CN104794484A - Time series data nearest-neighbor classifying method based on subsection orthogonal polynomial decomposition - Google Patents

Abstract

The invention discloses a time series data nearest-neighbor classifying method based on subsection orthogonal polynomial decomposition. The time series data nearest-neighbor classifying method includes dividing a time sequence into subsequences comprising complete fluctuation trends on the basis of time sequence coded identification turning points; extracting Chebyshev coefficient as subsequence features by means of a first type Chebyshev polynomial decomposition subsequences, and constructing subsequence feature vectors; finally in the nearest-neighbor classifier, classifying by the dynamic planning algorithm based on local mode matching as distance metric function. Classifying accuracy and efficiency are superior to other nearest-neighbor classifiers to the great extent, and the time series data nearest-neighbor classifying method plays an important role in daily activity of people and industrial production, such as in applications of banking transactions, traffic control, air quality and temperature monitoring, industrial process monitoring, medical diagnosis and the like, massive sampling data or high-speed dynamic data can be classified and predicted, abnormalities can be detected and online modes are identified.

Description

Based on the time series data arest neighbors sorting technique that segmentation orthogonal polynomial is decomposed

Technical field

The present invention relates to the fields such as database, data mining, machine learning, information retrieval, particularly relate to data time series analysis and excavation.

Background technology

Time series is extensively present in daily life and commercial production, as the real-time transaction data of fund or stock, the day sales volume data of retail market, the Sensor monitoring data of process industry, astronomical sight data, Aero-Space radar, satellite monitoring data, real-time weather temperature and air quality index etc.In order to make full use of the time series data of magnanimity, industry member needs to be classified it usually, could therefrom find valuable information and knowledge.Therefore, time series classification method to have a wide range of applications demand in industry member.

At present, the sorter that industry member is conventional has artificial neural network, support vector machine, Naive Bayes Classifier, nearest neighbor classifier etc.Artificial neural network, by the interconnected nonlinear model formed of a large amount of processing unit, by adjusting the interconnecting relation of internal node, analyzes the potential rule grasped between inputoutput data, is embodied as new data and calculates result.The method has stronger self study and adaptive ability, but lacks the interpretability to reasoning process.Support vector machine finds an optimal hyperlane in higher dimensional space, under the prerequisite ensureing nicety of grading, the blank spacing of lineoid both sides maximized.Support vector machine can do optimal dividing to linear separability data in theory, but but can only process two classification problems.Naive Bayes Classifier is based on Bayesian formula, utilizes the prior probability of object calculate the posterior probability of its generic and realize classification.Although the theory of the method is simple, operability is comparatively strong, ensure higher accuracy, needs to adopt Large-Scale Training Data Set training pattern.Nearest neighbor classifier is a kind of method based on distance metric, and it realizes classifying apart from minimum neighbour with object of classification by searching in training set.This sorting technique not only has good interpretation and ease for operation, and without the need to training data model, namely has very strong dirigibility and data adaptability.Because nearest neighbor classifier is using distance metric function as kernel, so it is determined by time series distance metric method completely to the nicety of grading of time series data and efficiency.

The time series distance metric method that current industry member is commonly used can be divided into lock-step measure and DE metering method.The former have employed man-to-man metric form, i.e. time series T ₁and T ₂between distance be by strictly comparing T ₁and T ₂right at the point of respective i-th position, then the distance of cumulative all-pair obtains.These class methods are modal manhatton distance, Euclidean distance and Chebyshev's distance, and they are all L _pthe special case of-norms distance when p gets different value.These class methods have the advantages such as easy realization, low, the satisfied distance triangle inequality of computation complexity, nothing ginseng; But, its accuracy of measurement to noise, abnormity point, amplitude is flexible and drift, phase offset etc. are very responsive, and can only be used for measuring isometric time series.DE metering method have employed the metric form of one-to-many, i.e. time series T ₁a point can with T ₂multiple continuity points corresponding, travel through T by dynamic programming method ₁and T ₂all-pair between distance.The modal mutation (as LCSS, EDR, ERP) etc. having dynamic time warping distance (DTW) and editing distance of these class methods.Compared with measuring with lock-step, elasticity tolerance can realize two seasonal effect in time series best alignment coupling, can effectively the processing time is bending, phase offset, amplitude are flexible and the grown form such as drift changes, and has robustness to noise and abnormity point, therefore, DE measurer has the higher accuracy of measurement.But these class methods have higher computation complexity, high time overhead can be caused when measuring the time series of higher-dimension, being difficult to process large-scale time series or dynamic dataflow at a high speed in the industrial production.

