Related papers: Wasserstein t-SNE
Measuring similarities between different tasks is critical in a broad spectrum of machine learning problems, including transfer, multi-task, continual, and meta-learning. Most current approaches to measuring task similarities are…
This paper addresses a new active learning strategy for regression problems. The presented Wasserstein active regression model is based on the principles of distribution-matching to measure the representativeness of the labeled dataset. The…
We introduce a novel, geometry-aware distance metric for the family of von Mises-Fisher (vMF) distributions, which are fundamental models for directional data on the unit hypersphere. Although the vMF distribution is widely employed in a…
Data visualisation helps understanding data represented by multiple variables, also called features, stored in a large matrix where individuals are stored in lines and variable values in columns. These data structures are frequently called…
The performance of unsupervised methods such as clustering depends on the choice of distance metric between features, or ground metric. Commonly, ground metrics are decided with heuristics or learned via supervised algorithms. However,…
Feature representation is an important aspect of remote-sensing based image classification. While deep convolutional neural networks are able to effectively amalgamate information, large numbers of parameters often make learned features…
This paper studies iterative schemes for measure transfer and approximation problems, which are defined through a slicing-and-matching procedure. Similar to the sliced Wasserstein distance, these schemes benefit from the availability of…
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…
Estimating a $d$-dimensional distribution $\mu$ by the empirical measure $\hat{\mu}_n$ of its samples is an important task in probability theory, statistics and machine learning. It is well known that $\mathbb{E}[\mathcal{W}_p(\hat{\mu}_n,…
The nested distance builds on the Wasserstein distance to quantify the difference of stochastic processes, including also the information modelled by filtrations. The Sinkhorn divergence is a relaxation of the Wasserstein distance, which…
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…
Resource-efficiently computing representations of probability distributions and the distances between them while only having access to the samples is a fundamental and useful problem across mathematical sciences. In this paper, we propose a…
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…
\v{C}ech Persistence diagrams (PDs) are topological descriptors routinely used to capture the geometry of complex datasets. They are commonly compared using the Wasserstein distances $OT_{p}$; however, the extent to which PDs are stable…
We provide an implementation to compute the flat metric in any dimension. The flat metric, also called dual bounded Lipschitz distance, generalizes the well-known Wasserstein distance $W_1$ to the case that the distributions are of unequal…
Random probabilities are a key component to many nonparametric methods in Statistics and Machine Learning. To quantify comparisons between different laws of random probabilities several works are starting to use the elegant Wasserstein over…
Dimensionality reduction is crucial both for visualization and preprocessing high dimensional data for machine learning. We introduce a novel method based on a hierarchy built on 1-nearest neighbor graphs in the original space which is used…
Progressive Visual Analytics aims at improving the interactivity in existing analytics techniques by means of visualization as well as interaction with intermediate results. One key method for data analysis is dimensionality reduction, for…
We propose a hyperbolic set-to-set distance measure for computing dissimilarity between sets in hyperbolic space. While point-to-point distances in hyperbolic space effectively capture hierarchical relationships between data points, many…
Consider the empirical measure, $\hat{\mathbb{P}}_N$, associated to $N$ i.i.d. samples of a given probability distribution $\mathbb{P}$ on the unit interval. For fixed $\mathbb{P}$ the Wasserstein distance between $\hat{\mathbb{P}}_N$ and…