基于广义核的多核学习及拓展研究

Kernel method is a powerful statistical learning technique in machine learning, which has been widely applied in many research fields, such as classification, regression and clustering. Kernel selection is the key content in kernel method, since it is an important part to improve the generalization performance of kernel method. Multiple kernel learning utilizes a combination of multiple basic kernels instead of a single one and thus converts the problem of kernel selection into the choice of combination coefficients, which improves kernel method effectively. However, most of multiple kernel learning methods are confined to the convex combination of positive definite kernels, which leads to the limitations in their performance and applications. Generalized kernel is an emerging kernel class that breaks the constraints on the positive definiteness of the kernels and shows much better empirical classification results. However, existing generalized kernel methods are based on a single kernel which also limits their performance improvements. Consequently, the combination of generalized kernel method with multiple kernel learning is a new thought to improve the generalization performance of kernel method. However, the non-convexity of the generalized kernels and the multi-parametric property of multiple kernel learning present some challenges in this non-trivial combination. The project aims to develop a general framework for multiple kernel classification learning based on generalized kernel and design a series of effective algorithms on the basis of sufficient consideration about the characteristics in the two kinds of kernel methods, in order to overcome their existing deficiencies. The corresponding research emphasizes on model construction, non-convex optimization, generalization performance analysis and experimental comparison, and further expands the framework to some other learning and application fields.

核方法是机器学习中一类强有力的统计学习技术，被广泛应用于分类、回归、聚类等诸多领域。核选择是核方法的关键内容，因其是提高核方法泛化性能的重要一环。多核学习通过利用多个基本核的组合代替单核，将核选择问题转化为对组合系数的选择，有效地改进了核方法。但是，因其大都局限于正定核的凸组合，导致了性能和应用受限。广义核是一类新兴的核，打破了对核的正定性约束，取得了很好的经验分类效果。然而，现有广义核方法均基于单核，亦限制了其性能提高。因此，将广义核方法和多核学习相结合，是提高核方法泛化性能的一种新思路。但是，广义核的非凸性和多核学习的多参数性，对这种非平凡的结合提出了挑战。本项目旨在充分考虑两者特性的基础上，发展出一个基于广义核的一般性多核分类学习框架并设计出一系列有效算法，以克服现有不足。重点针对模型构建、非凸优化求解、泛化性能分析、实验对比等方面展开研究，并将在多个学习和应用领域进行深层次拓展。

核方法是机器学习中一类强有力的统计学习技术，被广泛应用于分类、聚类、特征选择等诸多领域。本项目着眼于核方法中的两个研究热点——广义核和多核学习，围绕基于广义核的核方法开展了一系列深入与广泛的研究。在深度上，从基于广义核的单核分类器模型出发，逐步发展出更具一般性的、充分融合多种核学习范式优点的基于广义核的多核学习框架。该框架不仅统一刻画了现有众多有力的广义核和多核分类器，而且从中设计出的多种核分类器具有良好的泛化性能。受此框架引导，项目组进一步将其推广至聚类和特征选择等领域，并在多个应用领域中开展了一系列广泛的研究，其中：1）在分类学习方面的成果有：基于广义核的多核学习判别性正则化框架、基于广义核的多核学习主问题框架、利用凸差规划求解广义核支持向量机、基于混合范数的广义核多核学习等；2）在聚类学习方面的成果有：面向两类和多类问题的广义核大间隔聚类算法等；3）在特征选择方面的成果有：基于广义核的多核特征选择算法等；4）在应用领域的成果有：基于广义核的多视图分类、多表情识别、多年龄估计、多基因识别算法等，为将基于广义核的核学习更好地运用于机器学习领域提供了有益的指导和实践。