The Procrustes-Wasserstein problem consists in matching two high-dimensional
point clouds in an unsupervised setting, and has many applications in natural
language processing and computer vision. We consider a planted model with two
datasets $X,Y$ that consist of $n$ datapoints in $\mathbb{R}^d$, where $Y$ is a
noisy version of $X$, up to an orthogonal transformation and a relabeling of
the data points. This setting is related to the graph alignment problem in
geometric models. In this work, we focus on the euclidean transport cost
between the point clouds as a measure of performance for the alignment. We
first establish information-theoretic results, in the high ($d \gg \log n$) and
low ($d \ll \log n$) dimensional regimes. We then study computational aspects
and propose the Ping-Pong algorithm, alternatively estimating the orthogonal
transformation and the relabeling, initialized via a Franke-Wolfe convex
relaxation. We give sufficient conditions for the method to retrieve the
planted signal after one single step. We provide experimental results to
compare the proposed approach with the state-of-the-art method of Grave et al.
(2019).

我们研究了 Procrustes-Wasserstein 问题，使用欧几里得传输成本作为性能度量，提出了 Ping-Pong 算法，用于匹配高维点云，并与现有方法进行比较。

对齐嵌入和几何随机图：Procrustes-Wasserstein 问题的信息结果和计算方法

Aligning Embeddings and Geometric Random Graphs: Informational Results  and Computational Approaches for the Procrustes-Wasserstein Problem

In this paper, we describe our method for the detection of lexical semantic
change, i.e., word sense changes over time. We examine semantic differences
between specific words in two corpora, chosen from different time periods, for
English, German, Latin, and Swedish. Our method was created for the SemEval
2020 Task 1: \textit{Unsupervised Lexical Semantic Change Detection.} We ranked
$1^{st}$ in Sub-task 1: binary change detection, and $4^{th}$ in Sub-task 2:
ranked change detection. Our method is fully unsupervised and language
independent. It consists of preparing a semantic vector space for each corpus,
earlier and later; computing a linear transformation between earlier and later
spaces, using Canonical Correlation Analysis and Orthogonal Transformation; and
measuring the cosines between the transformed vector for the target word from
the earlier corpus and the vector for the target word in the later corpus.

本文介绍我们在 SemEval2020 任务 1 中创造性的提出了语义变化检测方法，该方法是全自动的，不需要人工干预，且独立于语言；我们利用标准相关分析和正交变换计算语义空间之间的线性变换，并通过比较早期和晚期语料库中目标单词的向量之间的余弦相似度来检测语义变化。