强稀疏非负矩阵分解下的特征学习

Nonnegative Matrix Decomposition (NMF) expresses reconstructed images as a series of nonnegative subtractive overlays by nonnegative constraints on base and coefficients. This reconstruction process is close to the process of human visual perception. However, NMF is not a strictly subspace learning method, the direct processing of new test data lacks the necessary projection basis. To this end, we hope that based on the basis of the original NMF, we can explore the non-negative matrix decomposition learning method of sparse constrained graphs which can be directly used for feature extraction and have sparsely structured, localized and discriminating performance. In this project, we propose to introduce the rule of the flow pattern and the maximum boundary criterion, introduce the R1 norm metric, embed the regularization graph and the sparse form of the reinforcement matrix, so that the non-negative decomposition of the matrix is more in line with the sparse mechanism of human perception image. The successful development of this project will enrich and develop the pattern extraction technology and theoretical system of pattern recognition, and at the same time can greatly improve the computer's ability of identification and understanding, and provide researchers with relevant scientific research work such as feature analysis, extraction and acquisition Reliable guidance and reference.

非负矩阵分解（NMF）通过对基和系数的非负约束，将重构图像表示为一系列非负基图像的非减叠加组合。这种重建过程接近人类视觉由局部感知整体的过程，具有明确的物理意义。然而，NMF不是严格的子空间学习方法，直接处理新的测试数据缺乏必要的投影依据。为此，我们希望在传统的NMF基础上，找到一个强稀疏NMF方法，直接用于特征提取，并具有稀疏性、局部性和鉴别性等优点。该项目拟从保持流形结构和最大化边界准则出发，嵌入正则化图，引入R1范数强化矩阵因子的稀疏结构，并把结果推广到高维希尔伯特空间，希望分解结果符合人类感知图像的稀疏机制，以便我们学习具有一致的特征选择功能和一致解释功能的非负矩阵鉴别子空间。该项目的顺利开展，有助于丰富和发展模式提取技术和理论体系，同时可以大幅度提高计算机的识别和理解能力，为从事特征分析、提取和采集等相关科研工作的研究人员提供靠的指导与参考意见。

对传统的非负矩阵分解（NMF)强加稀疏，进而得到稀疏NMF，这使得提取的特征更具可解析性。在矩阵现有的研究基础上，我们对其作了三阶甚至更高阶稀疏张量拓展。本项目主要围绕三部分内容开展：一是基于最大边界的非负矩阵分解下的稀疏鉴别投影；二是高阶张量稀疏分解以及在盲源分离中的应用；三是基于嵌入式的最大边界的非负矩阵分解下的稀疏鉴别投影。结合稀疏非负矩阵分解、高阶张量分解,稀疏投影相关知识，本项目提出了五类结合张量分解和稀疏NMF的欠定线性盲分离算法；两类稀疏边界流形嵌入算法；以及具有自适应局部性保留的鲁棒判别分析方法等，实现人脸稀疏特征提取，以及盲源分离，并在实验中成功高效地从观察到的混合音中分离出心肺音，非常有助于医生诊断心肺疾病，深入了解患者当前的健康状况，这在临床医学上具有重要现实意义。