Based on a kind of effective ways that seasonal effect in time series feature calculation elasticity tolerance is its high computation complexity of improvement, namely first adopt data presentation technique original time series to be mapped to the feature space of low-dimensional, then carry out elasticity tolerance.The data presentation technique that current industry member is commonly used can be divided into non-data adaptation method and data adaptation method.For the former, conversion parameter does not affect by independent time series, and remains constant; Such represents mostly based on spectral decomposition realization, and as discrete Fourier transformation, wavelet transform, discrete cosine transform, they, mainly through doing the conversion of corresponding frequency domain to original time series, extract main spectral coefficient as feature; The each defectiveness of these class methods, can only gross morphological features be extracted as discrete Fourier transformation and have ignored local feature, wavelet transform can only treated length be the time series of the index time of 2, and the information dropout of discrete cosine transform is more, larger to the reconstructed error of raw data.Data adaptability represent refer to conversion parameter determination need rely on data itself; By increasing the selection processing procedure of data sensitive, most of non-data adaptation method can be become data adaptation method.These class methods have that approximate, piece wire approximation is assembled in segmentation, approximate, svd is assembled in symbolism, principal component analysis (PCA) etc., first three kind all needs first to carry out segmentation to original time series, then processes separately each subsegment: it is average to each section that segmentation is assembled approximate; Piece wire approximation does line-fitting to each section; It is assemble on approximate basic in segmentation to turn to symbol by discrete for every section of mean value that symbolism is assembled approximate; The feature extracted due to them is comparatively single, makes it more weak to the ability to express of time series fluctuation model.Svd and principal component analysis (PCA) decompose realization by doing unified eigenmatrix to all time serieses; The typical defect of these two class methods is, they have very high computation complexity, and decomposable process can only complete at internal memory, and the extensibility of data scale is very low.

Summary of the invention

The problem to be solved in the present invention is time series of how classifying accurately and efficiently.In order to solve this problem, the present invention proposes the time series data arest neighbors sorting technique of decomposing based on segmentation orthogonal polynomial.

The object of the invention is to be achieved through the following technical solutions: a kind of time series data arest neighbors sorting technique of decomposing based on segmentation orthogonal polynomial, comprises the following steps:

(1) adaptivity segmentation, specifically comprises following sub-step:

(1.1) every bar time series T of reading database successively;

(1.2) Z-standardization processing is done to time series T, obtain normalized time series T';

(1.3) gliding smoothing process is done to normalized time series T', obtain smoothingtime sequence T ";

(1.4) intercept T successively based on moving window " adjacent 3 points, and calculating mean value, by judging that the magnitude relationship of each point and mean value is encoded to it, obtains the coded sequence C of T _t, and define turnover pattern table TP_table;

(1.5) order scans C _t, to the turnover pattern in often couple of adjacent encoder query composition TP_table, if pattern match, then using this coded combination position as waypoint;

(1.6) scanned, T is divided into N cross-talk sequence, obtains subsequence set S={S ₁..., S _n;

(2) factorization, specifically comprises following sub-step:

(2.1) every bar subsequence S of T is read successively _i;

(2.2) Chebyshev polynomial of the first kind is adopted to decompose S _i, a multinomial coefficient c before calculating _i, constructor sequence signature vector V _i=[c ₁, c ₂..., c _a];

(2.3) scanned, the segmentation chebyshev approximation obtaining T represents PCHA (T)={ V ₁..., V _n, and stored in database;

(3) arest neighbors classification, specifically comprises following sub-step:

(3.1) read test concentrates cutting to be that the segmentation chebyshev approximation of the time series Q of M cross-talk sequence represents PCHA (Q)={ V ₁..., V _m;

(3.2) the segmentation chebyshev approximation reading every bar time series T of training set successively represents PCHA (T)={ V' ₁..., V' _n;

(3.3) initialization dynamic programming table Table=cell (M, N);

