High-dimensional datasets present substantial challenges in statistical
modeling across various disciplines, necessitating effective dimensionality
reduction methods. Deep learning approaches, notable for their capacity to
distill essential features from complex data, facilitate modeling,
visualization, and compression through reduced dimensionality latent feature
spaces, have wide applications from bioinformatics to earth sciences. This
study introduces a novel workflow to evaluate the stability of these latent
spaces, ensuring consistency and reliability in subsequent analyses. Stability,
defined as the invariance of latent spaces to minor data, training
realizations, and parameter perturbations, is crucial yet often overlooked.
Our proposed methodology delineates three stability types, sample,
structural, and inferential, within latent spaces, and introduces a suite of
metrics for comprehensive evaluation. We implement this workflow across 500
autoencoder realizations and three datasets, encompassing both synthetic and
real-world scenarios to explain latent space dynamics. Employing k-means
clustering and the modified Jonker-Volgenant algorithm for class alignment,
alongside anisotropy metrics and convex hull analysis, we introduce adjusted
stress and Jaccard dissimilarity as novel stability indicators.
Our findings highlight inherent instabilities in latent feature spaces and
demonstrate the workflow's efficacy in quantifying and interpreting these
instabilities. This work advances the understanding of latent feature spaces,
promoting improved model interpretability and quality control for more informed
decision-making for diverse analytical workflows that leverage deep learning.

高维数据集在各个学科的统计建模中带来了很大的挑战，需要高效的降维方法。深度学习方法通过降维的潜在特征空间从复杂数据中提取关键特征，有着广泛的应用，从生物信息学到地球科学等领域。本研究通过引入一个新的工作流程来评估这些潜在空间的稳定性，确保后续分析的一致性和可靠性。该工作流程囊括了三种稳定性类型：样本稳定性、结构稳定性和推断稳定性，并引入了一套综合评估指标。研究结果揭示了潜在特征空间固有的不稳定性，并证明了该工作流程在量化和解释这些不稳定性方面的功效。这项工作推进了对潜在特征空间的理解，促进了深度学习在各种分析工作流中的模型可解释性和质量控制，为更加明智的决策提供了基础。

评估深度学习潜在特征空间的稳定性

Evaluating the Stability of Deep Learning Latent Feature Spaces

In open-set recognition (OSR), classifiers should be able to reject
unknown-class samples while maintaining high closed-set classification
accuracy. To effectively solve the OSR problem, previous studies attempted to
limit latent feature space and reject data located outside the limited space
via offline analyses, e.g., distance-based feature analyses, or complicated
network architectures. To conduct OSR via a simple inference process (without
offline analyses) in standard classifier architectures, we use distance-based
classifiers instead of conventional Softmax classifiers. Afterwards, we design
a background-class regularization strategy, which uses background-class data as
surrogates of unknown-class ones during training phase. Specifically, we
formulate a novel regularization loss suitable for distance-based classifiers,
which reserves sufficiently large class-wise latent feature spaces for known
classes and forces background-class samples to be located far away from the
limited spaces. Through our extensive experiments, we show that the proposed
method provides robust OSR results, while maintaining high closed-set
classification accuracy.

本研究提出在标准分类器结构中使用基于距离的分类器，通过背景类正则化策略来增强开放集识别的鲁棒性，从而避免了复杂的离线分析和网络设计，同时保持高准确性的闭集分类。

通过背景类别正则化实现准确的开放式识别

Towards Accurate Open-Set Recognition via Background-Class  Regularization

Most conventional crowd counting methods utilize a fully-supervised learning
framework to learn a mapping between scene images and crowd density maps. Under
the circumstances of such fully-supervised training settings, a large quantity
of expensive and time-consuming pixel-level annotations are required to
generate density maps as the supervision. One way to reduce costly labeling is
to exploit self-structural information and inner-relations among unlabeled
images. Unlike the previous methods utilizing these relations and structural
information from the original image level, we explore such self-relations from
the latent feature spaces because it can extract more abundant relations and
structural information. Specifically, we propose S$^2$FPR which can extract
structural information and learn partial orders of coarse-to-fine pyramid
features in the latent space for better crowd counting with massive unlabeled
images. In addition, we collect a new unlabeled crowd counting dataset
(FUDAN-UCC) with 4,000 images in total for training. One by-product is that our
proposed S$^2$FPR method can leverage numerous partial orders in the latent
space among unlabeled images to strengthen the model representation capability
and reduce the estimation errors for the crowd counting task. Extensive
experiments on four benchmark datasets, i.e. the UCF-QNRF, the ShanghaiTech
PartA and PartB, and the UCF-CC-50, show the effectiveness of our method
compared with previous semi-supervised methods. The source code and dataset are
available at this https URL.

本研究利用自身结构信息及内部关联来减少代价昂贵的像素级注释，通过在潜在特征空间中的 S^2FPR 方法来提取结构信息和学习由粗到细的部分顺序以更好地计算大规模未标记图像的人数，该方法在 UCF-QNRF、ShanghaiTech PartA 和 PartB、UCF-CC-50 等四个基准数据集上的实验表明了与以往半监督方法的有效性。