Related papers: t-SNE, Forceful Colorings and Mean Field Limits

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…

This paper investigates the theoretical foundations of the t-distributed stochastic neighbor embedding (t-SNE) algorithm, a popular nonlinear dimension reduction and data visualization method. A novel theoretical framework for the analysis…

Dimensionality reduction and manifold learning methods such as t-Distributed Stochastic Neighbor Embedding (t-SNE) are routinely used to map high-dimensional data into a 2-dimensional space to visualize and explore the data. However, two…

t-SNE is a popular tool for embedding multi-dimensional datasets into two or three dimensions. However, it has a large computational cost, especially when the input data has many dimensions. Many use t-SNE to embed the output of a neural…

The t-distributed Stochastic Neighbor Embedding (tSNE) algorithm has become in recent years one of the most used and insightful techniques for the exploratory data analysis of high-dimensional data. tSNE reveals clusters of high-dimensional…

Neighbor embeddings are a family of methods for visualizing complex high-dimensional datasets using $k$NN graphs. To find the low-dimensional embedding, these algorithms combine an attractive force between neighboring pairs of points with a…

$t$-SNE is an embedding method that the data science community has widely Two interesting characteristics of t-SNE are the structure preservation property and the answer to the crowding problem, where all neighbors in high dimensional space…

t-distributed Stochastic Neighborhood Embedding (t-SNE) is a method for dimensionality reduction and visualization that has become widely popular in recent years. Efficient implementations of t-SNE are available, but they scale poorly to…

t-SNE has gained popularity as a dimension reduction technique, especially for visualizing data. It is well-known that all dimension reduction techniques may lose important features of the data. We provide a mathematical framework for…

Conditional t-SNE (ct-SNE) is a recent extension to t-SNE that allows removal of known cluster information from the embedding, to obtain a visualization revealing structure beyond label information. This is useful, for example, when one…

Dimensionality reduction methods such as t-SNE and UMAP are popular methods for visualizing data with a potential (latent) clustered structure. They are known to group data points at the same time as they embed them, resulting in…

This paper introduces NN-STNE, a neural network using t-distributed stochastic neighbor embedding (t-SNE) as a hidden layer to reduce input dimensions by mapping long time-series data into shapelet membership probabilities. A Gaussian…

Dimensionality reduction methods such as t-SNE are designed to preserve local neighborhood structure but do not explicitly account for how probability mass is distributed, often leading to distortions of data density. We reformulate…

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…

Dimension reduction, widely used in science, maps high-dimensional data into low-dimensional space. We investigate a basic mathematical model underlying the techniques of stochastic neighborhood embedding (SNE) and its popular variant…

Molecular simulation trajectories represent high-dimensional data. Such data can be visualized by methods of dimensionality reduction. Non-linear dimensionality reduction methods are likely to be more efficient than linear ones due to the…

Central to the widespread use of t-distributed stochastic neighbor embedding (t-SNE) is the conviction that it produces visualizations whose structure roughly matches that of the input. To the contrary, we prove that (1) the strength of the…

This work considers large-data asymptotics for t-distributed stochastic neighbor embedding (tSNE), a widely-used non-linear dimension reduction algorithm. We identify an appropriate continuum limit of the tSNE objective function, which can…

The clustering and visualisation of high-dimensional data is a ubiquitous task in modern data science. Popular techniques include nonlinear dimensionality reduction methods like t-SNE or UMAP. These methods face the `scale-problem' of…

Adversarial examples, designed to trick Artificial Neural Networks (ANNs) into producing wrong outputs, highlight vulnerabilities in these models. Exploring these weaknesses is crucial for developing defenses, and so, we propose a method to…