Tolerance-based Granular Computing Methods in Learning: Foundations and Applications

所提出的研究的主要意义是从一个基于容忍度的框架，不同形式的知识表示和学习。本研究弥合了知识结构的近似形式和清晰形式之间的差距。容差方法为几乎所有的解在某种近似下都是有效的提供了形式化的基础，这是真实的世界问题和应用所需要的。利用各种形式的基于集合和基于图的方法以及特征向量的接近距离泛函，使得在三个不同的领域中支持近似学习成为可能：网络信息标签、社交网络以及基于感知的图像和音频信息。所提出的方法还探讨了这三个领域中大数据的计算挑战。这项研究的一个直接结果是它在许多应用领域的实用性。这项工作的新奇之处在于：i）在不同但相关的领域中统一公差方法和接近度测量的主题，ii）基于区域和区域集合及其与经典空间接近度的相互作用建立描述性交叉的基本结果，iii）导致诸如图像分析的广泛应用的视觉描述性接近度的独特方法，iv）基于Voronoi镶嵌的聚类，在有效的邻域方法中有用，v）在视觉监视中有用的变化检测，以及vi）技术转让的潜力，特别是自动地图制作。这项工作也将有助于揭示，通过棱镜的公差的代表性结构有很大的流动性，并结合几何视图有潜力整合概念结构在不同层次的粒度。

The primary significance of the proposed research accrues from a tolerance-based framework for different forms of knowledge representation and learning. This research bridges the gap between approximate and crisp forms of knowledge structures. Tolerance methods provide a formal foundation for almost solutions that are valid within some approximation, which is required for real world problems and applications. The utilization of various forms of set-based and graph-based approaches and nearness distance functionals of feature vectors make it possible to support approximate learning in three distinct areas: web information labelling, social networks and perception-based image and audio information. The proposed approach also explores computational challenges with big data in the three areas. A direct result of this research is its utility in a number of application areas. The novelty of the work is in: i) unifying theme of tolerance methods and nearness measures in distinct yet related areas, ii) establishing fundamental results of descriptive intersection based on regions and collections of regions and their interplay with classical spatial proximity, iii) unique approach to visual descriptive proximity leading to a broad spectrum of applications such as image analysis, iv) clustering based on Voronoi tessellations useful in efficient neighbourhood methods, v) change detection useful in visual surveillance, and vi) potential for technology transfer specifically with automated map production. This work will also help reveal that the representational structures viewed through the prism of tolerance have a great deal of fluidity and combined with a geometric view have the potential of integrating conceptual structures at different levels of granularity.