CN103279643B - A kind of computational methods of time series similarity - Google Patents

Abstract

The invention discloses the computational methods of a kind of time series similarity in computer information technology processing technology field.Including: respectively by two time serieses S to be compared₁And S₂It is divided into chronon sequence S in the same fashion₁(i) and S₂(i)；Set each chronon sequence S₁(i) and S₂Weight w of (i)_i；Calculate the distance between corresponding chronon sequence；According to the distance between corresponding chronon sequence and the weight of chronon sequence, calculate time series S₁And S₂Similarity.The present invention can the shape similarity degree of preferably reflecting time sequence, its complexity is low and judges that speed is fast.

Description

A kind of computational methods of time series similarity

Technical field

The invention belongs to computer information technology processing technology field, particularly relate to the calculating of a kind of time series similarity Method.

Background technology

Time series is present in the application necks such as business, finance, medicine, Astronomy, Meteorology, Aero-Space, electric power energy in a large number Territory.During data time series analysis, how to judge that the similarity of time series data is a underlying issue, extensively apply In the work such as seasonal effect in time series inquiry, pattern match, classification and data mining.

Existing time series similarity computational methods based on distance are broadly divided into two kinds, i.e. based on Euclidean distance The method of (or class Euclidean distance) and method based on dynamic time warping distance.Method based on Euclidean distance Do not possesses form identification ability, it is impossible to recognition time sequence patterns of change under different resolution.Based on dynamic time warping The method of distance carries out alignment coupling according to the Time Warp path of minimum cost, it would be preferable to support seasonal effect in time series time shaft is stretched Contracting, but it is unsatisfactory for distance triangle inequality, particularly it calculates time complexity is O (n²) (the wherein length of n express time sequence Degree), amount of calculation is very big, cannot actual apply under many circumstances.

The computational accuracy existed for current time series similarity computational methods is the highest, calculate the problems such as complicated, this A kind of time series similarity computational methods based on improvement distance of bright offer, can realize the quick, accurate of time series similarity Really judge.

Summary of the invention

It is an object of the invention to, it is provided that a kind of time series similarity computational methods based on improvement distance, be used for solving The deficiency that certainly existing time series similarity computational methods exist.

To achieve these goals, the technical scheme that the present invention proposes is, the computational methods of a kind of time series similarity, It is characterized in that described method includes:

Step 1: respectively by two time serieses S to be compared₁And S₂It is divided into chronon sequence S in the same fashion₁ (i) and S₂(i)；Wherein, i=1,2 ..., n, n are the number of chronon sequence；

Step 2: set each chronon sequence S_jWeight w of (i)_i；Wherein, j=1,2, i=1,2 ..., n；

Step 3: calculate the distance between corresponding chronon sequence；

Step 4: according to the distance between corresponding chronon sequence and the weight of chronon sequence, calculates time series S₁ And S₂Similarity；

Described respectively by two time serieses S to be compared₁And S₂It is divided into chronon sequence S₁(i) and S₂I () is concrete It is:

Use and wait point seasonal effect in time series model split chronon sequence, if time series S₁Element number L₁It is the whole of n Several times, then by time series S₁Being divided into n section, each section is a chronon sequence, the element number of each chronon sequence For

If time series S₁Element number L₁It not the integral multiple of n, then by time series S₁Being divided into n section, each section is One chronon sequence, the element number of the 1st section to (n-1)th section is[] is rounding operation, the element number of n-th section ForOr, the element number of the 2nd section to n-th section is[] is rounding operation, the element of the 1st section Number is

If time series S₂Element number L₂It is the integral multiple of n, then by time series S₂Being divided into n section, each section is One chronon sequence, the element number of each chronon sequence is

If time series S₂Element number L₂It not the integral multiple of n, then by time series S₂Being divided into n section, each section is One chronon sequence, the element number of the 1st section to (n-1)th section is[] is rounding operation, the element number of n-th section ForOr, the element number of the 2nd section to n-th section is[] is rounding operation, the element of the 1st section Number is

Described each chronon sequence S_jWeight w of (i)_iAccording to formulaSet；Wherein, L_jI () is chronon Sequence S_jThe element number of (i), L_jFor time series S_jElement number, j=1,2, i=1,2 ..., n, n are the number of subsequence Mesh.

