我们讨论集群分析的拓扑方面，并表明在聚类之前推断数据集的拓扑结构可以大大增强群集检测：理论论证和经验证据表明，聚类嵌入向量，代表数据歧管的结构，而不是观察到的特征矢量他们自己是非常有益的。为了证明，我们将流形学习方法与基于密度的聚类方法DBSCAN结合了歧管学习方法UMAP。合成和真实数据结果表明，这既简化和改善了多种低维问题，包括密度变化和/或纠缠形状的群集。我们的方法简化了聚类，因为拓扑预处理始终降低DBSCAN的参数灵敏度。然后，用dbscan聚类所得的嵌入可以超过诸如spectacl和clustergan之类的复杂方法。最后，我们的调查表明，聚类中的关键问题似乎不是数据的标称维度或其中包含多少不相关的功能，而是\ textIt {可分离}群集在环境观察空间中的\ textit {可分离}，它们嵌入了它们中。 ，通常是数据特征定义的（高维）欧几里得空间。我们的方法之所以成功，是因为我们将数据投影到更合适的空间后，从某种意义上说，我们执行了群集分析。

本文在线学习和优化框架内提出并开发了一种用于电力市场中风能交易的新算法。特别是，我们将梯度下降算法的组成部分自适应变体与功能驱动的新闻册模型的最新进展相结合。这导致了一种在线产品的方法，能够利用数据丰富的环境，同时适应能源发电和发电市场的非平稳特征，并且具有最小的计算负担。根据几个数值实验，对我们的方法的性能进行了分析，既显示了对非平稳性不确定参数的更好适应性和显着的经济增长。

提取手写文本是数字化信息的最重要组成部分之一，并使其可用于大规模设置。手写光学角色读取器（OCR）是计算机视觉和自然语言处理计算的研究问题，对于英语，已经完成了许多工作，但是不幸的是，对于乌尔都语（例如乌尔都语）的低资源语言，几乎没有完成工作。乌尔都语语言脚本非常困难，因为它具有基于其相对位置的角色形状的草书性质和变化，因此，需要提出一个模型，该模型可以理解复杂的特征并将其推广到各种手写样式。在这项工作中，我们提出了一个基于变压器的乌尔都语手写文本提取模型。由于变压器在自然语言理解任务中非常成功，因此我们进一步探索它们以了解复杂的乌尔都语手写。

Adaptive partial linear beamforming meets the need of 5G and future 6G applications for high flexibility and adaptability. Choosing an appropriate tradeoff between conflicting goals opens the recently proposed multiuser (MU) detection method. Due to their high spatial resolution, nonlinear beamforming filters can significantly outperform linear approaches in stationary scenarios with massive connectivity. However, a dramatic decrease in performance can be expected in high mobility scenarios because they are very susceptible to changes in the wireless channel. The robustness of linear filters is required, considering these changes. One way to respond appropriately is to use online machine learning algorithms. The theory of algorithms based on the adaptive projected subgradient method (APSM) is rich, and they promise accurate tracking capabilities in dynamic wireless environments. However, one of the main challenges comes from the real-time implementation of these algorithms, which involve projections on time-varying closed convex sets. While the projection operations are relatively simple, their vast number poses a challenge in ultralow latency (ULL) applications where latency constraints must be satisfied in every radio frame. Taking non-orthogonal multiple access (NOMA) systems as an example, this paper explores the acceleration of APSM-based algorithms through massive parallelization. The result is a GPUaccelerated real-time implementation of an orthogonal frequency-division multiplexing (OFDM)based transceiver that enables detection latency of less than one millisecond and therefore complies with the requirements of 5G and beyond. To meet the stringent physical layer latency requirements, careful co-design of hardware and software is essential, especially in virtualized wireless systems with hardware accelerators.