基于非凸目标函数的稀疏学习及其在医疗诊断中的应用

Sparse learning is a kind of machine learning method, which requires additional property of sparsity for the solution compared with general machine learning methods. In the theoretical aspect, sparse learning follows the principle of parsimony; in the application aspect, it has been widely applied in many fields such as pattern recognition and biomedical data processing. However, since 0-norm is involved, the difficulty for solving the sparse learning problem is NP-hard. The common solution towards this barrier is to solve its equivalent (e.g. 1-norm) solution or approximate solution under certain conditions such as Restricted Isometry Property (RIP). In this proposal, we will use sparse representation, compressed sensing and optimization techniques to develop a novel method for non-convex objective function based sparse learning. Our novelties lie in that the minimization problem with L0-norm is converted into an equivalent matrix rank minimization problem or a truncated L1-norm minimization problem, so that the problem can be solved directly via matrix manuipulation or the difference of convex functions (DC) programming,.respectively. It is expected that the algorithms proposed in this proposal will perform better than most major sparse learning algorithms in terms of the properties, accuracy and speed. Preliminary results shows that the algorithm can be sucessfully applied to the analysis of significant indices and progrssion prediction of Alzheimer Disease. The ultimate result of this project will provide a new way for sparse learning.

稀疏学习是一类机器学习方法，它相对于一般机器学习算法，还额外要求问题的解有一定的稀疏性。稀疏学习方法在理论上符合科学基本原则中的简约(parsimony)原则，在实践中已在模式识别、生物数据处理等方面得到广泛应用。但其求解因涉及到0-范数，难度为NP hard。目前的求解方法是在一定条件下(如RIP条件)求其等价(如1-范数)或近似解。本项目将运用稀疏表示、压缩感知和优化等手段，发展出一套新的针对非凸目标函数的稀疏学习的求解算法。其创新在于：将含有0-范数的极值问题转换成等价的矩阵秩的极值问题，然后运用矩阵算法求解；或转换为截断的1-范数的极值问题，采用DC(凸函数之差)规划求解。预计，本项目的结果在解的性质、精度和速度等方面总体而言将优于当前各主要的稀疏学习算法。初步实验表明，该套算法能成功应用于老年痴呆症的关键病情指标分析和病情发展预测。本项目的最终成果将为稀疏学习提供新的思路和途径。

本项目针对非凸目标函数的稀疏学习问题，运用了稀疏表示、压缩感知、优化和深度学习等手段，发展了一整套新的求解算法，并成功用于医疗诊断等领域。我们认真开展了相关的科学研究工作，严格执行了项目的研究计划，完成了研究任务，实现了预期研究目标，取得了原创性成果。具体地，我们 1) 运用低秩正则的方法，将含有0-范数的极值问题转换成等价的矩阵秩的极值问题，然后运用矩阵算法快速求解，成功地将图像的超分辨率重构问题转化为稀疏学习问题，在解的理论和实际效果中都有所突破；2) 结合迁移学习和模糊逻辑系统，构造出非凸目标函数，提出了相应的稀疏学习算法，成功解决了脑电图中癫痫信号的识别问题；3) 运用深度学习算法，集图像处理和深度学习为一体，使用图像处理的相关技术对图像进行预处理和特征提取，然后将提取的特征作为深度学习模型的输入，成功研制了乳腺癌医疗图像诊断系统；4) 运用梯度提升决策树和Logistic回归方法, 利用气象大数据, 实现了航班变更的成功预测. 我们还在骨科局部膝关节置换的手术导航方面，运用了特征提取方法，成功进行了图像特征提取，为手术导航的配准提供了有力技术支持。本项目的科学意义在于给出了非凸目标函数的稀疏学习的理论模型，将待求解的稀疏模型转化为可求解的形式，给出了快速求解方法，并拓展了稀疏学习在医学诊断等领域的应用。本项目的最终成果为稀疏学习提供了新的思路和途径。