(3.4) the 1st the sub-sequence characteristics vector V of PCHA (Q) is calculated successively ₁with N number of sub-sequence characteristics vector V' of PCHA (T) ₁~ V' _nbetween standardization distance { dist (V ₁, V' ₁) ..., dist (V ₁, V' _n), and stored in the 1st row Table (1,1:N) of Table;

(3.5) the 1st the sub-sequence characteristics vector V' of PCHA (T) is calculated successively ₁with M the sub-sequence characteristics vector V of PCHA (Q) ₁~ V _mbetween standardization distance { dist (V ₁, V' ₁) ..., dist (V _m, V' ₁), and arrange Table (1:M, 1) stored in the 1st of Table;

(3.6) utilize dynamic programming method, scan the 2 to the M the sub-sequence characteristics vector V of PCHA (Q) successively ₂~ V _mwith the 2 to the N number of sub-sequence characteristics vector V' of PCHA (T) ₂~ V' _n, calculate each cell value of Table (2:M, 2:N) based on standardization distance, comprise following sub-step:

(3.6.1) order scans V ₂~ V _m, for i-th sub-sequence characteristics vector V _i, calculate it and V' successively ₂~ V' _nbetween standardization distance { dist (V _i, V' ₂) ..., dist (V _i, V' _n);

(3.6.2) according to the order scanning Table (2:M of Row Column, 2:N), at each unit Table (i, j), in, Table (i-1, j), Table (i is first compared, and Table (i-1 j-1), j-1) size, selects minimum value to be designated as min, then calculates dist (V _i, V' _j)+min value give Table (i, j);

(3.7) value returning Table (M, N) as T and Q distance metric result and preserve;

(3.8) training set is scanned, selects with Q apart from minimum time series T _minclass label as the class label of Q, complete classification.

The invention has the beneficial effects as follows:

1, in the adaptivity segmentation stage, have employed simple and effective coding method and turnover mode identification method, can efficient identification turning point, ensure that the subsequence be syncopated as has complete fluctuation tendency.

2, in the factorization stage, have employed chebyshev approximating polynomial original time series, there is less error of fitting, and using Chebyshev coefficient as feature, the fluctuation information of pull-in time sequence can be used for similarity measurement.

3, at arest neighbors sorting phase, dynamic programming based on local mode level calculates, overcome the phase offset problem between local mode that Time Warp causes, achieve higher time series global schema coupling, make arest neighbors to classify efficiently and accurately more thus.

Accompanying drawing explanation

Fig. 1 is the time series data arest neighbors sorting technique process flow diagram decomposed based on segmentation orthogonal polynomial;

Fig. 2 is the process flow diagram of adaptivity split time sequence;

Fig. 3 represents seasonal effect in time series process flow diagram for adopting segmentation chebyshev approximation;

Fig. 4 is time series arest neighbors classification process figure.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further detail.

As shown in Figure 1, the present invention is based on the time series data arest neighbors sorting technique that segmentation orthogonal polynomial is decomposed, comprise the following steps:

(1) adaptivity segmentation, as shown in Figure 2, specifically comprises following sub-step:

(1.1) every bar time series T={t of reading database successively ₁, t ₂..., t _i..., t _n;

(1.2) calculate mean value m and the standard deviation sigma of the sampled point of T, according to formula (1), Z-standardization processing is done to T, obtain normalized time series T'={t' ₁, t' ₂..., t' _i..., t' _n;

${t^{\′}}_i=\frac{t_i-m}{\mathrm{\σ}}---\left(1\right)$

(1.3) calculate the mean value of adjacent 3 of T' successively, gliding smoothing process is done to it, obtain smoothingtime sequence T "={ t " ₁, t " ₂..., t " _i..., t " _n;

(1.4) intercept T successively based on moving window " adjacent 3 and calculating mean value, by judging that the magnitude relationship of each point and mean value is encoded to it, obtain the coded sequence C of T _t, and define turnover pattern table TP_table, this process comprises following sub-step:

(1.4.1) adopt moving window W, intercept T " adjacent 3 <t " successively _i-1, t " _i, t " _i+1>, and calculating mean value m ^t _i;

(1.4.2) <t is judged " _i-1, t " _i, t " _i+1the each point of > and mean value m ^t _irelation, if t " _i>m ^t _i, then code (t " _i)=1; Otherwise code (t " _i)=0, thus by <t " _i-1, t " _i, t " _i+1> is encoded to d ^t _i=<c ^t _i-1, c ^t _i, c ^t _i+1>, obtains the coded sequence C of T _t={ d ^t ₁, d ^t ₂..., d ^t _n;

