连续框架下复杂数据场可视分析方法及应用研究

复杂数据场由于数据结构复杂、规模大、高维等特点，本质特征结构往往嵌入在低维空间里，恢复或导出其隐藏的特征结构才能有效理解和利用这些数据。运用完备的数学理论与工具挖掘复杂数据场整体的、可靠的本质特征尤为关键，目前该领域的研究面临着巨大的机会和挑战。.本项目研究内容包括两大部分：.1. 以复杂数据场为研究对象，为其建立高阶连续模型，在满足完备数学理论的基础上，运用微分几何、代数拓扑、张量分析等理论与工具，挖掘数据场整体的几何、拓扑、结构域等本质特征，并实现高质量可视化，完善复杂数据场连续框架下可视分析方法体系；..2. 以DTI影像（多变量数据场）的数据集为研究对象，针对人脑轻度认知障碍（MCI）程度分类问题，首先运用连续框架下可视分析方法提取数据场本质特征，然后提出本质特征融合的深度学习方法，归类并选取关键特征进行分类学习，结合人脑智能和机器智能两者的优势，建立MCI分类的精准医疗诊断模型。

Complicated data fields usually have complex data structures, big sizes and high dimensions. Their essential feature structures hide in some low-dimension spaces. Only when these feature structures are discovered, we can understand and utilize the data well. Using perfect mathematical theory and tools to extract the overall, accurate and essential features becomes the most important thing. In current, the research work in this area is faced with great opportunities and challenges. . Main research contents will include two parts: . 1. For a complex data field, we establish a parametric spline model with high-order continuity, which satisfies many mathematical theories. So those existing theories and tools in differential geometry, algebraic topology and tensor analysis etc. can be used to dig essential geometric, topological and structural domain features of the overall data field. Then we achieve high-quality visualization based on extracting essential features. The system of visual analysis of complex data fields under our continuous framework will become complete. . 2. For the set of DTI data (multi-fields), we apply the methods of visual analysis under our continuous framework to extract essential features of multi-fields at first. In order to diagnose MCI, we propose a deep learning method based on essential features in which key features classified and selected in advance are inputs. So the merits of both Brain Intelligence and Machine Intelligence are combined to build an exact diagnose model for classifying MCI.