JP2007240779A - Time-series similarity scoring method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for stably digitizing and evaluating similarities by finding distances between complex frequencies of time series. <P>SOLUTION: An input section 100 acquires and samples time series s1(t) and s2(t) at prescribed time intervals Δt. Then a pole analysis section 102 takes pole analyses of the sampled time series according to a prescribed model. Then a complex frequency calculation section 104 obtains complex frequencies from results of the pole analyses. A distance calculation section 106 calculates the distance between the complex frequencies and a scoring section 108 evaluates the similarity between the time series based upon the distance. An output section 110 outputs the evaluation result in prescribed format. As a method of calculating the complex frequencies, there are a method using an all-pole models, a zero/pole model, etc. Thus, the similarity between the time series is evaluated based upon the distance between the complex frequencies to perform feature extraction which is tolerant of a phase shift and level variation. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a method for evaluating the degree of similarity between systems that generate each time series when a plurality of time series are given in the time series analysis. The time series is for digital signals such as electrical signals and audio signals that are stored inside the computer (temporarily or permanently).

Time series similarity assessment is generally difficult. Using a method of taking a cross-correlation between time series or power spectra P ₁ (f) and P ₂ (f) obtained by performing Fourier transform as shown in FIG.

However, these methods have a problem that they are vulnerable to the phase fluctuation of each frequency component constituting the time series and the level fluctuation of the time series itself. As a feature extraction method that is resistant to level fluctuations, a method using wavelet transformation and Merin transformation has been proposed (Patent Document 1). However, since features are extracted as image information, they are not suitable for scoring similarity. It is. In addition to this, a method of performing matching based on formant frequency distribution statistics has been proposed (Patent Document 2), but this is a Marubat type evaluation and does not evaluate the similarity by scoring.

Japanese Patent No. 3174777 Japanese Patent No. 3453130 JP 2005-249967 A

  In order to solve the above problem, the greatest feature is to characterize the time series using complex frequencies obtained by performing polar analysis and evaluate the similarity by obtaining the distance between the complex frequencies thus obtained.

  As a complex frequency calculation method, in addition to a method using an all-pole model, a method using a zero / pole model, a method using a linear prediction method, a complex frequency obtained by the method described in Patent Document 3 (frequency analysis method and apparatus) There are methods to use. Using the complex frequency information thus obtained, the similarity is evaluated by obtaining the distance between the complex frequencies.

  By the above method, the time series similarity can be stably quantified and evaluated.

  As shown in FIG. 2, the present invention maximizes the evaluation of similarity by characterizing a time series using complex frequencies obtained by performing polar analysis and obtaining the distance between the complex frequencies thus obtained. It is characterized by. FIG. 3 shows the correspondence between the time-series spectral representation and the complex frequency representation. Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

  4, 100 is an input unit, 102 is a polar analysis unit, 104 is a complex frequency calculation unit, 106 is a distance calculation unit, 108 is a scoring unit, and 110 is an output unit.

The time series s ₁ (t) and s ₂ (t) are acquired by the input unit 100, sampled at the sampling interval Δt, and the polar analysis unit 102 according to a model such as an all-pole model, a zero / pole model, or a linear prediction model. Polar analysis and transfer function with α _n and β _{n ″} as parameters

Parameters α _n and β _{n ″} are obtained for each of the time series s ₁ (t) and s ₂ (t), and parameters α _n and β _{n ″} are determined. Here, in the case of an all-pole model or a linear prediction model, N ″ = 0 and the order of β _{n ″} is zero, so it can be said that this corresponds to the case where β _{n ″} = 0. Assuming for obtaining the parameters α _n β _{n 'using} the following formula to parameters of a _n

Coefficients a _n , n = 1. . N sets of simultaneous equations

A _n , n = 1. . Using N, by relationship α _n = -a _n, the parameter alpha _n is determined. N is preferably a value of about 4 to 20 depending on the number of complex frequencies to be used for distance calculation.

