结合随机矩阵理论和张量分解的非线性导航大数据异常识别

Anomaly identification of nonlinear navigation big data bycombining random matrix theory and tensor decomposition

为了提高导航大数据的精度,需要识别其中存在的异常数据。为了提升非线性导航大数据异常识别精度和效率,提出了基于张量分解的非线性导航大数据异常识别方法。首先,对非线性导航大数据进行张量分解,采用滑动矩形窗划分数据获得若干个时窗段,然后引入db4小波多尺度分解各窗内数据,获得尺度不同的小波系数,并利用重构小波系数张量代替缺失数据,完成数据缺失值填补,提高数据完整度;其次,将互信息作为度量标准,建立数据的互信息矩阵,对互信息矩阵中的元素展开规范化和中心化处理,通过奇异值分解获得数据特征;再次,引入随机矩阵理论对特征展开优化选择,计算导航大数据特征的重要度,获得高精度的数据特征;最后,建立孤立树,通过孤立树给出数据特征的异常得分,以此完成非线性导航大数据的异常识别。实验结果表明,所提方法的缺失值填补精度保持在0.9以上,特征提取覆盖率达到86.3%,特征冗余度低于6.12%,异常识别精度G-mean值高于60%,识别时间低于8 s,有效提升了非线性导航大数据的特征提取精度、识别精度及识别效率。

In order to improve the accuracy of navigation big data,it is necessary to identify the abnormal data within it.In order to improve the accuracy and efficiency of the anomaly recognition for nonlinear navigation big data,an anomaly recognition method of nonlinear navigation big data is proposed based on a tensor decomposition.Firstly,tensor decomposition is carried out for nonlinear navigation big data,and the sliding rectangular windows are used to partition data into several time window segments,then db4 wavelet is introduced for multi-scale decomposition of data within each window to obtain wavelet coefficients with different scales,and reconstructed wavelet coefficient tensors are used to replace missing data,for filling the missing value and improving data integrity;secondly,taking mutual information as a metric,a mutual information matrix for data is established,the elements in the mutual information matrix are normalized and centralized,and the data features are obtained through singular value decomposition;thirdly,random matrix theory is introduced to optimize feature selection,calculate the importance of navigation big data features,and obtain high-precision data features;finally,an isolated tree is established to provide anomaly scores for data features,and thereby completing anomaly recognition of nonlinear navigation big data.The experimental results show that the missing value filling accuracy of the proposed method remains above 0.9,the feature extraction coverage reaches 86.3%,the feature redundancy is less than 6.12%,the anomaly recognition accuracy G-mean value is higher than 60%,and the recognition time is less than 8 s,which effectively improves the feature extraction accuracy,recognition accuracy,and recognition efficiency of nonlinear navigation big data.