Data stream has been the underlying challenge in the age of big data because it calls for real-time data processing with the absence of a retraining process and/or an iterative learning approach. In the realm of the fuzzy system community, data stream is handled by algorithmic development of self-adaptive neuro-fuzzy systems (SANFS) characterized by the single-pass learning mode and the open structure property that enables effective handling of fast and rapidly changing natures of data streams. The underlying bottleneck of SANFSs lies in its design principle, which involves a high number of free parameters (rule premise and rule consequent) to be adapted in the training process. This figure can even double in the case of the type-2 fuzzy system. In this paper, a novel SANFS, namely parsimonious learning machine (PALM), is proposed. PALM features utilization of a new type of fuzzy rule based on the concept of hyperplane clustering, which significantly reduces the number of network parameters because it has no rule premise parameters. PALM is proposed in both type-1 and type-2 fuzzy systems where all of which characterize a fully dynamic rule-based system. That is, it is capable of automatically generating, merging, and tuning the hyperplane-based fuzzy rule in the single-pass manner. Moreover, an extension of PALM, namely recurrent PALM, is proposed and adopts the concept of teacher-forcing mechanism in the deep learning literature. The efficacy of PALM has been evaluated through numerical study with six real-world and synthetic data streams from public database and our own real-world project of autonomous vehicles. The proposed model showcases significant improvements in terms of computational complexity and number of required parameters against several renowned SANFSs, while attaining comparable and often better predictive accuracy.

中文翻译：

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PALM：用于数据流回归的超平面的增量构建

数据流一直是大数据时代的潜在挑战，因为它需要实时数据处理，而无需再培训过程和/或迭代学习方法。在模糊系统领域，数据流由自适应神经模糊系统 (SANFS) 的算法开发处理，其特点是单程学习模式和开放结构属性，可以有效处理快速和快速变化的性质的数据流。SANFS 的潜在瓶颈在于其设计原则，它涉及在训练过程中要适应的大量自由参数（规则前提和规则结果）。在类型 2 模糊系统的情况下，这个数字甚至可以翻倍。在本文中，提出了一种新颖的 SANFS，即简约学习机（PALM）。PALM的特点是利用了一种基于超平面聚类概念的新型模糊规则，由于没有规则前提参数，大大减少了网络参数的数量。PALM 是在类型 1 和类型 2 模糊系统中提出的，所有这些系统都表征了一个完全动态的基于规则的系统。也就是说，它能够以单程方式自动生成、合并和调整基于超平面的模糊规则。此外，提出了 PALM 的扩展，即循环 PALM，并采用了深度学习文献中教师强制机制的概念。PALM 的功效已通过数值研究通过来自公共数据库的六个真实世界和合成数据流以及我们自己的自动驾驶汽车真实世界项目进行了评估。