Anomaly Detection Of Multivariate Time Series Based On Riemannian Manifolds

Multivariate time series recorded multiple attribute values changed with time in somefields. Its high-dimensional and high-complexity caused some difficulties to data mining.However, the data points which does not conform to the rule that caused by theenvironment or human factors had increased the challenge to the data analysis largely.In order to solve the inconvenience that the abnormal bring to the data analysis, thispaper puts forward a kind of multivariate time series of anomaly detection algorithm basedon Riemannian manifold. This method takes the sliding window as a tool of dividingsubsequences, and calculates each covariance matrix of subsequence. Making thecovariance matrix as the descriptor, Riemannian distance as the similarity measure,statistical process control charts as the evaluation and the distribution of the covariancematrix and its visualization to intuitively show the existence of abnormal. Because thecovariance matrix intact all information of the time series and the symmetry positivesemi-definite of the covariance matrix satisfy the Riemannian measure. So, it is concludedthat the result in this paper is more significant than other methods.In the end, with MA mock data flow, MIT-BIH ECG and the a Space Shuttle MarottaValve time series which in National Aeronautics and Space Administration as experimentobject, the anomaly detection method is verified and the experimental results show thatthis method is reasonable and effective. The accuracy of the simulated data reached100%,the arrhythmia data’s was80%, and the NASA data’s was95%. With other manifold andEuclidean distance as the similarity measure, and the results of this article has carried onthe contrast, show that the proposed method can get more accurate results.