Using the α _n thus obtained, the complex frequency calculation unit 104 uses the complex frequencies f _{1, n} = x _{1, n} + i _{1, n} , f _{2, n} = x _{2, n} + i y _{2, n} (n = 1... N ) Is calculated. These complex frequencies are obtained by factoring the denominator of the transfer function.

Obtained by. The distance calculation unit 106 uses the complex frequencies f _{1, n} and f _{2, n} obtained in this way.

In order to obtain the distance _, the ordering of the complex frequencies f _{1, n} and f _{2, n} is arranged in order from the smaller real part of each. Here, the complex frequencies f _{1, n} and f _{2, n} may be arranged excluding those having a negative real part. This is because the complex frequencies f _{1, n} and f _{2, n} always have complex conjugate pairs when the transfer function coefficient α _n is a real number. It is standard that m is 2. Using the distance L calculated by the distance calculation unit 106, the scoring unit 108 calculates the score S = deexp (−cL) (c> 0) and passes it to the output unit 110. Here, the score may be d = 1 when the highest score is 1, and d = 100 when the highest score is 100. The value of c may be small when the evaluation of similarity is desired to be sweet, and may be increased when it is desired to be severe. Usually, the reciprocal of the Nyquist frequency f _Ny is used to take c = f _Ny ^−m. Good.

  Referring to FIG. 5, reference numeral 200 denotes an input unit, 202 denotes a complex frequency calculation unit, 204 denotes a distance calculation unit, 206 denotes a scoring unit, and 208 denotes an output unit.

The time series s ₁ (t) and s ₂ (t) are acquired by the input unit 200, sampled at the sampling interval Δt, and the complex frequency f _{1, n} = x ₁ according to the method described in Patent Document 3 by the complex frequency calculation unit 202. _{, N} + iy1 _{, n} , f2 _{, n} = x2 _{, n} + iy2 _{, n} (n = 1... N) are calculated for each of the time series s ₁ (t) and s ₂ (t). The distance calculation unit 204 uses the complex frequencies f _{1, n} and f _{2, n} calculated in this way to calculate the distance.

However, in calculating the distance _, the ordering of the complex frequencies f _{1, n} and f _{2, n} is calculated using all possible combinations (permutation combinations), and the resulting L Among them, the smallest one is selected as the distance L. Using the distance L calculated by the distance calculation unit 204, the scoring unit 206 calculates the score S = deexp (−cL) (c> 0) and passes it to the output unit 208. Here, the score may be d = 1 when the highest score is 1, and d = 100 when the highest score is 100. The value of c is small when it is desired to make the evaluation of similarity low, and large when it is desired to be severe. Usually, the value of c is approximately c = f _Ny ^−m using the reciprocal of the Nyquist frequency f _Ny. Good.

  6, 300 is an input unit, 302 is a polar analysis unit, 304 complex frequency calculation unit, 306 is a distance calculation unit, 308 is a scoring unit, and 310 is an output unit.

The time series s ₁ (t) and s ₂ (t) are acquired by the input unit 300, sampled at a sampling interval Δt, and the pole analysis unit 302 follows a model such as an all-pole model, a zero / pole model, or a linear prediction model. Polar analysis and transfer function with α _n and β _{n ″} as parameters

For each of the time series s ₁ (t) and s ₂ (t). Here, in the case of an all-pole model or a linear prediction model, N ″ = 0. For example, if a linear prediction model is used, M is an integer of 1 or more, and

Coefficients a _n , n = 1. . N sets of simultaneous equations

Is obtained by solving With resulting alpha _n = -a _n this way, the complex frequency _f 1 in the complex frequency calculator _{304, n = x 1, n} + iy 1, n, f 2, n = x 2, n + iy 2, n (n = 1. Calculate N). These complex frequencies are obtained by factoring the denominator of the transfer function.

