特征自学习的鲁棒非凸非光滑稀疏表示分类算法研究

Pattern recognition (PR) under multi-noises environment is a challenging problem in the big-data era. Sparse representation classification (SRC) is one of the state-of-the-art methods for PR with noises. A distinguishing feature of SRC lies in its flexibility and discriminability since it could fully utilize the priori structures of datasets to model the error and representation coefficients. However, SRC does not fully take the prior knowledge of the error caused by the noises into consideration, thus the instability of the recognition performance may occur in practical situation. We propose a general framework of robust sparse classification with adaptive feature weights learning and nonconvex nonsmooth prior constraints. First, we give consideration to both spatial structures and inherent structures embedded in input features, which makes the proposed algorithms be with the merits of both locality and noise-suppression. Second, we introduce the feature weights into objective cost function to adaptively select the suitable error metrics. Third, we widely explore different types of nonconvex nonsmooth functions and carefully select them as the prior constraints of representation coefficients for better sparsity and robustness. Finally, we derive an efficient algorithm, termed as iterative re-constrained gradient minimization, to simultaneously optimize the feature weights and representation coefficients, which processes a fast convergence rate and wide adaptability to various optimization problems. According to this study, we manage to implement robust sparse classification against various noises, which can be vastly applied in video tracking, face recognition with occlusion, hyperspectral image classification and other scenarios.

噪声污染下的数据分类问题是大数据时代一个极具挑战性的课题。基于稀疏表示的分类方法是该领域的前沿方法之一，其主要特点是利用数据的先验结构对误差和系数建模，具有极大的灵活性和天然的鉴别性；然而，在实际非受控环境下，其性能往往因噪声类型的不同而有很大差别。本项目提出特征自学习的鲁棒非凸非光滑稀疏表示分类框架：兼顾样本间空间分布结构和特征本身的差异性结构，使算法兼具保局性和抗噪性；将特征权值引入目标代价函数，针对混合噪声自适应地选取误差度量算子；深入探讨各种非凸非光滑函数，将其作为表示系数的先验约束，提升算法的稀疏性和鲁棒性；提出迭代重约束梯度法进行模型优化，混合求解特征权值和表示系数，具有快速收敛性且能广泛地应用于各类凸优化或非凸优化问题。通过该研究实现面向混合噪声干扰的鲁棒稀疏分类算法，能广泛地应用于视频目标跟踪、有遮挡的人脸识别、超光谱图像分类等热点领域。

混合噪声环境下的数据分类聚类是机器视觉领域最具挑战性的问题之一。以先验属性为约束的重构表示型算法是该方向的前沿研究分支之一，具有形式灵活、天然抗噪等优势。然而在实际应用中，其识别性能受具体属性形式、数据特征、噪声分布等变化呈现出很大差异，限制了分类器的可扩展性。本项目围绕增强的属性逼近函数开展研究，采用多属性联合约束、空时信息融合、光滑函数优选等关键技术，构造新的重构模型，以适应多元数据类型并抑制复杂噪声干扰。具体研究内容为：1) 探索泛化能力更强的属性正则项及其融合约束方案，研究非凸惩罚下的函数凸化条件和核心优化子问题的闭式解；2) 提出空间和时序结构联合保持策略，并将抗噪机制从数据保真项扩展至属性约束项，构建强鲁棒性的目标函数；3) 设计模型参数的自适应更新规则，挖掘其与函数单调性之间的关系，并在Moreau近似法则下制定一致性求解方案。该理论框架可实现复杂环境下的鲁棒数据重构算法，能广泛应用于可视化修复、多目标跟踪等热点领域。