CN103279643A - Method for calculating time sequence similarity - Google Patents

Abstract

The invention discloses a method for calculating time sequence similarity in the technical field of computer information technology processing. The method includes the steps of dividing a time sequence S1 to be compared and a time sequence S2 to be compared into time subsequences S1 (i) and time subsequences S2 (i) respectively with the same mode, setting the weight (wi) of each time subsequence S1 (i) and the weight (wi) of each time subsequence S2 (i), calculating distances between the corresponding time subsequences, and calculating the similarity of the time sequence S1 and the time sequence S2 according to the distances between the corresponding time subsequences and the weights of the time subsequences. The method can better reflect the similarity of shapes of the time sequences and is low in complexity and quick in judgment.

Description

A kind of time series calculation of similarity degree method

Technical field

The invention belongs to the computer information technology processing technology field, relate in particular to a kind of time series calculation of similarity degree method.

Background technology

Time series is present in applications such as commerce, finance, medicine, astronomical meteorology, Aero-Space, electric power energy in a large number.In the data time series analysis process, how the similarity of judgement time sequence data is a underlying issue, is widely used in the work such as seasonal effect in time series inquiry, pattern match, classification and data mining.

Existing time series similarity calculating method based on distance mainly is divided into two kinds, namely based on the method for Euclidean distance (perhaps class Euclidean distance) with based on the method for dynamic time warping distance.Method based on Euclidean distance does not possess the form recognition capability, can not the patterns of change of recognition time sequence under different resolution.According to the time crooked route of the minimum cost coupling of aliging, can support the seasonal effect in time series time shaft flexible, but not satisfy apart from triangle inequality that particularly its, complexity was O (n computing time based on the method for dynamic time warping distance ²) (wherein n represents seasonal effect in time series length), calculated amount is very big, under many circumstances can't practical application.

Problems such as the computational accuracy that exists at present time series similarity calculating method is not high, calculation of complex the invention provides a kind of time series similarity calculating method based on the improvement distance, can realize quick, the accurately judgement of time series similarity.

Summary of the invention

The objective of the invention is to, provide a kind of based on the time series similarity calculating method that improves distance, be used for solving the deficiency that existing time series similarity calculating method exists.

To achieve these goals, the technical scheme of the present invention's proposition is that a kind of time series calculation of similarity degree method is characterized in that described method comprises:

Step 1: respectively with two time series S to be compared ₁And S ₂Be divided into chronon sequence S according to identical mode ₁(i) and S ₂(i); Wherein, i=1,2 ..., n, n are the number of chronon sequence;

Step 2: set each chronon sequence S _j(i) weight w _iWherein, j=1,2, i=1,2 ..., n;

Step 3: calculate the distance between the time corresponding subsequence;

Step 4: according to the weight of the distance between the time corresponding subsequence and chronon sequence, computing time sequence S ₁And S ₂Similarity.

Described with time series S ₁/ S ₂Be divided into chronon sequence S ₁(i)/S ₂(i) specifically:

Employing waits branch seasonal effect in time series mode time division subsequence, if time series S ₁/ S ₂Element number L ₁/ L ₂Be the integral multiple of n, then with time series S ₁/ S ₂Be divided into the n section, each section is a chronon sequence, and the element number of each chronon sequence is

If time series S ₁/ S ₂Element number L ₁/ L ₂Not the integral multiple of n, then with time series S ₁/ S ₂Be divided into the n section, each section is a chronon sequence, and the 1st section element number to the n-1 section is

[] is rounding operation, and the element number of n section is

Perhaps, the 2nd section element number to the n section is

[] is rounding operation, and the 1st section element number is $L_1-(n-1)\left[\frac{L_1}{n}\right]/L_2-(n-1)\left[\frac{L_2}{n}\right].$

Described with time series S ₁/ S ₂Be divided into chronon sequence S ₁(i)/S ₂(i) specifically:

