4.7 Article

A linear transportation LP distance for pattern recognition

Related references

Note: Only part of the references are listed.
Article Mathematics, Applied

Linear optimal transport embedding: provable Wasserstein classification for certain rigid transformations and perturbations

Caroline Moosmuller et al.

Summary: Discriminating between distributions is a significant problem in various scientific fields. The introduction of Linear Optimal Transportation (LOT) effectively embeds the distribution space into an L-2 -space, enabling efficient computation and classification boundary determination. This paper characterizes the conditions in which LOT can linearly separate families of distributions in arbitrary dimensions, and it proves the approximate isometry between the L-2 distance of LOT embedding and Wasserstein-2 distance between distributions. The computational benefits of LOT are demonstrated through various distribution classification problems.

INFORMATION AND INFERENCE-A JOURNAL OF THE IMA (2023)

Article Computer Science, Artificial Intelligence

Dual-Constrained Deep Semi-Supervised Coupled Factorization Network with Enriched Prior

Yan Zhang et al.

Summary: A new dual-constrained deep semi-supervised coupled factorization network is proposed in this paper for learning hierarchical representations. It integrates error correction mechanism and feature fusion strategy to improve representation ability, enriches prior knowledge through coefficients-based label prediction, and incorporates additional label and structure constraints to enhance discriminating abilities. Integration of adaptive dual-graph learning and fine-tuning process further improve the accuracy of representations.

INTERNATIONAL JOURNAL OF COMPUTER VISION (2021)

Article Astronomy & Astrophysics

Linearized optimal transport for collider events

Tianji Cai et al.

PHYSICAL REVIEW D (2020)

Article Mathematics, Applied

Asymptotic analysis of the Ginzburg-Landau functional on point clouds

Matthew Thorpe et al.

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS (2019)

Article Mathematics, Applied

ANALYSIS OF p-LAPLACIAN REGULARIZATION IN SEMISUPERVISED LEARNING

Dejan Slepcev et al.

SIAM JOURNAL ON MATHEMATICAL ANALYSIS (2019)

Article Mathematics, Applied

Variational Limits of k-NN Graph-Based Functionals on Data Clouds

Nicolas Garcia Trillos

SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE (2019)

Article Mathematics, Applied

A variational approach to the consistency of spectral clustering

Nicolas Garcia Trillos et al.

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS (2018)

Article Mathematics, Applied

CONTINUUM LIMITS OF POSTERIORS IN GRAPH BAYESIAN INVERSE PROBLEMS

Nicolas Garcia Trillos et al.

SIAM JOURNAL ON MATHEMATICAL ANALYSIS (2018)

Proceedings Paper Computer Science, Artificial Intelligence

Representing and Learning High Dimensional Data with the Optimal Transport Map from a Probabilistic Viewpoint

Serim Park et al.

2018 IEEE/CVF CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION (CVPR) (2018)

Article Mathematics, Applied

A new analytical approach to consistency and overfitting in regularized empirical risk minimization

Nicolas Garcia Trillos et al.

EUROPEAN JOURNAL OF APPLIED MATHEMATICS (2017)

Editorial Material Engineering, Electrical & Electronic

Optimal Mass Transport Signal processing and machine-learning applications

Soheil Kolouri et al.

IEEE SIGNAL PROCESSING MAGAZINE (2017)

Article Computer Science, Artificial Intelligence

A Transportation Distance for Signal Analysis

Matthew Thorpe et al.

JOURNAL OF MATHEMATICAL IMAGING AND VISION (2017)

Article Mathematics, Applied

CONSISTENCY OF DIRICHLET PARTITIONS

Braxton Osting et al.

SIAM JOURNAL ON MATHEMATICAL ANALYSIS (2017)

Article Mathematics, Applied

CONVERGENCE OF ENTROPIC SCHEMES FOR OPTIMAL TRANSPORT AND GRADIENT FLOWS

Guillaume Carlier et al.

SIAM JOURNAL ON MATHEMATICAL ANALYSIS (2017)

Article Statistics & Probability

ESTIMATING PERIMETER USING GRAPH CUTS

Nicolas Garcia Trillos et al.

ADVANCES IN APPLIED PROBABILITY (2017)

Article Mathematics, Applied

Continuum Limit of Total Variation on Point Clouds

Nicolas Garcia Trillos et al.

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS (2016)

Article Computer Science, Artificial Intelligence

A continuous linear optimal transport approach for pattern analysis in image datasets

Soheil Kolouri et al.

PATTERN RECOGNITION (2016)

Article Business, Finance

Estimating Beta

Fabian Hollstein et al.

JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSIS (2016)

Article Computer Science, Software Engineering

Convolutional Wasserstein Distances: Efficient Optimal Transportation on Geometric Domains

Justin Solomon et al.

ACM TRANSACTIONS ON GRAPHICS (2015)

Article Mathematics, Applied

ITERATIVE BREGMAN PROJECTIONS FOR REGULARIZED TRANSPORTATION PROBLEMS

Jean-David Benamou et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2015)

Article Computer Science, Artificial Intelligence

Sliced and Radon Wasserstein Barycenters of Measures

Nicolas Bonneel et al.

JOURNAL OF MATHEMATICAL IMAGING AND VISION (2015)

Article Multidisciplinary Sciences

Detecting and visualizing cell phenotype differences from microscopy images using transportbased morphometry

Saurav Basu et al.

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA (2014)

Article Computer Science, Artificial Intelligence

A Linear Optimal Transportation Framework for Quantifying and Visualizing Variations in Sets of Images

Wei Wang et al.

INTERNATIONAL JOURNAL OF COMPUTER VISION (2013)

Article Computer Science, Interdisciplinary Applications

Bayesian inference with optimal maps

Tarek A. El Moselhy et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2012)

Article Computer Science, Software Engineering

A Multiscale Approach to Optimal Transport

Quentin Merigot

COMPUTER GRAPHICS FORUM (2011)

Article Computer Science, Artificial Intelligence

Penalized Fisher discriminant analysis and its application to image-based morphometry

Wei Wang et al.

PATTERN RECOGNITION LETTERS (2011)

Article Mathematics

ON HOLDER CONTINUITY-IN-TIME OF THE OPTIMAL TRANSPORT MAP TOWARDS MEASURES ALONG A CURVE

Nicola Gigli

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY (2011)

Article Mathematics, Applied

AN EFFICIENT NUMERICAL METHOD FOR THE SOLUTION OF THE L-2 OPTIMAL MASS TRANSFER PROBLEM

Eldad Haber et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2010)

Article Computer Science, Artificial Intelligence

An image morphing technique based on optimal mass preserving mapping

Lei Zhu et al.

IEEE TRANSACTIONS ON IMAGE PROCESSING (2007)

Article Computer Science, Artificial Intelligence

Optimal mass transport for registration and warping

S Haker et al.

INTERNATIONAL JOURNAL OF COMPUTER VISION (2004)

Article Mathematics, Applied

Minimizing flows for the Monge-Kantorovich problem

S Angenent et al.

SIAM JOURNAL ON MATHEMATICAL ANALYSIS (2003)

Article Mathematics

Monge's transport problem on a Riemannian manifold

M Feldman et al.

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY (2002)

Article Mathematics, Applied

The geometry of dissipative evolution equations: The porous medium equation

F Otto

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS (2001)