(1.4.3) according to all turnover pattern TP of coding definition, obtain turnover pattern table TP_table={ and rise-decline: 001-100,001-110,011-100,011-110,001/011-010-100/110; Decline-rise: 100-001,100-011,110-001,110-011,100/110-101-001/011};

(1.5) order scans C _t, to often couple of adjacent encoder combination <d ^t _i, d ^t _i+1> inquires about TP_table, if pattern match, then using i as waypoint, obtain i-th subsequence S of T _i;

(1.6) scanned to T, obtain the subsequence set S={S of T ₁, S ₂..., S _n;

(2) factorization, as shown in Figure 3, specifically comprises following sub-step:

(2.1) scan S, read every bar subsequence S of T successively _i;

(2.2) the segmentation chebyshev approximation of initialization T represents that PCHA (T) is empty set, according to formula (2) ~ (4), to S _ido Chebyshev's factorization, the individual Chebyshev coefficient c of a (<10) before extracting _ias feature, structure S _isub-sequence characteristics vector V _i=[c ₁, c ₂..., c _a], and insert PCHA (T);

F _δ(cos(t))＝cos(δ·t) (2)

$S_i\left(t\right)\&cong;\underset{i=0}{\overset{\mathrm{\&delta;}}{\mathrm{\&Sigma;}}}{c}_i{F}_i\left(t\right)---\left(3\right)$

$c_i=\frac{k}{\mathrm{\&delta;}}\underset{j=1}{\overset{\mathrm{\&delta;}}{\mathrm{\&Sigma;}}}{S}_i\left(t_j\right)F_i\left(t_j\right)---\left(4\right)$

Wherein, δ represents the exponent number of Chebyshev polynomials, when δ=0, and k=1, otherwise, k=2;

(2.3) scanned to S, the segmentation chebyshev approximation obtaining T represents PCHA (T)={ V ₁..., V _n, and stored in database;

(3) arest neighbors classification, as shown in Figure 4, specifically comprises following sub-step:

(3.1) read test concentrates cutting to be that the segmentation chebyshev approximation of the time series Q of M cross-talk sequence represents PCHA (Q)={ V ₁..., V _m;

(3.2) the segmentation chebyshev approximation reading every bar time series T of training set successively represents PCHA (T)={ V' ₁..., V' _n;

(3.3) initialization dynamic programming table Table=cell (M, N);

(3.4) according to formula (5), the 1st the sub-sequence characteristics vector V of PCHA (Q) is calculated successively ₁with N number of sub-sequence characteristics vector V' of PCHA (T) ₁~ V' _nbetween standardization distance { dist (V ₁, V' ₁) ..., dist (V ₁, V' _n), and successively stored in the 1st row Table (1,1:N) of Table;

$\mathrm{dist}(V,V^{\&prime;})=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{\left|c_i\right|-\left|{c^{\&prime;}}_i\right|}{|c_i+{c^{\&prime;}}_i|}---\left(5\right)$

(3.5) according to formula (5), the 1st the sub-sequence characteristics vector V' of PCHA (T) is calculated successively ₁with M the sub-sequence characteristics vector V of PCHA (Q) ₁~ V _mbetween standardization distance { dist (V ₁, V' ₁) ..., dist (V _m, V' ₁), and successively stored in the 1st row Table (1:M, 1) of Table;

(3.6) utilize dynamic programming method, calculate each cell value of Table (2:M, 2:N) based on formula (5), this process comprises following sub-step:

(3.6.1) order scans V ₂~ V _m, for i-th sub-sequence characteristics vector V of PCHA (Q) _i, calculate it and V' successively ₂~ V' _nbetween standardization distance { dist (V _i, V' ₂) ..., dist (V _i, V' _n);

(3.6.2) as scanning V _iwith V' _jtime, first compare the size of Table (i-1, j), Table (i, j-1) and Table (i-1, j-1), select minimum value to be designated as min, then calculate dist (V _i, V' _j)+min value give Table (i, j).

(3.7) value returning Table (M, N) as T and Q distance metric result and preserve;

(3.8) training set is scanned, selects with Q apart from minimum time series T _minclass label as the class label of Q, complete classification.