Adopt non-five equilibrium seasonal effect in time series mode time division subsequence, to whole time series S ₁/ S ₂The independent segmentation of several periods that the similarity influence is bigger, the length of described period is the length of chronon sequence, to time series S ₁/ S ₂In other periods then divide subsequence by five equilibrium seasonal effect in time series mode, simultaneously to satisfy the span of the weight of chronon sequence be (0,1) to the chronon sequence, and the weight sum of all chronon sequences equals 1, namely $\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{w}_i=1.$

Described each chronon sequence S _j(i) weight w _iAccording to formula w _i=L _j(i)/L _jSet; Wherein, L _j(i) be chronon sequence S _j(i) element number, L _jBe time series S _jElement number, j=1,2, i=1,2 ..., n, n are the number of subsequence.

Distance between the described calculating time corresponding subsequence adopts formula $d(S_1\left(i\right),S_2\left(i\right))=\sqrt{\underset{p=1}{\overset{m}{\mathrm{\Σ}}}{(S_1^p\left(i\right)-S_2^p\left(i\right))}^2}+\mathrm{\σ};$ Wherein:

D (S ₁(i), S ₂(i)) be time corresponding subsequence S ₁(i) and S ₂(i) distance between;

Be chronon sequence S ₁(i) p element;

Be chronon sequence S ₂(i) p element;

M is chronon sequence S ₁(i) and S ₂(i) element number, i=1,2 ..., n;

σ is chronon sequence S ₁(i) and S ₂(i) standard deviation of the difference of Dui Ying element and $\mathrm{\σ}=\sqrt{\frac{1}{m}\underset{p=1}{\overset{m}{\mathrm{\Σ}}}{(S_1^p\left(i\right)-S_2^p\left(i\right)-\mathrm{\μ})}^2};$

μ is chronon sequence S ₁(i) and S ₂(i) the arithmetic mean value of the difference of Dui Ying element and $\mathrm{\μ}=\frac{1}{m}\underset{p=1}{\overset{m}{\mathrm{\Σ}}}(S_1^p\left(i\right)-S_2^p\left(i\right)).$

Described computing time sequence S ₁And S ₂Similarity adopt formula $\mathrm{Sim}(S_1,S_2)=\frac{1}{1+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{w}_i\×d(S_1\left(i\right),S_2\left(i\right))};$ Wherein:

Sim (S ₁, S ₂) be time series S ₁And S ₂Similarity;

D (S ₁(i), S ₂(i)) be time corresponding subsequence S ₁(i) and S ₂(i) distance between;

w _iBe chronon sequence S ₁(i)/S ₂(i) weight;

N is the number of subsequence.

The present invention carries out isometric or not isometric segmentation with time series and the weight of each chronon sequence is set, and the actual similarity that can satisfy under the different situations is judged demand; In addition, chronon sequence distance calculating method provided by the invention is compared traditional distance calculating method, can reflect seasonal effect in time series shape similarity degree (being the similarities and differences of the local trend of time sequence) better, more meet the contrast of human daily experience and vision, it is more accurate to judge; At last, segmentation subsequence computing time distance of the present invention, again according to subsequence apart from calculating similarity, computation complexity is low, can realize the quick judgement of time series similarity.

Description of drawings

Fig. 1 is time series calculation of similarity degree method flow diagram provided by the invention.

Embodiment

Below in conjunction with accompanying drawing, preferred embodiment is elaborated.Should be emphasized that following explanation only is exemplary, rather than in order to limit the scope of the invention and to use.

Fig. 1 is time series calculation of similarity degree method flow diagram provided by the invention, and as shown in Figure 1, time series calculation of similarity degree method comprises:

Step 1: respectively with two time series S to be compared ₁And S ₂Be divided into chronon sequence S according to identical mode ₁(i) and S ₂(i); Wherein, i=1,2 ..., n, n are the number of chronon sequence.