The described distance calculated between corresponding chronon sequence uses formula $d\left(S_1\right(i),S_2(i\left)\right)=\sqrt{\underset{p=1}{\overset{m}{\Σ}}{\left(S_1^p\right(i)-S_2^p(i\left)\right)}^2}+\mathrm{\σ};$ Wherein:

d(S₁(i),S₂(i)) it is corresponding chronon sequence S₁(i) and S₂Distance between (i)；

For chronon sequence S₁Pth the element of (i)；

For chronon sequence S₂Pth the element of (i)；

M is chronon sequence S₁(i) and S₂The element number of (i), i=1,2 ..., n；

σ is chronon sequence S₁(i) and S₂The standard deviation of the difference of i element that () is corresponding and $\mathrm{\σ}=\sqrt{\frac{1}{m}\underset{p=1}{\overset{m}{\Σ}}{\left(S_1^p\right(i)-S_2^p(i)-\mathrm{\μ})}^2};$

μ is chronon sequence S₁(i) and S₂The arithmetic average of the difference of i element that () is corresponding and $\mathrm{\μ}=\frac{1}{m}\underset{p=1}{\overset{m}{\Σ}}\left(S_1^p\right(i)-S_2^p(i\left)\right).$

Described calculating time series S₁And S₂Similarity use formula Wherein:

Sim(S₁,S₂) it is time series S₁And S₂Similarity；

d(S₁(i),S₂(i)) it is corresponding chronon sequence S₁(i) and S₂Distance between (i)；

w_iFor chronon sequence S₁(i) and S₂Weight between (i)；

N is the number of subsequence.

Time series is carried out equal or different length segmentation and arranges the weight of each chronon sequence, Ke Yiman by the present invention Actual similarity under the different situation of foot judges demand；It addition, the chronon sequence distance computational methods that the present invention provides, compare Tradition distance calculating method, can the shape similarity degree of preferably reflecting time sequence (i.e. time series local trend is different With), more meet mankind's daily experience and visual contrast, it is judged that more accurate；Finally, segmentation of the present invention calculate chronon sequence away from From, calculating similarity further according to subsequence distance, computation complexity is low, it is possible to realize the quick judgement of time series similarity.

Accompanying drawing explanation

Fig. 1 is the computational methods flow chart of the time series similarity that the present invention provides.

Detailed description of the invention

Below in conjunction with the accompanying drawings, preferred embodiment is elaborated.It is emphasized that the description below is merely exemplary Rather than in order to limit the scope of the present invention and application thereof.

Fig. 1 is the computational methods flow chart of the time series similarity that the present invention provides, as it is shown in figure 1, time series phase Include like the computational methods spent:

Step 1: respectively by two time serieses S to be compared₁And S₂It is divided into chronon sequence S in the same fashion₁ (i) and S₂(i)；Wherein, i=1,2 ..., n, n are the number of chronon sequence.

Concrete practical application request is judged, if the local similarity of time series day part is to time series according to similarity Global similarity influence degree is identical, then point seasonal effect in time series model split subsequence such as can use.By time series by long (if can not isometric divide equally, first or last chronon sequence length can not wait to spend the isometric n of being divided into a chronon sequence In other sub-sequence length).The concrete length value of each chronon sequence is relevant to time series feature, according to different field Time series fluctuating characteristic is arranged by the following method: seasonal effect in time series data value fluctuating margin is the least, and chronon sequence length takes It is worth the biggest；The time series that data value fluctuation is the most violent, chronon sequence length value is the least.Generally, chronon The length value of sequence is between 5-15.If time series global similarity is affected by the local similarity of time series day part Difference, the i.e. data of some (or several) period are relatively big on the impact of whole seasonal effect in time series similarity, other period data pair The impact of whole seasonal effect in time series similarity is less, then can use non-decile seasonal effect in time series model split chronon sequence.Ratio As, the independent segmentation of data of the one (or several) period bigger on the impact of whole Time Series Similarity, this (or several Individual) length of period is the length of this (or several) chronon sequence, and other period data of time series then press decile Seasonal effect in time series model split subsequence.

