Related papers: The Tree-SNE Tree Exists
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…
To address the dual challenges of the curse of dimensionality and the difficulty in separating intra-cluster and inter-cluster structures in high-dimensional manifold embedding, we proposes an Adaptive Multi-Scale Manifold Embedding (AMSME)…
Unsupervised machine learning has recently gained much attention in the field of molecular dynamics (MD). Particularly, dimensionality reduction techniques have been regularly employed to analyze large volumes of high-dimensional MD data to…
The chemical sciences are producing an unprecedented amount of large, high-dimensional data sets containing chemical structures and associated properties. However, there are currently no algorithms to visualize such data while preserving…
t-distributed stochastic neighbor embedding (t-SNE) is a well-established visualization method for complex high-dimensional data. However, the original t-SNE method is nonparametric, stochastic, and often cannot well prevserve the global…
The paper presents an O(N log N)-implementation of t-SNE -- an embedding technique that is commonly used for the visualization of high-dimensional data in scatter plots and that normally runs in O(N^2). The new implementation uses…
Modern inference and learning often hinge on identifying low-dimensional structures that approximate large scale data. Subspace clustering achieves this through a union of linear subspaces. However, in contemporary applications data is…
Modern datasets and models are notoriously difficult to explore and analyze due to their inherent high dimensionality and massive numbers of samples. Existing visualization methods which employ dimensionality reduction to two or three…
Tree projections provide a unifying framework to deal with most structural decomposition methods of constraint satisfaction problems (CSPs). Within this framework, a CSP instance is decomposed into a number of sub-problems, called views,…
Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…
A hierarchical scheme for clustering data is presented which applies to spaces with a high number of dimension ($N_{_{D}}>3$). The data set is first reduced to a smaller set of partitions (multi-dimensional bins). Multiple clustering…
Modern methods in dimensionality reduction are dominated by nonlinear attraction-repulsion force-based methods (this includes t-SNE, UMAP, ForceAtlas2, LargeVis, and many more). The purpose of this paper is to demonstrate that all such…
Datasets in high-dimension do not typically form clusters in their original space; the issue is worse when the number of points in the dataset is small. We propose a low-computation method to find statistically significant clustering…
Driven by advances in recording technology, large-scale high-dimensional datasets have emerged across many scientific disciplines. Especially in biology, clustering is often used to gain insights into the structure of such datasets, for…
It has become standard to use gradient-based dimensionality reduction (DR) methods like tSNE and UMAP when explaining what AI models have learned. This makes sense: these methods are fast, robust, and have an uncanny ability to find…
UMAP has supplanted t-SNE as state-of-the-art for visualizing high-dimensional datasets in many disciplines, but the reason for its success is not well understood. In this work, we investigate UMAP's sampling based optimization scheme in…
T-SNE is a well-known approach to embedding high-dimensional data and has been widely used in data visualization. The basic assumption of t-SNE is that the data are non-constrained in the Euclidean space and the local proximity can be…
Subspace clustering refers to the problem of clustering high-dimensional data into a union of low-dimensional subspaces. Current subspace clustering approaches are usually based on a two-stage framework. In the first stage, an affinity…
Dimensionality reduction methods, also known as projections, are frequently used for exploring multidimensional data in machine learning, data science, and information visualization. Among these, t-SNE and its variants have become very…
The goal of dimension reduction tools is to construct a low-dimensional representation of high-dimensional data. These tools are employed for a variety of reasons such as noise reduction, visualization, and to lower computational costs.…