Study On Time Series Pattern Classification Based On Geometric Algebra Presention Principle

Time series is widely applied in many fields, such as the scientific experiments,economy and finance, industrial control, and biomedicine. Efficient analysis of time seriestypes of date and mining the information contained in the data help reveal regular indeveloping and changing to provide evidences in correctly understanding the things natureand making scientific decision. Therefore, as an important branch of data mining the timeseries data mining has important theoretical research value and practical applicationsignificance.Time series pattern classification is an important task of the time series data mining.Reasonable time series representation is the prerequisite and basis for the correctclassification. There is the problem that related information among the features does notbe extracted and effective dimension does not be reduced, with serial fusion method usedby currently time series representation. This paper proposed a time series patternclassification method based on geometric algebra representation principle. This methodmakes the multiple characteristics of time series embedded in algebraic geometry spacefor parallel representation and parallel processing to achieve the effective integration ofmulti-features. The three parts of the paper are as follows:Firstly, this paper researches the generalized model of geometric algebra embeddedrepresentation for univariate and multivariate time series. Based on the proposed model,we extracted four nodes wavelet packet coefficient characteristics of original time series,giving the parallel representation of the embedd quaternion. Using quaternion principalcomponent analysis algorithm for parallel wavelet packet sequence dimension reduction,and carrying out geometric product operation for the quaternion principal components,Geometry product reflects the associated informations of the features. Classificationexperiments were done for normal and epileptic EEG time series data set, discussing theaffection for the classification results of two key algorithms parameters: the number ofquaternion principle components and wavelet type respectively. Meanwhile, we comparedwith the traditional time series serial feature representation and extraction methods.Secondly, this paper reasearches the geometry object representation of time seriesmulti-dimensional characteristics and geometry feature extraction method. The originaltime series was first divided into sub-space, then extracting multi-dimensional features ineach sub-sequence space and mapping to points in high-dimensional space, and giving the geometry object representation in high-dimensional feature space of the feature points,finally extracting the geometric features of the geometry object. One task of the reasearchis to use geometry algebraic language to describe geometric objects of feature space andusing geometry calculation to extract geometric features. In the two-dimensional spaceand three-dimensional space to build multi-ECG morphology triangles, determining themost effective parameters of the geometric structure and the pattern classification weredone on five types of ECG time series of the MIT/BIH arrhythmia database.Lastly, this paper researches the symbol representation of time series multi-featurequaternion fusion and symbolic entropy feature extraction method. Geometric algebraembedding representation of time series multiple high-order cumulant were given, thehigh-order cumulant were embedded in quaternion to represent in parallel, and calculatingthe2–norm values and the determinant value of quaternion components matrix as theintegration of multiple high-order cumulants. On the basis of symbolic aggregationapproximation algorithm, conducting symbolic representation and extracting symbolentropy features of the integration features sequence. Classification experiment researcheswere done on three different states of EEG time series data of absence epilepsy rats,symbolic representation of the high-order cumulant integration features of different EEGrhythms in different states of seizures, symbol histogram and quaternion integrationsymbolic entropy characteristics of three types of EEG under different symbols parameterswere given.The research results show the proposed time series pattern classification methodbased on the principle of geometric algebra representation can briefly represent multiplefeatures of the original time series in parallel and conduct effective integration andclassification. Geometric algebra can be used as a new mathematical tool for time seriesdata mining and can be applied to other areas of time series pattern classification.