Related papers: Dimensionality Reduction using Elastic Measures
Deep distance metric learning (DDML), which is proposed to learn image similarity metrics in an end-to-end manner based on the convolution neural network, has achieved encouraging results in many computer vision tasks.$L2$-normalization in…
Multidimensional efficiency maps are commonly used in high energy physics experiments to mitigate the limitations in the generation of large samples of simulated events. Binned multidimensional efficiency maps are however strongly limited…
Estimating the intrinsic dimensionality (ID) of data is a fundamental problem in machine learning and computer vision, providing insight into the true degrees of freedom underlying high-dimensional observations. Existing methods often rely…
An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…
Explicitly or implicitly, most of dimensionality reduction methods need to determine which samples are neighbors and the similarity between the neighbors in the original highdimensional space. The projection matrix is then learned on the…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
Nonlinear dimensionality reduction methods are a popular tool for data scientists and researchers to visualize complex, high dimensional data. However, while these methods continue to improve and grow in number, it is often difficult to…
Inspired by the success of deep learning techniques in the physical and chemical sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension reduction of molecular dynamics data. We can show that…
Stochastic Neighbor Embedding (SNE) algorithms like UMAP and tSNE often produce visualizations that do not preserve the geometry of noisy and high dimensional data. In particular, they can spuriously separate connected components of the…
Scientists and engineers rely on accurate mathematical models to quantify the objects of their studies, which are often high-dimensional. Unfortunately, high-dimensional models are inherently difficult, i.e. when observations are sparse or…
Understanding complex phenomena often requires analyzing high-dimensional data to uncover emergent properties that arise from multifactorial interactions. Here, we present EMUSES (Emerging-properties Mapping Using Spatial Embedding…
Embedding and visualizing large-scale high-dimensional data in a two-dimensional space is an important problem since such visualization can reveal deep insights out of complex data. Most of the existing embedding approaches, however, run on…
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…
Nonlinear dimensional reduction with the manifold assumption, often called manifold learning, has proven its usefulness in a wide range of high-dimensional data analysis. The significant impact of t-SNE and UMAP has catalyzed intense…
High-dimensional data are ubiquitous in contemporary science and finding methods to compress them is one of the primary goals of machine learning. Given a dataset lying in a high-dimensional space (in principle hundreds to several thousands…
Dimension Estimation (DE) and Dimension Reduction (DR) are two closely related topics, but with quite different goals. In DE, one attempts to estimate the intrinsic dimensionality or number of latent variables in a set of measurements of a…
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…
Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid…
Parametric embedding methods such as parametric t-SNE (pt-SNE) have been widely adopted for data visualization and out-of-sample data embedding without further computationally expensive optimization or approximation. However, the…
Scalability of statistical estimators is of increasing importance in modern applications and dimension reduction is often used to extract relevant information from data. A variety of popular dimension reduction approaches can be framed as…