Popular word embedding methods such as GloVe and Word2Vec are related to the
factorization of the pointwise mutual information (PMI) matrix. In this paper,
we link correspondence analysis (CA) to the factorization of the PMI matrix. CA
is a dimensionality reduction method that uses singular value decomposition
(SVD), and we show that CA is mathematically close to the weighted
factorization of the PMI matrix. In addition, we present variants of CA that
turn out to be successful in the factorization of the word-context matrix, i.e.
CA applied to a matrix where the entries undergo a square-root transformation
(ROOT-CA) and a root-root transformation (ROOTROOT-CA). An empirical comparison
among CA- and PMI-based methods shows that overall results of ROOT-CA and
ROOTROOT-CA are slightly better than those of the PMI-based methods.

本文将对应分析（CA）与点间互信息矩阵（PMI 矩阵）的分解联系起来，并提出了 CA 的变体 ——ROOT-CA 和 ROOTROOT-CA，这些方法在词 - 上下文矩阵的分解中比基于 PMI 的方法稍微好一些。

对比通信分析与基于 PMI 的词嵌入方法的比较

A comparison of correspondence analysis with PMI-based word embedding  methods

There is a broad consensus that news media outlets incorporate ideological
biases in their news articles. However, prior studies on measuring the
discrepancies among media outlets and further dissecting the origins of
semantic differences suffer from small sample sizes and limited scope. In this
study, we collect a large dataset of 1.8 million news headlines from major U.S.
media outlets spanning from 2014 to 2022 to thoroughly track and dissect the
semantic discrepancy in U.S. news media. We employ multiple correspondence
analysis (MCA) to quantify the semantic discrepancy relating to four prominent
topics - domestic politics, economic issues, social issues, and foreign
affairs. Additionally, we compare the most frequent n-grams in media headlines
to provide further qualitative insights into our analysis. Our findings
indicate that on domestic politics and social issues, the discrepancy can be
attributed to a certain degree of media bias. Meanwhile, the discrepancy in
reporting foreign affairs is largely attributed to the diversity in individual
journalistic styles. Finally, U.S. media outlets show consistency and high
similarity in their coverage of economic issues.

通过采用多重对应分析 (MCA) 测量及洞悉 2014 年至 2022 年间 1.8 百万份美国主要媒体新闻头条的语义差异，该研究发现美国国内政治和社会问题的媒体报道存在一定程度的媒体偏见，而外交报道的偏差主要来自个人的新闻风格多样性，而在经济问题的报道上，美国媒体呈现出一致性和高度相似性。

偏见还是多样性？揭开美国新闻标题中的语义差异

Bias or Diversity? Unraveling Semantic Discrepancy in U.S. News Headlines

Many data types arising from data mining applications can be modeled as
bipartite graphs, examples include terms and documents in a text corpus,
customers and purchasing items in market basket analysis and reviewers and
movies in a movie recommender system. In this paper, we propose a new data
clustering method based on partitioning the underlying bipartite graph. The
partition is constructed by minimizing a normalized sum of edge weights between
unmatched pairs of vertices of the bipartite graph. We show that an approximate
solution to the minimization problem can be obtained by computing a partial
singular value decomposition (SVD) of the associated edge weight matrix of the
bipartite graph. We point out the connection of our clustering algorithm to
correspondence analysis used in multivariate analysis. We also briefly discuss
the issue of assigning data objects to multiple clusters. In the experimental
results, we apply our clustering algorithm to the problem of document
clustering to illustrate its effectiveness and efficiency.

本文提出了一种基于分割二分图的新型数据聚类方法，旨在最小化未匹配的顶点之间的边权重总和，通过边权重矩阵的奇异值分解来近似解决这个最小化问题并且在文档聚类问题上取得了显著的效果。