Related papers: Kernel t-distributed stochastic neighbor embedding

Subspace clustering aims to group data points into multiple clusters of which each corresponds to one subspace. Most existing subspace clustering approaches assume that input data lie on linear subspaces. In practice, however, this…

This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to…

We consider the mobile localization problem in future millimeter-wave wireless networks with distributed Base Stations (BSs) based on multi-antenna channel state information (CSI). For this problem, we propose a Semi-supervised tdistributed…

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…

Stochastic Neighbor Embedding (SNE) methods minimize the divergence between the similarity matrix of a high-dimensional data set and its counterpart from a low-dimensional embedding, leading to widely applied tools for data visualization.…

We present a new method GTSNE to visualize high-dimensional data points in the two dimensional map. The technique is a variation of t-SNE that produces better visualizations by capturing both the local neighborhood structure and the macro…

Low-dimensional embeddings and visualizations are an indispensable tool for analysis of high-dimensional data. State-of-the-art methods, such as tSNE and UMAP, excel in unveiling local structures hidden in high-dimensional data and are…

We introduce a new coarse-graining algorithm, tensor network skeletonization, for the numerical computation of tensor networks. This approach utilizes a structure-preserving skeletonization procedure to remove short-range correlations…

Visualization methods based on the nearest neighbor graph, such as t-SNE or UMAP, are widely used for visualizing high-dimensional data. Yet, these approaches only produce meaningful results if the nearest neighbors themselves are…

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…

Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…

The fundamental goal of self-supervised learning (SSL) is to produce useful representations of data without access to any labels for classifying the data. Modern methods in SSL, which form representations based on known or constructed…

This work is concerned with the continuum limit of a graph-based data visualization technique called the t-Distributed Stochastic Neighbor Embedding (t-SNE), which is widely used for visualizing data in a variety of applications, but is…

Stochastic neighbor embedding (SNE) methods $t$-SNE, UMAP are two most popular dimensionality reduction methods for data visualization. Contrastive learning, especially self-supervised contrastive learning (SSCL), has showed great success…

Data visualization is important in understanding the characteristics of data that are difficult to see directly. It is used to visualize loss landscapes and optimization trajectories to analyze optimization performance. Popular optimization…

Manifold learning now plays a very important role in machine learning and many relevant applications. Although its superior performance in dealing with nonlinear data distribution, data sparsity is always a thorny knot. There are few…

Tensor, a multi-dimensional data structure, has been exploited recently in the machine learning community. Traditional machine learning approaches are vector- or matrix-based, and cannot handle tensorial data directly. In this paper, we…

Unsupervised dimensionality reduction is one of the commonly used techniques in the field of high dimensional data recognition problems. The deep autoencoder network which constrains the weights to be non-negative, can learn a low…

Widely used pipelines for analyzing high-dimensional data utilize two-dimensional visualizations. These are created, for instance, via t-distributed stochastic neighbor embedding (t-SNE). A crucial element of the t-SNE embedding procedure…

Although recovering an Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown. To fill in this void, we study a simple distance matrix estimate based upon the…