Illustrate with decile seasonal effect in time series model split subsequence below.If time series S₁(S₂) element Number L₁(L₂) be the integral multiple of n, then by time series S₁(S₂) it is divided into n section.Each section is a chronon sequence, Mei Geshi Between the element number of subsequence beSuch as, chronon sequence to be divided has 20 elements, i.e. acquires 20 The data of time point, will be divided into 5 chronon sequences, then can make 4 elements (data of time point) is one section, group Become chronon sequence, be like this just divided into 4 chronon sequences.

If time series S₁(S₂) element number L₁(L₂) not the integral multiple of n, then by time series S₁(S₂) it is divided into n Section, each section is a chronon sequence, and the element number of the 1st section to (n-1)th section is [] is for rounding fortune Calculating, the element number of n-th section isOr, the element number of the 2nd section to n-th section For[] is rounding operation, and the element number of the 1st section isAlso It is to have as a example by 20 elements by chronon sequence to be divided, if to be divided into 6 chronon sequences, then can make 1 section to the 5th section every section has 3 elements, and the 6th section is 5 elements；Or, the 2nd section can be made to have 3 elements to the 6th section every section, 1st section is 5 elements.

Step 2: set each chronon sequence S_jWeight w of (i)_i。

In the present invention, arranging its weight by the length scale of each chronon sequence, concrete grammar is: a chronon sequence Weight value be i.e. the ratio of length and whole length of time series of this chronon sequence.The power of chronon sequence s (i) Weight w_iComputational methods such as following formula:

w_i=L_j(i)/L_j (1)

In above formula (1), w_iIt it is chronon sequence S₁(i) and S₂The weight of (i), L_jI () is chronon sequence S_jThe element of (i) Number, namely chronon sequence S_jThe length of (i)；L_jFor time series S_jElement number, namely time series S_jLength, j =1,2, i=1,2 ..., n, n are the number of subsequence.

For using the chronon sequence of non-decile seasonal effect in time series model split, can be according to each chronon sequence pair The size of time series global similarity influence degree arranges the weight of each chronon sequence, the chronon that influence degree is the biggest Sequence weights value is the biggest, and the chronon sequence weights value that influence degree is the least is the least, but the span of weight to be made is (0,1), ensures that the weight sum of all chronon sequences of time series division gained is equal to 1, i.e. satisfied following constraint simultaneously:

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

In above formula (2), w_iIt it is chronon sequence S₁(i) and S₂I the weight of (), n is the number of chronon sequence.

Step 3: calculate the distance between corresponding chronon sequence.

Distance employing formula between the chronon sequence that calculating is corresponding:

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

In above-mentioned (3) formula, d (S₁(i),S₂(i)) it is corresponding chronon sequence S₁(i) and S₂Distance between (i),For chronon sequence S₁Pth the element of (i), i.e. time subsequence S₁The data of pth the time point of (i),For Chronon sequence S₂I pth the element of (), m is chronon sequence S₁(i) and S₂I the element number of (), σ is chronon sequence S₁ (i) and S₂The standard deviation of the difference of i element that () is corresponding, the computational methods of σ are as follows:

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

In above-mentioned (4) formula, μ is chronon sequence S₁(i) and S₂The arithmetic average of the difference of i element that () is corresponding, μ Computational methods as follows:

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

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

Step 4: according to the distance between corresponding chronon sequence and the weight of chronon sequence, calculates time series S₁ And S₂Similarity.

Calculate time series S₁And S₂Similarity use formula

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

In above-mentioned formula (6), Sim (S₁,S₂) it is time series S₁And S₂Similarity, d (S₁(i),S₂(i)) it is corresponding Chronon sequence S₁(i) and S₂Distance between (i), w_iFor chronon sequence S₁(i) and S₂I the weight of (), n is chronon sequence Number.