Judge concrete practical application request according to similarity, if the local similar of time series day part is identical to time series global similarity influence degree, branch seasonal effect in time series mode such as then can adopt to divide subsequence.With time series by the isometric n of being divided into of a length chronon sequence (if can not isometricly divide equally, first or last chronon sequence length can be not equal to other sub-sequence length).The concrete length value of each chronon sequence is relevant with the time series feature, and arrange by the following method according to different field time series fluctuating characteristic: seasonal effect in time series data value fluctuating range is more little, and chronon sequence length value is more big; The time series that the data value fluctuation is violent relatively, chronon sequence length value is more little.Generally speaking, the length value of chronon sequence is between 5-15.If the local similar of time series day part influences difference to the time series global similarity, namely the data of some (or several) periods are bigger to whole seasonal effect in time series similarity influence, other the time segment data less to the influence of whole seasonal effect in time series similarity, then can adopt non-five equilibrium seasonal effect in time series mode time division subsequence.Such as, to the whole Time Series Similarity influence independent segmentation of data of bigger (or several) period, the length of this (or several) period is the length of this (or several) chronon sequence, time series other the time segment data then divide subsequence by five equilibrium seasonal effect in time series mode.

Dividing subsequence in five equilibrium seasonal effect in time series mode below describes.If time series S ₁(S ₂) element number L ₁(L ₂) be the integral multiple of n, then with time series S ₁(S ₂) be divided into the n section.Each section is a chronon sequence, and the element number of each chronon sequence is

Such as, chronon sequence to be divided has 20 elements, has namely gathered the data of 20 time points, it to be divided into 5 chronon sequences, then can make 4 elements (data of time point) is one section, and the makeup time subsequence like this just is divided into 4 chronon sequences.

If time series S ₁(S ₂) element number L ₁(L ₂) not the integral multiple of n, then with time series S ₁(S ₂) being divided into the n section, each section is a chronon sequence, the 1st section element number to the n-1 section is

[] is rounding operation, and the element number of n section is Perhaps, the 2nd section element number to the n section is

[] is rounding operation, and the 1st section element number is

Still with chronon sequence to be divided 20 elements being arranged is example, if it is divided into 6 chronon sequences, then can make the 1st section to the 5th section every section 3 elements are arranged, and the 6th section is 5 elements; Perhaps, can make the 2nd section to the 6th section every section 3 elements are arranged, the 1st section is 5 elements.

Step 2: set each chronon sequence S _j(i) weight w _i

Among the present invention, by the length scale of each chronon sequence its weight is set, concrete grammar is: the weight value of a chronon sequence namely is the ratio of length and the whole length of time series of this chronon sequence.The weight w of chronon sequence s (i) _iComputing method as shown in the formula:

w _i＝L _j(i)/L _j （1）

In the following formula (1), w _iBe chronon sequence S ₁(i) and S ₂(i) weight, L _j(i) be chronon sequence S _j(i) element number also is time subsequence S _j(i) length; L _jBe time series S _jElement number, also be time sequence S _jLength, j=1,2, i=1,2 ..., n, n are the number of subsequence.

For the chronon sequence that adopts non-five equilibrium seasonal effect in time series mode to divide, the weight of each chronon sequence can be set the size of time series global similarity influence degree according to each chronon sequence, the chronon sequence weight value that influence degree is more big is more big, the chronon sequence weighted value that influence degree is more little is more little, but make that the span of weight is (0,1), the weight sum that guarantees all chronon sequences of time series division gained simultaneously equals 1, namely satisfies following constraint:

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{w}_i=1---\left(2\right)$

In the following formula (2), w _iBe chronon sequence S ₁(i) and S ₂(i) weight, n is the number of chronon sequence.

Step 3: calculate the distance between the time corresponding subsequence.

