基于几何代数的分布式多观测矢量数据流建模与分类

The traditional classification methods are not spatio-temporal unified, with weak ability of multi-dimensional expansion and parallel processing for distributed data streams, which are not suitable for multiclass classification in resource-constrained sensor networks. To handle these difficult problems, the generalized geometric representation and parallel computing model with multi-dimensional unification, and the multiclass classification method with low complexity for distributed multiple-measurement-vector (MMV) data streams are proposed based on Clifford algebra. Theoretically, the multi-dimensional unified geometric representation and computational model with temporal and spatial correlation for distributed MMV Data Streams is proposed. And the feature extraction and fusion methods are designed in parallel way. A novel multiclass classification model of MMV data streams based on joint sparse representation and Clifford fuzzy support vector machines is proposed, which can eliminate abnormal data effectively, and avoid the concept turbulence with high-speed data streams. The relationship among random projection, sparse geometric feature fusion, and classification accuracy is revealed in order to make the classification and compression of data streams associated effectively. Technically, the incremental ensemble learning method with multi-task hybrid dictionary is designed to improve the classification accuracy and applicability in complex scenes. The adaptive data streams compression method with dynamic feedback based on random projection and sparse geometric feature fusion is also provided according to expert analysis, classification accuracy and network conditions. Our work can provide the novel theories and methods for the MMV data streams mining application in sensor networks, such as ecological environment, photovoltaic power station, and large-scale engineering structural health monitoring, etc.

针对复杂场景下传感器网络多维数据流分类挖掘难点，本课题利用几何代数建立数据流的多维统一表达与并行计算，构造低复杂度的多分类挖掘方法，解决现有方法存在时空表达不统一、高维难以扩展、并行处理困难、无法适用于资源约束的传感器网络等问题。理论上：建立时空相关、多维统一的多观测矢量数据流几何表达与计算模型，实现多维特征并行提取与融合；构造基于联合稀疏表示与Clifford模糊支持向量机的数据流多分类模型，解决数据流概念漂移问题；揭示随机投影、稀疏几何特征融合与分类精度之间的关系，建立数据流压缩与分类的有效关联。技术方法上：提出多任务混合字典的增量式集成学习算法，提高复杂场景下多分类的精度与适用性；设计基于随机投影与稀疏几何特征融合的动态反馈自适应数据流压缩，平衡分类精度与网络能耗。本项目成果将为生态环境、光伏电站、大规模工程结构健康监测等传感器网络多维矢量数据流分类挖掘应用提供新的理论依据和方法。

本课题利用几何代数建立数据流的多维统一表达与并行计算，构造低复杂度的多分类挖掘方法，解决现有方法存在时空表达不统一、高维难以扩展、并行处理困难、无法适用于资源约束的传感器网络等问题。取得的研究成果如下：①提出了几何代数的多通道图像/信号多矢量稀疏表示模型，揭示了多维矢量信号间的稀疏相关性与内部依赖性，构建了其稀疏重建机制。包括几何代数的多光谱图像稀疏表示模型，可交换几何代数的多通道图像联合稀疏表示模型，几何代数的多维信号L1范数稀疏重建算法。②提出了几何代数的多通道图像/信号等多维矢量数据流预处理与快速特征提取方法，保障了多维矢量信号处理的精确性和高效性。包括几何代数的多光谱图像快速特征提取，几何代数的多通道视频时空兴趣点检测算法，几何代数的多维信号自适应滤波预处理算法。③提出了几何代数的多维矢量卷积神经网络模型，有效解决了非欧几里得空间高维数据的分类识别问题。包括几何代数与可交换几何代数的多维矢量数据流卷积神经网络模型。④提出了几何代数的模糊支持向量回归机预测模型，有效处理多矢量信号预测分析时存在的随机性和模糊性，实现快速准确的预测分析。⑤提出了一种新型几何代数ESPRIT算法，以解决三维电磁波矢量信号流的方向角估计实际问题。⑥提出了多种结合注意力机制、多尺度等神经网络框架的视频数据流人体姿态估计与识别方法，给出了基于该理论模型的人体姿态估计识别应用。⑦基于分布式传感器网络数据流，提出了多任务Fisher判别字典学习与混合字典学习的运动车辆识别应用。出版学术专著2本，发表期刊论文36篇，会议论文3篇，其中SCIE检索28篇，培养参与项目研究的硕士研究生20名。本项目的研究成果可应用于战场环境目标识别，交通流量监测与识别，生态环境、光伏电站、大规模工程结构健康监测，智能视觉识别等场景。