共形变换核的多核拓展及其优化学习方法

Multiple kernel learning (MKL) has become more and more important for the theoretical development and real-world applications of the kernel method. Since the non-linear MKL model usually outperforms the linear MKL model in many applications, in this project, we are going to study a speific non-linear MKL model, referred as the conformal transformation of multiple kernels (CTMK), and robust ways to optimize it. CTMK is a data-dependent combination of multiple kernels, being of many promising properties. Based on our previous research concerning the existing methods of multiple kernel learning, the project will focus on how to improve the existing CTMK learning methods, and find out a more robust way to learn CTMK. The research plan of the project is partitioned into three topics: 1)the model extension of the conformal transformation of kernel; 2)how to optimize CTMK robustly and efficiently; 3)applying the CTMK learning to various real-world applications. The goal of the project is to develop a more efficient and robust way to optimize QCTK, and then, find way to apply the CTMK learning skill to promote the performaces of various learning machines in such areas as bioinformatics and visual pattern recognition.

鉴于多核学习在核方法理论和应用研究方面的重要性，特别是非线性组合的数据依赖多核所显示的许多良好特性，课题拟研究针对共形变换多核的稳健的优化学习方法，发展和完善多核学习的理论和应用基础。在深入研究现有多核学习理论和方法的基础上，针对现有共形变换核学习方法中存在的问题，重点研究共形变换核模型的多核拓展、共形变换多核的稳健优化学习方法、共形变换多核学习的应用等几方面的内容。研究目标是在理论上发展和完善共形变换多核的优化学习方法，并在生物信息识别和视觉模式识别两方面的应用中取得优于其它方法的成果

课题组研究了1）基于Fisher准则的共形变换单核多核的优化算法及其在图像识别上的应用，改进和完善了Fisher准则下多类问题的共形变换单核优化学习算法，并将这种改进算法拓展到共形变换多核上；2）SVM框架下共形变换多核的优化学习算法，在SVM优化框架下,采用类似simpleMKL算法中分步寻优的策略优化共形变换多核的算法；3）面向共形变换核的稀疏学习方法和目标显著性计算及其应用，采用稀疏表示和字典学习方法，在获取稀疏表示和字典的同时优化共形变换核；4）核方法在图像目标检测识别方面的应用。总体来看，课题组的研究拓展了共形变换核模型，发展了在SVM优化框架和Fisher准则下优化共形变换多核的有效算法，并在图像识别应用中验证了共形变换核方法的有效性。