Nonnegative matrix factorization (NMF) is widely used for clustering with
strong interpretability. Among general NMF problems, symmetric NMF is a special
one that plays an important role in graph clustering where each element
measures the similarity between data points. Most existing symmetric NMF
algorithms require factor matrices to be nonnegative, and only focus on
minimizing the gap between similarity matrix and its approximation for
clustering, without giving a consideration to other potential regularization
terms which can yield better clustering. In this paper, we explore factorizing
a symmetric matrix that does not have to be nonnegative, presenting an
efficient factorization algorithm with a regularization term to boost the
clustering performance. Moreover, a more general framework is proposed to solve
symmetric matrix factorization problems with different constraints on the
factor matrices.

本文提出了使用正则项优化的高效因式分解算法来提高聚类性能，同时进一步探索了使用不同约束条件解决对称矩阵分解问题的通用框架。

对称矩阵分解的再思考：更一般且更优的聚类视角

Rethinking Symmetric Matrix Factorization: A More General and Better Clustering Perspective

A rich set of interpretable dimensions has been shown to emerge in the latent
space of the Generative Adversarial Networks (GANs) trained for synthesizing
images. In order to identify such latent dimensions for image editing, previous
methods typically annotate a collection of synthesized samples and train linear
classifiers in the latent space. However, they require a clear definition of
the target attribute as well as the corresponding manual annotations, limiting
their applications in practice. In this work, we examine the internal
representation learned by GANs to reveal the underlying variation factors in an
unsupervised manner. In particular, we take a closer look into the generation
mechanism of GANs and further propose a closed-form factorization algorithm for
latent semantic discovery by directly decomposing the pre-trained weights. With
a lightning-fast implementation, our approach is capable of not only finding
semantically meaningful dimensions comparably to the state-of-the-art
supervised methods, but also resulting in far more versatile concepts across
multiple GAN models trained on a wide range of datasets.

该研究使用生成式对抗网络（GANs）的内部编码，通过直接分解预训练权重，提出了一种闭式因式分解算法，从而发现了语义上更丰富的维度，用于图像编辑和无监督学习。

GAN 中潜在语义的闭式因式分解

Closed-Form Factorization of Latent Semantics in GANs

A simple prior free factorization algorithm \cite{dai2014simple} is quite
often cited work in the field of Non-Rigid Structure from Motion (NRSfM). The
benefit of this work lies in its simplicity of implementation, strong
theoretical justification to the motion and structure estimation, and its
invincible originality. Despite this, the prevailing view is, that it performs
exceedingly inferior to other methods on several benchmark datasets
\cite{jensen2018benchmark,akhter2009nonrigid}. However, our subtle
investigation provides some empirical statistics which made us think against
such views. The statistical results we obtained supersedes Dai {\it{et
al.}}\cite{dai2014simple} originally reported results on the benchmark datasets
by a significant margin under some elementary changes in their core algorithmic
idea \cite{dai2014simple}. Now, these results not only exposes some unrevealed
areas for research in NRSfM but also give rise to new mathematical challenges
for NRSfM researchers. We argue that by \textbf{properly} utilizing the
well-established assumptions about a non-rigidly deforming shape i.e, it
deforms smoothly over frames \cite{rabaud2008re} and it spans a low-rank space,
the simple prior-free idea can provide results which is comparable to the best
available algorithms. In this paper, we explore some of the hidden intricacies
missed by Dai {\it{et. al.}} work \cite{dai2014simple} and how some elementary
measures and modifications can enhance its performance, as high as approx. 18\%
on the benchmark dataset. The improved performance is justified and empirically
verified by extensive experiments on several datasets. We believe our work has
both practical and theoretical importance for the development of better NRSfM
algorithms.

通过充分利用非刚性形状针对平稳变形和跨越低秩空间的假设，这篇研究论文摆脱了简单先验算法的约束，对其核心算法进行了一些基本改进措施，从而实现了比先前最优算法还高约 18% 的性能提升，并在多个数据集上进行了验证。