---
title: "Two-Sided Wasserstein Procrustes Analysis"
authors:
  - "Kun Jin"
  - "Chaoyue Liu"
  - "Cathy Xia"
doi: "10.24963/ijcai.2021/484"
url: "https://ijcai.org/proceedings/2021/484"
pdf: "https://ijcai.org/proceedings/2021/0484.pdf"
venue: "Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence"
year: 2021
pages: "3515-3521"
track: "Main Track"
keywords:
  - "Machine Learning Applications: Bio/Medicine"
  - "Machine Learning Applications: Applications of Unsupervised Learning"
  - "Machine Learning: Transfer, Adaptation, Multi-task Learning"
---

# Two-Sided Wasserstein Procrustes Analysis

Kun Jin, Chaoyue Liu, Cathy Xia

*Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence*, pages 3515-3521. DOI: [10.24963/ijcai.2021/484](https://doi.org/10.24963/ijcai.2021/484)

## Abstract

Learning correspondence between sets of objects is a key component in many machine learning tasks.Recently, optimal Transport (OT) has been successfully applied to such correspondence problems and it  is  appealing  as  a  fully  unsupervised  approach. However,  OT  requires  pairwise  instances  be  directly comparable in a common metric space. This limits its applicability when feature spaces are of different dimensions or not directly comparable. In addition,  OT only focuses on pairwise correspondence without sensing global transformations.  To address these challenges, we propose a new method to jointly learn the optimal coupling between twosets,  and  the  optimal  transformations  (e.g.   rotation,  projection and scaling) of each set based on a two-sided Wassertein Procrustes analysis (TWP). Since the joint problem is a non-convex optimization problem, we present a reformulation that renders the problem component-wise convex. We then propose a novel algorithm to solve the problem harnessing a Gauss–Seidel method. We further present competitive  results  of TWP  on  various  applicationscompared with state-of-the-art methods.