Obtained by. Among the complex frequencies f _{1, n} and f _{2, n} obtained in this way, the distance is calculated by the distance calculation unit 306 using the one satisfying the following conditions.
(A) | x |> b | y | (b> 0): The real part of the complex frequency is larger than b times the imaginary part. (B) | y | <b ′ (b ′> 0): Complex frequency There are four ways to consider that the imaginary part of is less than a certain constant value b ′, (a) only, (b) only, (a) and (b), (a) or (b) . As a method of selecting b and b ′, for example, there is a method in which 1 is set for b and Nyquist frequency is set for b ′.

For the time series s ₁ (t) and s ₂ (t), the number of complex frequencies satisfying the above condition will be expressed as N ₁ ′ and N ₂ ′. In general, the two values are different, but for the calculation of the distance, all possible combinations of the two are used, and | N ₁ '-N ₂ ' | N ₀ = min (N ₁ ′, N ₂ ′)

And the one having the smallest value is adopted as the distance L. Using the distance L calculated by the distance calculation unit 306, the scoring unit 308 calculates S = deexp (−cL) (c> 0) and passes it to the output unit 310. Here, the score may be d = 1 when the highest score is 1, and d = 100 when the highest score is 100. The value of c may be small if the evaluation of similarity is desired to be sweet, and may be increased if it is desired to be severe. Usually, the value of c should be approximately c = f _Ny ^−m using the reciprocal of the Nyquist frequency f _Ny. .

It is a figure for demonstrating the conventional method of integrating the difference of a power spectrum and evaluating similarity. It is a figure for demonstrating the method to evaluate the similarity in this invention. It is a figure which shows the correspondence of the time-series spectrum expression and complex frequency expression. It is a figure which shows the processing block which evaluates the similarity of a time series by 1st Example of this invention. It is a figure which shows the processing block which evaluates the similarity of a time series by the 2nd Example of this invention. It is a figure which shows the processing block which evaluates the similarity of a time series by the 3rd Example of this invention.

Explanation of symbols

100, 200, 300 Input unit 102, 302 Polar analysis unit 104, 202, 304 Complex frequency calculation unit 106, 204, 306 Distance calculation unit 108, 206, 308 Scoring unit 110, 208, 310 Output unit

Claims (9)

In the evaluation of the time series similarity of the time series s ₁ (t) and s ₂ (t), a set of complex frequencies f _{1, n} = x _{1, n} + ii _{1, n} , (n = 1. .N), N ≧ 1 and f _{2, n ′} = x _{2, n ′} + iy _{2, n ′} , (n ′ = 1... N ′), N ′ ≧ 1, and a set of these complex frequencies A time-series similarity scoring method characterized in that evaluation of time-series similarity is performed by using.   2. A time series similarity scoring method, wherein polar analysis is used to calculate a set of complex frequencies according to claim 1.   3. A time series similarity scoring method using an all-pole model or a zero / pole model for pole analysis according to claim 2.   A time series similarity scoring method using the complex frequency deriving method described in JP-A-2005-249967 for deriving the complex frequency set according to claim 1.   Scoring is performed using only complex frequencies satisfying the condition (a) | x |> b | y | (b> 0) among a group of complex frequencies which are elements of the set of complex frequencies according to claim 1. Or (b) scoring using only complex frequencies satisfying the condition | y | <b ′ (b ′> 0), or using only complex frequencies satisfying both conditions (a) and (b). Or scoring using only complex frequencies that satisfy either condition (a) or (b). Using the set of complex frequencies according to claim 1, N ₀ = min (N, N ′), and the distance L between the time series is

Or the time series similarity scoring method characterized by giving with this constant multiple.   7. A time series similarity scoring method using the distance L according to claim 6 and giving a time series similarity score S as S = exp (−cL) (c> 0) or a constant multiple thereof. _2. A time-series similarity scoring method, wherein the ordering of f1 _{, n} , f2 _{, n '} according to claim 1 is performed in the ascending order of each real part. The ordering of f _{1, n} , f _{2, n ′} according to claim 1 is performed by all possible combinations, and the distance L between the time series obtained by the method according to claim 6 according to each combination. Among them, a time series similarity scoring method characterized by adopting the smallest one as the distance L between time series.

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