百家争鸣还是一枝独秀：树状度量空间索引数据划分的归一化研究

类型繁多是大数据面临的一个多样性挑战。度量空间对数据内部结构不作要求，只需数据间定义满足三角不等性等的距离函数，可以涵盖多种类型。申请人前期提出了大数据泛构模式，把数据抽象到度量空间，利用距离函数性质进行通用的数据管理和分析，是应对多样性挑战的途径之一。按照数据划分和剪枝的方式，树状度量空间索引可以分为包络球、超平面、及球形划分等三大流派。长期以来，三大流派各自发展，性能比较多以实验为主，不同来源的实验结果时有矛盾，缺乏理论分析。应该继续三大流派各自发展还是集中发展某个最优流派，这是一个决定领域发展方向的根本问题，一直亟待攻克。本项目拟基于申请人前期提出的支撑点空间模型，首先把包络球和超平面划分统一起来，然后把超平面和球形划分统一起来，使三大流派可以用不同参数的相同模型描述，最后研究划分性能评测机制，并推演最优的流派。本项目研究有望为度量空间索引数据划分发展方向的确定提供根本的理论依据。

The variety of data types is a challenge for big data. Metric space requires nothing about the inner structure of data, but only a distance function on data pairs satisfying the triangle inequality and so on, and thus covers a lot of data types. The applicant previously proposed the big data genhierarchy paradigm that abstracts data into metric space and performs universal management and analysis exploiting the distance function, which is a solution to the variety challenge for big data. Based on the way data is partitioned, tree-structure metric-space indexing methods can be categorized into three categories, namely covering sphere, general hyper-plane, and ball partitioning. From the very beginning, these three categories have been developing independently, and usually compared by experimental results without much theoretical analysis. However, experimental results from different sources usually contradict. To continue the independent development of the three categories or to focus on one best category is a fundamental but almost never touched problem, dominating the research direction of the area. In this project, based on the pivot space model previously proposed by the applicant, we will first unify covering sphere and general hyper-plane partitioning, then unifying GHT and ball partitioning so that categories can be described by a same model with different parameters, and finally study performance evaluation mechanism of partitioning categories and deduce the best partitioning. This project could provide research direction for partitioning of metric-space indexing.