Quaternion Visualization And Classification Of Physiological Time Series

Time series of physiological signals are physiological data that changes over time,containing too many and much complex information is its characteristic, it reflects theactive state of the physiological system, provides support for the physician during theanalysis and diagnosis of diseases, has great significance in medical research.A novel approach is put forward for classifying physiological signals based onquaternion Riemann feature and wavelet packet decomposition．First, applying waveletpacket decomposition on original sequence to make it become multivariate time series,and the decomposition layer is decided by the sampling rate and the frequency range thatthe characteristic wave belongs. Second, calculate the covariance matrix of each sequence,covariance matrix refeclts the orrelation between the vectors, not only retains all theinformation of the original series, but also achieves the purpose of dimensionalityreduction.Covariance matrix can be decomposed into a diagonal matrix and an orthogonalmatrix, due to the covariance matrix are positive definite symmetric matrix that belongs tothe Riemannian manifold, so we can get the distance between the diagonal matrix and thedistance between the orthogonal matrix. The orthogonal matrix is the rotation matrix ofquaternion, and quternion represents the rotation in three-dimensional space exactly.Reduce the computational complexity when calculating the distance between quaternions,because of the number of variables in it is less the number (nine) of orthogonal matrix.Finally, a new distance will be produced as a weighted sum calculated between diagonalmatrix distance and quaternion distance, it is the distance between covariance matix,applying this distance on the classification of physiological signals, in the visulization wayof covariance matrix to show the classification results.The classification method is validated with the cardiac arrhythmia signals obtainedfrom MIT-BIH database and the epileptic EEG data in Bonn database, the results showthat the classification method that based on quaternion Riemann features is reasonable andeffective, the classification accuracy of epilepsy EEG data is98.58%, the accuracy ofarrhythmia data reaches97.80%.