我们提出了一种新型的强大分散图聚类算法，该算法与流行的光谱聚类方法相当。我们提出的方法使用现有的波方程聚类算法，该算法基于通过图的传播波。但是，我们提出的方法没有在每个节点上使用快速的傅立叶变换（FFT）计算，而是利用了Koopman操作员框架。具体而言，我们表明，在图中传播波，然后在每个节点处进行局部动态模式分解（DMD）计算，能够检索图形laplacian的特征值和局部特征向量组件，从而为所有节点提供局部群集分配。我们证明，DMD计算比现有的基于FFT的方法更强大，并且需要减少波动方程的步骤20倍，以准确恢复群集信息并通过数量级减少相对误差。我们在一系列图集聚类问题上演示了分散的方法。

时间序列数据的生成和分析与许多从经济学到流体力学的定量字段相关。在物理科学中，诸如亚稳态和连贯的组的结构，慢松弛过程，集体变量显性过渡途径或歧管流动流动的概率流动可能非常重视理解和表征系统的动力动力学和机械性质。 Deeptime是一种通用Python库，提供各种工具来估计基于时间序列数据的动态模型，包括传统的线性学习方法，例如马尔可夫状态模型（MSM），隐藏的马尔可夫模型和Koopman模型，以及内核和深度学习方法如vampnets和深msms。该库主要兼容Scikit-Searn，为这些不同的模型提供一系列估计器类，但与Scikit-Ge劳说相比，还提供了深度模型类，例如，在MSM的情况下，提供了多种分析方法来计算有趣的热力学，动力学和动态量，例如自由能，松弛时间和过渡路径。图书馆专为易于使用而设计，而且易于维护和可扩展的代码。在本文中，我们介绍了Deeptime软件的主要特征和结构。

We consider autocovariance operators of a stationary stochastic process on a Polish space that is embedded into a reproducing kernel Hilbert space. We investigate how empirical estimates of these operators converge along realizations of the process under various conditions. In particular, we examine ergodic and strongly mixing processes and obtain several asymptotic results as well as finite sample error bounds. We provide applications of our theory in terms of consistency results for kernel PCA with dependent data and the conditional mean embedding of transition probabilities. Finally, we use our approach to examine the nonparametric estimation of Markov transition operators and highlight how our theory can give a consistency analysis for a large family of spectral analysis methods including kernel-based dynamic mode decomposition.

Diversity Searcher is a tool originally developed to help analyse diversity in news media texts. It relies on a form of automated content analysis and thus rests on prior assumptions and depends on certain design choices related to diversity and fairness. One such design choice is the external knowledge source(s) used. In this article, we discuss implications that these sources can have on the results of content analysis. We compare two data sources that Diversity Searcher has worked with - DBpedia and Wikidata - with respect to their ontological coverage and diversity, and describe implications for the resulting analyses of text corpora. We describe a case study of the relative over- or under-representation of Belgian political parties between 1990 and 2020 in the English-language DBpedia, the Dutch-language DBpedia, and Wikidata, and highlight the many decisions needed with regard to the design of this data analysis and the assumptions behind it, as well as implications from the results. In particular, we came across a staggering over-representation of the political right in the English-language DBpedia.

Artificial intelligence(AI) systems based on deep neural networks (DNNs) and machine learning (ML) algorithms are increasingly used to solve critical problems in bioinformatics, biomedical informatics, and precision medicine. However, complex DNN or ML models that are unavoidably opaque and perceived as black-box methods, may not be able to explain why and how they make certain decisions. Such black-box models are difficult to comprehend not only for targeted users and decision-makers but also for AI developers. Besides, in sensitive areas like healthcare, explainability and accountability are not only desirable properties of AI but also legal requirements -- especially when AI may have significant impacts on human lives. Explainable artificial intelligence (XAI) is an emerging field that aims to mitigate the opaqueness of black-box models and make it possible to interpret how AI systems make their decisions with transparency. An interpretable ML model can explain how it makes predictions and which factors affect the model's outcomes. The majority of state-of-the-art interpretable ML methods have been developed in a domain-agnostic way and originate from computer vision, automated reasoning, or even statistics. Many of these methods cannot be directly applied to bioinformatics problems, without prior customization, extension, and domain adoption. In this paper, we discuss the importance of explainability with a focus on bioinformatics. We analyse and comprehensively overview of model-specific and model-agnostic interpretable ML methods and tools. Via several case studies covering bioimaging, cancer genomics, and biomedical text mining, we show how bioinformatics research could benefit from XAI methods and how they could help improve decision fairness.