Time series classification can play a significant role in the daily routines and commercial production of people, and have a wide range of applications demand.The present invention is directed to the time series classification problem that industry member faces, propose the time series data arest neighbors sorting technique of decomposing based on segmentation orthogonal polynomial, adaptability segmentation can be carried out to time series data, and extraction time sequence fluctuation information be used for similarity measurement, realize the classification to seasonal effect in time series high-efficiency high-accuracy thus.The present invention classifying to extensive sampled data or high speed dynamic dataflow, predict, can play a significant role in abnormality detection, the task such as line model identification, meet industrial application demand greatly.

Claims (2)

1., based on the time series data arest neighbors sorting technique that segmentation orthogonal polynomial is decomposed, it is characterized in that, comprise the following steps:

(1) adaptivity segmentation, specifically comprises following sub-step:

(1.1) every bar time series of reading database successively t;

(1.2) to time series tdo z-standardization processing, obtains normalized time series t';

(1.3) to normalized time series t'do gliding smoothing process, obtain smoothingtime sequence t ";

(1.4) intercept successively based on moving window t "adjacent 3 points, and calculating mean value, by judging that the magnitude relationship of each point and mean value is encoded to it, obtains tcoded sequence c _t , and define turnover pattern table tP_table;

(1.5) order scanning c _t , to often pair of adjacent encoder query composition tP_tablein turnover pattern, if pattern match, then using this coded combination position as waypoint;

(1.6) scanned, will tbe divided into ncross-talk sequence, obtains subsequence set s = s ₁..., s _n ;

(2) factorization, specifically comprises following sub-step:

(2.1) read successively tevery bar subsequence s _i ;

(2.2) Chebyshev polynomial of the first kind is adopted to decompose s _i , before calculating aindividual multinomial coefficient c _i , constructor sequence signature vector v _i =[ c ₁, c ₂..., c _a ];

(2.3) scanned, obtain tsegmentation chebyshev approximation represent pCHA( t)={ v ₁..., v _n , and stored in database;

(3) arest neighbors classification, specifically comprises following sub-step:

(3.1) read test concentrates cutting to be mthe time series of cross-talk sequence qsegmentation chebyshev approximation represent pCHA( q)={ v ₁..., v _m ;

(3.2) every bar time series of training set is read successively tsegmentation chebyshev approximation represent pCHA( t)={ v' ₁..., v' _n ;

(3.3) initialization dynamic programming table table= cell( m, n);

(3.4) calculate successively pCHA( q) the 1st sub-sequence characteristics vector v ₁with pCHA( t) nindividual sub-sequence characteristics vector v' ₁~ v' _n between standardization distance dist( v ₁, v' ₁) ..., dist( v ₁, v' _n ), and stored in tablethe 1st row table(1,1: n);

(3.5) calculate successively pCHA( t) the 1st sub-sequence characteristics vector v' ₁with pCHA( q) mindividual sub-sequence characteristics vector v ₁~ v _m between standardization distance dist( v ₁, v' ₁) ..., dist( v _m , v' ₁), and stored in tablethe 1st row table(1: m, 1);

(3.6) utilize dynamic programming method, scan successively pCHA( q) the 2 to the mindividual sub-sequence characteristics vector v ₂~ v _m with pCHA( t) the 2 to the nindividual sub-sequence characteristics vector v' ₂~ v' _n , calculate based on standardization distance table(2: m, 2: n) each cell value;

(3.7) return table( m, n) value conduct twith qdistance metric result and preserve;

(3.8) training set is scanned, select with qapart from minimum time series t _min the conduct of class label qclass label, complete classification.

2., according to claim 1 based on the time series data arest neighbors sorting technique that segmentation orthogonal polynomial is decomposed, it is characterized in that, described step 3.6 comprises following sub-step:

(3.6.1) order scanning v ₂~ v _m , for iindividual sub-sequence characteristics vector v _i , calculate successively it with v' ₂~ v' _n between standardization distance dist( v _i , v' ₂) ..., dist( v _i , v' _n );

(3.6.2) scan according to the order of Row Column table(2: m, 2: n), at each unit table( i, j) in, first compare table( i-1, j), table( i, j-1) and table( i-1, j-1) size, selects minimum value to be designated as min, then calculate dist( v _i , v' _j )+ minvalue give table( i, j).