四元数体上的核分类器及其在特征级信息融合中的应用研究

The designing of classifier is an extremely important factor to influence the performance of feature-level information fusion. The traditional methods still take the simple processed multi-source datum as a single-source data which can not take full advantage of the category information comed from the multi-source datum. So the research of the classifier which can directly input the multi-source datum is quite meaningful for the feature-level information fusion. The quaternion field is a natural extension of the real number field and the complex field, so the quaternion-based classifier supporting four input can be extended from the classic classifier. The project focuses on the nonlinear classification problems in quaternion field and and investigates the following topics: Firstly, to propose the optimal schemes for the normalization of feature vector and measurement of the similarity in quaternion field based on the fusion mode of the quaternion field. Then, to investigate the fast algorithms on solving the orthogonal eigenvectors of the quaternion matrix and construct the kernel function for the designing of the kernel-based classifier aiming at the characteristic that dissatisfies the commutative property of multiplication. Thirdly, to deduce the kernel scatter matrix and extend the kernel-based classifiers of the real number field to the quaternion field. Fourthly, to apply the kernel-based classifiers in quaternion field to the issue of the multimodal biometrics and perfect the details in application. Meanwhile, the performance of the new designed classifiers would be demonstrated. Currently the research on the quaternion-based classifier is still at the initial stage, particularly for the kernel classifier. Therefore, the results of this project will promote the research of kernel trick, and provide the new tool of data processing and classification for the information fusion.

分类器设计是影响特征级信息融合性能的重要因素，传统方法大多将多源数据简单处理后仍视作单一源数据进行分类，未能充分利用多源数据的类别信息。四元数体是实数域和复数域的自然扩充，经典分类器在四元数体上的推广可得到直接处理最多四路输入的分类器。本项目针对四元数体上非线性可分问题展开研究，首先依据四元数体上多源信息融合模型，提出多源信息归一化和距离度量方案；进而针对四元数不满足乘法交换律的特性，研究四元数体上的四元数矩阵正交特征向量系求解的高效算法，并构造四元数体上的核函数；在此基础上，推导四元数核散度矩阵，提出四元数体上的核分类算法；最后，通过多模态生物特征的融合问题进一步完善四元数体上核分类器的应用细节，验证四元数核分类器的性能。目前，基于四元数的分类器研究尚处于起步阶段，而四元数体上非线性核分类器更有待深入探讨。本项目的研究成果将推进核方法的研究，为信息融合技术提供新型的数据处理和分类手段。

融合特征的分类器设计是特征级信息融合技术提升性能的重要方法。实数域和复数域上的分类器通常不能充分利用多元数据的区分信息，融合信息种类受限。本项目将经典分类器在四元数体上进行推广，直接处理三路或四路多源融合信息，设计四元数体上的分类器。首先，本项目依据四元数体上多源信息融合模型，提出了多源信息归一化和距离度量方案；进而针对四元数不满足乘法交换律的特性，研究了四元数体上的四元数矩阵正交特征向量系求解算法；最后，通过多模态生物特征的融合问题进一步完善四元数体上分类器的应用细节，验证了四元数分类器的性能。因此，本项目的研究成果将推进多源信息分类器设计的研究，为信息融合技术提供新型的数据处理和分类手段。