多目标低秩非参核学习模型与优化方法研究

Since nonparametric kernel learning (NPKL) methods are limited to single objective optimization, they cannot guarantee the generalization performance as well as the scalability of learning algorithms, that is, they cannot provide Pareto optimal solutions toward multiple conflicting objectives. Nonparametric kernel learning models are generally sensitive to high-dimensionality data. In addition, many single objective nonparametric kernel learning models only focus on the sparsity of kernel matrices by means of low rank constraints, but ignore how to find the optimal rank. To solve the above problems, this project intends to incorporate nonlinear dimensionality reduction models into single objective NPKL models, and propose a novel multi-objective low rank NPKL model and its algorithm for high dimensional data. The main research contents include the following aspects. Firstly, a single objective low rank NPKL model will be designed by integrating semi-supervised nonlinear dimensionality reduction models, and the unified objective function will be derived from them. Secondly, a constrained multi-objective low rank NPKL model will be presented and extended to unsupervised and supervised scenarios. Thirdly, a series of effective algorithms based on particle swarm optimization will be proposed to solve the constrained multi-objective low rank NPKL model. Finally, the proposed constrained multi-objective low rank NPKL model and it's algorithms will be applied to visual object tracking to improve the performance of object tracking algorithms. The research of this project will not only provide some novel NPKL models and multi-objective particle swarm optimization algorithms, but also apply them in visual object tracking.

传统的非参核学习方法仅局限于单目标优化，不能同时兼顾算法的泛化性能和可扩展性，对存在多个彼此冲突目标无法提供Pareto最优解，同时，模型大多对高维数据敏感。此外，现有单目标非参核学习模型的稀疏性研究主要关注核矩阵的低秩约束，而忽视了如何确定秩的最优解。针对上述问题，本项目拟结合非参核维数约简模型，提出具有高维数据处理能力的多目标低秩非参核学习模型和优化算法，以克服现有方法的不足。主要研究内容如下：1）研究半监督非线性维数约简与单目标低秩非参核学习融合方法，推导出统一的优化目标函数；2）构建约束多目标半监督低秩非参核学习模型，并进行有监督和无监督拓展；3）提出面向约束多目标低秩非参核的微粒群优化算法；4）将提出的模型和算法应用于视觉目标跟踪，进一步提升目标跟踪算法的性能。通过本项目的研究，我们将为非参核学习理论提供一些新的优化模型、新的学习算法以及在视觉目标跟踪上的应用。

非参核学习直接利用核矩阵隐式定义的非线性映射，将原始数据空间中的向量映射到高维特征空间，然后在高维特征空间中根据不同的准则建立相应的模型。近年来非参核学习已成为核学习问题的主要解决思路。为了增强现有的非参核学习方法处理高维数据的能力，解决算法的泛化性能和可扩展性两者之间的冲突。本项目围绕高维数据维数高、非线性、小样本等挑战，利用机器学习、模式识别和深度学习等多学科交叉的理论和方法，以维数约简、稀疏表示、深度学习等方法为基础，研究高维数据多目标非参核学习方法的新理论和新方法，使其能够有效的支持遥感图像分类、文本分类、语义关系和事件触发词抽取等任务。在非参核学习建模和模型优化算法的基础上，重点针对非参核学习方法与深度学习算法融合模型进行深入研究，包括循环神经网络与非参核学习方法融合模型和卷积神经网络与非参核学习方法的融合模型等。同时使用现实世界的高维标准数据集对非参核学习框架和算法进行实验验证。