the network paradigm across several areas of science, comparing and classifying graphs represent essential steps in the networks analysis of complex systems. Both tasks have been recently tackled via…
We introduce a new approach to nonlinear sufficient dimension reduction in cases where both the predictor and the response are distributional data, modeled as members of a metric space. Our key step is to build universal kernels…
Time series data analytics has been a problem of substantial interests for decades, and Dynamic Time Warping (DTW) has been the most widely adopted technique to measure dissimilarity between time series. A number of global-alignment kernels…
The kernel $k$-means is an effective method for data clustering which extends the commonly-used $k$-means algorithm to work on a similarity matrix over complex data structures. The kernel $k$-means algorithm is however computationally very…
Divergence measures play a central role and become increasingly essential in deep learning, yet efficient measures for multiple (more than two) distributions are rarely explored. This becomes particularly crucial in areas where the…
The k-nearest neighbors (k-NN) is a basic machine learning (ML) algorithm, and several quantum versions of it, employing different distance metrics, have been presented in the last few years. Although the Euclidean distance is one of the…
We examine the integrated squared difference, also known as the L2 distance (L2D), between two probability densities. Such a distance metric allows for comparison of differences between pairs of distributions or changes in a distribution…
Clustering is an important exploratory data analysis technique to group objects based on their similarity. The widely used $K$-means clustering method relies on some notion of distance to partition data into a fewer number of groups. In the…
We propose a novel Fr\'echet sufficient dimension reduction (SDR) method based on kernel distance covariance, tailored for metric space-valued responses such as count data, probability densities, and other complex structures. The method…
K-means algorithm is a very popular clustering algorithm which is famous for its simplicity. Distance measure plays a very important rule on the performance of this algorithm. We have different distance measure techniques available. But…
In this paper we present two related, kernel-based Distance Metric Learning (DML) methods. Their respective models non-linearly map data from their original space to an output space, and subsequent distance measurements are performed in the…