The distance of calculating between the time corresponding subsequence adopts formula:

$d(S_1\left(i\right),S_2\left(i\right))=\sqrt{\underset{p=1}{\overset{m}{\mathrm{\Σ}}}{(S_1^p\left(i\right)-S_2^p\left(i\right))}^2}+\mathrm{\σ}---\left(3\right)$

In above-mentioned (3) formula, d (S ₁(i), S ₂(i)) be time corresponding subsequence S ₁(i) and S ₂(i) distance between,

Be chronon sequence S ₁(i) p element, i.e. time subsequence S ₁The data of p time point (i),

Be chronon sequence S ₂(i) p element, m are chronon sequence S ₁(i) and S ₂(i) element number, σ are chronon sequence S ₁(i) and S ₂(i) standard deviation of the difference of Dui Ying element, the computing method of σ are as follows:

$\mathrm{\σ}=\sqrt{\frac{1}{m}\underset{p=1}{\overset{m}{\mathrm{\Σ}}}{(S_1^p\left(i\right)-S_2^p\left(i\right)-\mathrm{\μ})}^2}---\left(4\right)$

In above-mentioned (4) formula, μ is chronon sequence S ₁(i) and S ₂(i) the arithmetic mean value of the difference of Dui Ying element, the computing method of μ are as follows:

$\mathrm{\μ}=\frac{1}{m}\underset{p=1}{\overset{m}{\mathrm{\Σ}}}(S_1^p\left(i\right)-S_2^p\left(i\right))---\left(5\right)$

In above-mentioned formula (3) and (4), i=1,2 ..., n, n are the number of chronon sequence.

Step 4: according to the weight of the distance between the time corresponding subsequence and chronon sequence, computing time sequence S ₁And S ₂Similarity.

Computing time sequence S ₁And S ₂Similarity adopt formula

$\mathrm{Sim}(S_1,S_2)=\frac{1}{1+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{w}_i\×d(S_1\left(i\right),S_2\left(i\right))}---\left(6\right)$

In the above-mentioned formula (6), Sim (S ₁, S ₂) be time series S ₁And S ₂Similarity, d (S ₁(i), S ₂(i)) be time corresponding subsequence S ₁(i) and S ₂(i) distance between, w _iBe chronon sequence S ₁(i) and S ₂(i) weight, n is the number of chronon sequence.

The present invention has following remarkable advantage:

(1) this method is carried out isometric or not isometric segmentation according to the relation of time series local similar and global similarity and the weight of each chronon sequence is set, and judges demand with the actual similarity that satisfies different user.

(2) difference of time series section length, can portray seasonal effect in time series similar trend degree under the different time yardstick, judge the thickness granularity division that provides at different demands for the time series similarity, make this method have good time multiresolution characteristic.

(3) consider time series plesiomorphism factor, designed new chronon sequence distance calculating method, compare traditional distance, new method can reflect seasonal effect in time series shape similarity degree (being the similarities and differences of the local trend of time sequence) better, more meet the contrast of human daily experience and vision, it is more accurate to judge.

(4) this method computation complexity is low, can realize the quick judgement of time series similarity.

The above; only for the preferable embodiment of the present invention, but protection scope of the present invention is not limited thereto, and anyly is familiar with those skilled in the art in the technical scope that the present invention discloses; the variation that can expect easily or replacement all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection domain of claim.

Claims (6)

1. time series calculation of similarity degree method is characterized in that described method comprises:

Step 1: respectively with two time series S to be compared ₁And S ₂Be divided into chronon sequence S according to identical mode ₁(i) and S ₂(i); Wherein, i=1,2 ..., n, n are the number of chronon sequence;

Step 2: set each chronon sequence S _j(i) weight w _iWherein, j=1,2, i=1,2 ..., n;

Step 3: calculate the distance between the time corresponding subsequence;

Step 4: according to the weight of the distance between the time corresponding subsequence and chronon sequence, computing time sequence S ₁And S ₂Similarity.

