Faithful visualizations of data residing on manifolds must take the underlying geometry into account when producing a flat planar view of the data. In this paper, we extend the classic stochastic neighbor embedding (SNE) algorithm to data on general Riemannian manifolds. We replace standard Gaussian assumptions with Riemannian diffusion counterparts and propose an efficient approximation that only requires access to calculations of Riemannian distances and volumes. We demonstrate that the approach also allows for mapping data from one manifold to another, e.g. from a high-dimensional sphere to a low-dimensional one.
University of Pennsylvania（宾夕法尼亚大学）；Stanford University（斯坦福大学）
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 of t-SNE based on the gradient descent approach is presented. For the early exaggeration stage of t-SNE, we show its asymptotic equivalence to power iterations based on the underlying graph Laplacian, characterize its limiting behavior, and uncover its deep connection to Laplacian spectral clustering, and fundamental principles including early stopping as im…
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 structure in the data. This is particularly important for high-dimensional data that lie on continuous low-dimensional manifolds. We illustrate the performance of GTSNE on a wide variety of datasets and compare it the state of art methods, including t-SNE and UMAP. The visualizations produced by GTSNE are better than those produced by the other techniques on …
t-SNE remains one of the most popular embedding techniques for visualizing high-dimensional data. Most standard packages of t-SNE, such as scikit-learn, use the Barnes-Hut t-SNE (BH t-SNE) algorithm for large datasets. However, existing CPU implementations of this algorithm are inefficient. In this work, we accelerate the BH t-SNE on CPUs via cache optimizations, SIMD, parallelizing sequential steps, and improving parallelization of multithreaded steps. Our implementation (Acc-t-SNE) is up to 261x and 4x faster than scikit-learn and the state-of-the-art BH t-SNE implementation from daal4py, re…
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
Dimensionality reduction techniques aim at representing high-dimensional data in low-dimensional spaces to extract hidden and useful information or facilitate visual understanding and interpretation of the data. However, few of them take into consideration the potential cluster information contained implicitly in the high-dimensional data. In this paper, we propose LaptSNE, a new graph-layout nonlinear dimensionality reduction method based on t-SNE, one of the best techniques for visualizing high-dimensional data as 2D scatter plots. Specifically, LaptSNE leverages the eigenvalue information o…
University of Massachusetts Lowell（马萨诸塞大学洛厄尔分校）；University of Colorado Boulder（科罗拉多大学博尔德分校）
A fundamental task in machine learning involves visualizing high-dimensional data sets that arise in high-impact application domains. When considering the context of large imbalanced data, this problem becomes much more challenging. In this paper, the t-Distributed Stochastic Neighbor Embedding (t-SNE) algorithm is used to reduce the dimensions of an earthquake engineering related data set for visualization purposes. Since imbalanced data sets greatly affect the accuracy of classifiers, we employ Synthetic Minority Oversampling Technique (SMOTE) to tackle the imbalanced nature of such data set…
Cluster and then Embed: A Modular Approach for Visualization
Department of Mathematics, University of California, San Diego（数学系，加州大学圣地亚哥分校）；Halıcıoğlu Data Science Institute, University of California, San Diego（Halıcıoğlu数据科学研究所，加州大学圣地亚哥分校）
On the continuum limit of t-SNE for data visualization
School of Mathematics, University of Minnesota（明尼苏达大学数学学院）；Department of Mathematics, University of Utah（犹他大学数学系）；Department of Mathematics, North Carolina State University（北卡罗来纳州立大学数学系）
