模式识别中多元数据的对偶射影空间表示和可视化问题

项目名称： 模式识别中多元数据的对偶射影空间表示和可视化问题

项目编号： No.60873121

项目类型： 面上项目

立项/批准年度： 2009

项目学科： 金属学与金属工艺

项目作者： 徐永红

作者单位： 燕山大学

项目金额： 26万元

中文摘要： 面向模式识别任务，研究了多元数据的对偶射影子空间坐标表示和可视化问题。 首先研究了几种图表示方法的原理和特性，给出了子空间坐标图表示的一般模型。该模型将散点图、平行坐标和三角多项式等统一到同一个表示框架，有助于研究这些方法的区别与联系。以平行坐标为研究重点，定义了二维对偶坐标映射，研究其表示特性并证明了相关定理，开发了多元平行对偶图可视化方法。该方法中同一样本的对偶坐标和平行坐标具有确定几何关系，可根据需要在两种形式间切换。此外还研究了二维对偶坐标的三维推广、将机器算法和可视化方法结合的图形特征优化等问题。 本项目将高维子空间嵌入表示为几何代数空间的多向量，利用几何代数提取特征并进行识别。重点研究了四元代数表示和几何积特征提取，应用于人脸识别、生理时间序列分类等的结果表明，该方法在分类精度和可理解性方面都具有明显优势。 本项目利用对偶射影子空间表示模型将多元数据几何化，利用平行坐标将多元数据可视化，利用几何代数将几何实体代数化并进行几何特征提取的思路是模式识别的一种新思维，进一步的研究有望完善该方法，做出更富特色性的成果。

中文关键词： 信息可视化；模式识别；几何代数；对偶射影空间；平行坐标

英文摘要： For pattern recognition tasks, coordinates representation and visualization of multivariate dual projective subspaces were studied. Principles and natures of several graphical representation methods were investigated and a general model of subspace coordinates representation was gived. The scatter plot,parallel coordinates and Andrews'plot were united into the same representation framework, thus helped to research the differences and connections of these methods. Focus on parallel coordinates visualizations,the 2-D dual coordinates map was defined and several related theorems was proved. On this basis, a new visuallization method named parallel dual plot was developed. The dual coordinates and parallel coordinates of the same sample have a determined geometric relationship, which helps the transform of the two forms. The 3-D generalization of dula coordinates and optimization of graphical features by combining machine algorithms and visualization methods were also studied. This project embedded the high dimension subspaces into the geometric algebra space as multivectors, use geometric algebra as a tool to extract features and realize final recognitions. The quaternion representation and features by geometric product were focusly studied. The results of its application to face recognition and physiological time series classification indicatied the advantiges in both accuracy and easy understanding. The idea of this project to geometrinize multivariate data by the dual projective subspace representation model and visualize multivariate data by parallel coordinates, finally utilize geometric algebra to realize the computation and feature extraction of these geometric entities is new, further hard work will improve this method and obtain better results.

英文关键词： information visualization;pattern recognition;geometric algebra;dual projective space;parallel coordinates