2. computing method according to claim 1 is characterized in that described with time series S ₁/ S ₂Be divided into chronon sequence S ₁(i)/S ₂(i) specifically:

Employing waits branch seasonal effect in time series mode time division subsequence, if time series S ₁/ S ₂Element number L ₁/ L ₂Be the integral multiple of n, then with time series S ₁/ S ₂Be divided into the n section, each section is a chronon sequence, and the element number of each chronon sequence is

If time series S ₁/ S ₂Element number L ₁/ L ₂Not the integral multiple of n, then with time series S ₁/ S ₂Be divided into the n section, each section is a chronon sequence, and the 1st section element number to the n-1 section is

[] is rounding operation, and the element number of n section is

Perhaps, the 2nd section element number to the n section is [] is rounding operation, and the 1st section element number is $L_1-(n-1)\left[\frac{L_1}{n}\right]/L_2-(n-1)\left[\frac{L_2}{n}\right].$

3. computing method according to claim 1 is characterized in that described with time series S ₁/ S ₂Be divided into chronon sequence S ₁(i)/S ₂(i) specifically:

Adopt non-five equilibrium seasonal effect in time series mode time division subsequence, to whole time series S ₁/ S ₂The independent segmentation of several periods that the similarity influence is bigger, the length of described period is the length of chronon sequence, to time series S ₁/ S ₂In other periods then divide subsequence by five equilibrium seasonal effect in time series mode, simultaneously to satisfy the span of the weight of chronon sequence be (0,1) to the chronon sequence, and the weight sum of all chronon sequences equals 1, namely $\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{w}_i=1.$

4. according to claim 2 or 3 described computing method, it is characterized in that described each chronon sequence S _j(i) weight w _iAccording to formula w _i=L _j(i)/L _jSet; Wherein, L _j(i) be chronon sequence S _j(i) element number, L _jBe time series S _jElement number, j=1,2, i=1,2 ..., n, n are the number of subsequence.

5. computing method according to claim 4 is characterized in that the distance between the described calculating time corresponding subsequence adopts formula $d(S_1\left(i\right),S_2\left(i\right))=\sqrt{\underset{p=1}{\overset{m}{\mathrm{\Σ}}}{(S_1^p\left(i\right)-S_2^p\left(i\right))}^2}+\mathrm{\σ};$ Wherein:

D (S ₁(i), S ₂(i)) be time corresponding subsequence S ₁(i) and S ₂(i) distance between;

Be chronon sequence S ₁(i) p element;

Be chronon sequence S ₂(i) p element;

M is chronon sequence S ₁(i) and S ₂(i) element number, i=1,2 ..., n;

σ is chronon sequence S ₁(i) and S ₂(i) standard deviation of the difference of Dui Ying element and $\mathrm{\σ}=\sqrt{\frac{1}{m}\underset{p=1}{\overset{m}{\mathrm{\Σ}}}{(S_1^p\left(i\right)-S_2^p\left(i\right)-\mathrm{\μ})}^2};$

μ is chronon sequence S ₁(i) and S ₂(i) the arithmetic mean value of the difference of Dui Ying element and $\mathrm{\μ}=\frac{1}{m}\underset{p=1}{\overset{m}{\mathrm{\Σ}}}(S_1^p\left(i\right)-S_2^p\left(i\right)).$

6. computing method according to claim 5 is characterized in that described computing time of sequence S ₁And S ₂Similarity adopt formula $\mathrm{Sim}(S_1,S_2)=\frac{1}{1+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{w}_i\×d(S_1\left(i\right),S_2\left(i\right))};$ Wherein:

Sim (S ₁, S ₂) be time series S ₁And S ₂Similarity;

D (S ₁(i), S ₂(i)) be time corresponding subsequence S ₁(i) and S ₂(i) distance between;

w _iBe chronon sequence S ₁(i)/S ₂(i) weight;

N is the number of subsequence.