Kernel machines have sustained continuous progress in the field of quantum chemistry. In particular, they have proven to be successful in the low-data regime of force field reconstruction. This is because many physical invariances and symmetries can be incorporated into the kernel function to compensate for much larger datasets. So far, the scalability of this approach has however been hindered by its cubical runtime in the number of training points. While it is known, that iterative Krylov subspace solvers can overcome these burdens, they crucially rely on effective preconditioners, which are elusive in practice. Practical preconditioners need to be computationally efficient and numerically robust at the same time. Here, we consider the broad class of Nystr\"om-type methods to construct preconditioners based on successively more sophisticated low-rank approximations of the original kernel matrix, each of which provides a different set of computational trade-offs. All considered methods estimate the relevant subspace spanned by the kernel matrix columns using different strategies to identify a representative set of inducing points. Our comprehensive study covers the full spectrum of approaches, starting from naive random sampling to leverage score estimates and incomplete Cholesky factorizations, up to exact SVD decompositions.

We present an automatic method for annotating images of indoor scenes with the CAD models of the objects by relying on RGB-D scans. Through a visual evaluation by 3D experts, we show that our method retrieves annotations that are at least as accurate as manual annotations, and can thus be used as ground truth without the burden of manually annotating 3D data. We do this using an analysis-by-synthesis approach, which compares renderings of the CAD models with the captured scene. We introduce a 'cloning procedure' that identifies objects that have the same geometry, to annotate these objects with the same CAD models. This allows us to obtain complete annotations for the ScanNet dataset and the recent ARKitScenes dataset.

Objective: Imbalances of the electrolyte concentration levels in the body can lead to catastrophic consequences, but accurate and accessible measurements could improve patient outcomes. While blood tests provide accurate measurements, they are invasive and the laboratory analysis can be slow or inaccessible. In contrast, an electrocardiogram (ECG) is a widely adopted tool which is quick and simple to acquire. However, the problem of estimating continuous electrolyte concentrations directly from ECGs is not well-studied. We therefore investigate if regression methods can be used for accurate ECG-based prediction of electrolyte concentrations. Methods: We explore the use of deep neural networks (DNNs) for this task. We analyze the regression performance across four electrolytes, utilizing a novel dataset containing over 290000 ECGs. For improved understanding, we also study the full spectrum from continuous predictions to binary classification of extreme concentration levels. To enhance clinical usefulness, we finally extend to a probabilistic regression approach and evaluate different uncertainty estimates. Results: We find that the performance varies significantly between different electrolytes, which is clinically justified in the interplay of electrolytes and their manifestation in the ECG. We also compare the regression accuracy with that of traditional machine learning models, demonstrating superior performance of DNNs. Conclusion: Discretization can lead to good classification performance, but does not help solve the original problem of predicting continuous concentration levels. While probabilistic regression demonstrates potential practical usefulness, the uncertainty estimates are not particularly well-calibrated. Significance: Our study is a first step towards accurate and reliable ECG-based prediction of electrolyte concentration levels.

Earthquakes, fire, and floods often cause structural collapses of buildings. The inspection of damaged buildings poses a high risk for emergency forces or is even impossible, though. We present three recent selected missions of the Robotics Task Force of the German Rescue Robotics Center, where both ground and aerial robots were used to explore destroyed buildings. We describe and reflect the missions as well as the lessons learned that have resulted from them. In order to make robots from research laboratories fit for real operations, realistic test environments were set up for outdoor and indoor use and tested in regular exercises by researchers and emergency forces. Based on this experience, the robots and their control software were significantly improved. Furthermore, top teams of researchers and first responders were formed, each with realistic assessments of the operational and practical suitability of robotic systems.

Fine-grained semantic segmentation of a person's face and head, including facial parts and head components, has progressed a great deal in recent years. However, it remains a challenging task, whereby considering ambiguous occlusions and large pose variations are particularly difficult. To overcome these difficulties, we propose a novel framework termed Mask-FPAN. It uses a de-occlusion module that learns to parse occluded faces in a semi-supervised way. In particular, face landmark localization, face occlusionstimations, and detected head poses are taken into account. A 3D morphable face model combined with the UV GAN improves the robustness of 2D face parsing. In addition, we introduce two new datasets named FaceOccMask-HQ and CelebAMaskOcc-HQ for face paring work. The proposed Mask-FPAN framework addresses the face parsing problem in the wild and shows significant performance improvements with MIOU from 0.7353 to 0.9013 compared to the state-of-the-art on challenging face datasets.