基于个体分析的投影式非线性非负张量分解在高维非结构化数据模式分析中的研究

Non-negative tensor factorization (NTF) imitates the processes of human cognition and has become the hot topic in the field of high-dimensional pattern analysis. However,Existing NTF algorithms often have a poor generalization ability, are unable to excavate the intrinsic structure of high-dimensional data and revise learning model dynamically. This research is planning to study subspace projection, non-linear analysis and online learning techniques in non-negative tensor space, implement the projective non-linear non-negative tensor factorization with online learning and apply it into the pattern analysis of high unstructured data. Firstly, aiming to settle the out-of-sample problem and improve the generalization ability, each datum will be respected as an individual, and projective non-negative tensor factorization based on individual analysis is studied to construct the non-negative tensor basis space. Then structured tensor kernel function will be studied, which projects data to higher non-linear tensor space to excavate the non-linear structure embedded in high-dimensional space. Furthermore, the online learning technique of projective non-linear non-negative tensor factorization will be studied to revise the learning model quickly. Finally, the pattern analysis of high-dimensional unstructured data are applied to evaluate its performance. This research is helpful to improve the theoretical model of NTF and has vital scientific value to promote the development of high-dimensional pattern analysis.

非负张量分解模拟人脑感知世界的过程，已经成为高维非结构化数据模式分析的研究热点之一。然而，现有非负张量分解存在泛化能力低下，不能深入挖掘高维数据本征结构，无法动态修正学习模型等问题。本课题拟研究非负张量空间中的子空间投影，非线性分析和在线学习技术，设计能实现在线学习的投影式非线性非负张量分解算法，并将其应用于高维非结构化数据中。首先，本课题拟将高维数据视为个体，构建非负张量基空间，实现基于个体分析的投影式非负张量分解，解决样本外问题，增强算法的泛化能力；其次，拟研究结构化张量核函数，将样本投影到高维非线性张量空间，揭示嵌入在高维空间中非线性结构；再次，拟研究投影式非线性非负张量分解的在线学习技术，实现学习模型的快速修正；最后，本课题将提出的算法应用到高维非结构化数据模式分析中，对其性能进行评估和测试。本课题的研究有助于完善非负张量分解的理论模型，对推动高维模式分析的发展具有重要科学价值。

在大数据时代，基于张量表达的高维非结构化数据模式分析已经成为研究热点。针对现有张量分解算法的局限，本项目实现了张量分解的稀疏表达，基于图谱理论，提出了基于稀疏张量表达的判别分析算法，保留了张量数据本征的流形结构，揭示了数据之间内在的非线性关系；以当前流行的深度学习平台为基础，以张量表达为目标，设计了各类卷积神经网络框架，实现了从高维数据到低维特征的显式映射，增强了算法的泛化能力。本项目的开展对推动高维模式分析的发展具有重要科学价值。