The present invention has a following remarkable advantage:

(1) this method carries out equal or different length segmentation according to the relation of time series local similarity with global similarity And the weight of each chronon sequence is set, judge demand meeting the actual similarity of different user.

(2) difference of time series segmentation length, it is possible to portray seasonal effect in time series similar trend journey under different time scales Degree, judges to provide the thickness granularity division for different demands for time series similarity, makes this method be provided with good Time multi-resolution characteristics.

(3) consider time series plesiomorphism factor, devise new chronon sequence distance computational methods, compare tradition Distance, new method can the shape similarity degree (i.e. the similarities and differences of time series local trend) of preferably reflecting time sequence, more accord with Close mankind's daily experience and visual contrast, it is judged that more accurate.

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

The above, the only present invention preferably detailed description of the invention, but protection scope of the present invention is not limited thereto, Any those familiar with the art in the technical scope that the invention discloses, the change that can readily occur in or replacement, All should contain within protection scope of the present invention.Therefore, protection scope of the present invention should be with scope of the claims It is as the criterion.

Claims (2)

1. computational methods for time series similarity, is characterized in that described method includes:

Step 1: respectively by two time serieses S to be compared₁And S₂It is divided into chronon sequence S in the same fashion₁(i) And S₂(i)；Wherein, i=1,2 ..., n, n are the number of chronon sequence；

Step 2: set each chronon sequence S_jWeight w of (i)_i；Wherein, j=1,2, i=1,2 ..., n；

Step 3: calculate the distance between corresponding chronon sequence；

Step 4: according to the distance between corresponding chronon sequence and the weight of chronon sequence, calculates time series S₁And S₂ Similarity；

Described respectively by two time serieses S to be compared₁And S₂It is divided into chronon sequence S₁(i) and S₂I () specifically:

Use and wait point seasonal effect in time series model split chronon sequence, if time series S₁Element number L₁It it is the integer of n Times, then by time series S₁Being divided into n section, each section is a chronon sequence, and the element number of each chronon sequence is

If time series S₁Element number L₁It not the integral multiple of n, then by time series S₁Being divided into n section, each section is one Chronon sequence, the element number of the 1st section to (n-1)th section is[] is rounding operation, and the element number of n-th section isOr, the element number of the 2nd section to n-th section is[] is rounding operation, the element number of the 1st section For

If time series S₂Element number L₂It is the integral multiple of n, then by time series S₂Being divided into n section, each section is one Chronon sequence, the element number of each chronon sequence is

If time series S₂Element number L₂It not the integral multiple of n, then by time series S₂Being divided into n section, each section is one Chronon sequence, the element number of the 1st section to (n-1)th section is[] is rounding operation, and the element number of n-th section isOr, the element number of the 2nd section to n-th section is[] is rounding operation, the element number of the 1st section For

Described each chronon sequence S_jWeight w of (i)_iAccording to formulaSet；Wherein, L_jI () is chronon sequence S_jThe element number of (i), L_jFor time series S_jElement number, j=1,2, i=1,2 ..., n, n are the number of subsequence；

The described distance calculated between corresponding chronon sequence uses formula Wherein:

d(S₁(i),S₂(i)) it is corresponding chronon sequence S₁(i) and S₂Distance between (i)；

For chronon sequence S₁Pth the element of (i)；

For chronon sequence S₂Pth the element of (i)；

M is chronon sequence S₁(i) and S₂The element number of (i), i=1,2 ..., n；

σ is chronon sequence S₁(i) and S₂The standard deviation of the difference of i element that () is corresponding and

μ is chronon sequence S₁(i) and S₂The arithmetic average of the difference of i element that () is corresponding and

Computational methods the most according to claim 1, is characterized in that described calculating time series S₁And S₂Similarity use public affairs FormulaWherein:

Sim(S₁,S₂) it is time series S₁And S₂Similarity；

d(S₁(i),S₂(i)) it is corresponding chronon sequence S₁(i) and S₂Distance between (i)；

w_iFor chronon sequence S₁(i) and S₂Weight between (i)；

N is the number of subsequence.