JP2007240779A - Time-series similarity scoring method - Google Patents

Time-series similarity scoring method Download PDF

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JP2007240779A
JP2007240779A JP2006061839A JP2006061839A JP2007240779A JP 2007240779 A JP2007240779 A JP 2007240779A JP 2006061839 A JP2006061839 A JP 2006061839A JP 2006061839 A JP2006061839 A JP 2006061839A JP 2007240779 A JP2007240779 A JP 2007240779A
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JP4728842B2 (en
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Fumihiko Ishiyama
文彦 石山
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Nippon Telegraph and Telephone Corp
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<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

本発明は、時系列解析において複数の時系列が与えられたとき、各時系列を生成するシステム間の類似度を評価する方法に関するものである。時系列は、電気信号や音声信号等をデジタル化し、計算機内部に(一時的にまたはパーマネントに)蓄えられたものを対象とする。   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).

時系列の類似度評価は一般的には難しい。時系列間の相互相関を取る方法や、図1に示すように、フーリエ変換を行って得られるパワースペクトルP(f),P(f)を用い、両者の差の積分 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.

Figure 2007240779
Figure 2007240779

を用いる方法などがあるが、これらは時系列を構成する各周波数成分の位相変動や、時系列自身のレベル変動に弱いという問題がある。レベル変動に強い特徴抽出方法としては、ウェーブレット変換とメリン変換とを用いる方法が提案されている(特許文献1)が、イメージ情報として特徴が抽出されることから、類似度のスコアリングには不向きである。このほか、ホルマント周波数分布統計によるマッチングを行う方法が提案されている(特許文献2)が、これはマルバツ式の評価であり、類似度を点数付けして評価するものとはなっていない。 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.

特許第3174777号公報Japanese Patent No. 3174777 特許第3453130号公報Japanese Patent No. 3453130 特開2005−249967号公報JP 2005-249967 A

上記課題の解決に、極解析を行って得られる複素周波数を用いて時系列を特徴づけ、こうして得られた複素周波数間の距離を求めることによって類似度を評価することを最大の特徴とする。   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.

複素周波数算出方法としては、全極モデルを用いる方法、零・極モデルを用いる方法、線形予測法を用いる方法の他、特許文献3(周波数解析方法および装置)記載の方法によって得られる複素周波数を用いる方法などがある。こうして得られる複素周波数の情報を用い、複素周波数間の距離を求めることによって類似度を評価する。   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.

上記の方法により、時系列の類似度を安定的に数値化して評価することができる。   By the above method, the time series similarity can be stably quantified and evaluated.

本発明は、図2に示すように、極解析を行って得られる複素周波数を用いて時系列を特徴づけ、こうして得られた複素周波数間の距離を求めることによって類似度を評価することを最大の特徴とする。図3は、時系列のスペクトル表現と複素周波数表現の対応関係を示している。以下、図面を参照しながら本発明の実施形態について詳細に説明する。   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.

図4を参照して、100は入力部、102は極解析部、104は複素周波数算出部、106は距離計算部、108はスコアリング部、110は出力部である。   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.

入力部100で時系列s(t),s(t)を取得し、サンプリング間隔Δtでサンプリングし、極解析部102で、全極モデル、零・極モデル、線形予測モデル等のモデルに従って極解析を行い、αとβn”をパラメーターとする伝達関数 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

Figure 2007240779
Figure 2007240779

のパラメーターαとβn”を時系列s(t),s(t)のそれぞれに対して求め、パラメーターαとβn”を決定する。ここで、全極モデル、線形予測モデルであれば、N”=0となり、βn”の次数が零であることから、βn”=0とする場合に対応するともいえる。例えば全極モデルを用いてパラメーターαとβn’を求めるものとすれば、aをパラメーターとする次の式 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

Figure 2007240779
Figure 2007240779

により与えられるEを最小とするような係数a,n=1..Nの組を、連立方程式 Coefficients a n , n = 1. . N sets of simultaneous equations

Figure 2007240779
Figure 2007240779

を解くことによって得られるa,n=1..Nを用いて、α=−aという関係により、パラメーターαが求まる。Nは、距離算出に用いたい複素周波数の数に応じて4〜20程度の値とするのがよい。 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.

こうして得られるαを用い、複素周波数算出部104で複素周波数f1,n=x1,n+iy1,n,f2,n=x2,n+iy2,n(n=1..N)を算出する。これらの複素周波数は、上記伝達関数の分母を因数分解して得られる式 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.

Figure 2007240779
Figure 2007240779

によって得られる。こうして得られる複素周波数f1,nとf2,nを用いて距離算出部106で距離 Obtained by. The distance calculation unit 106 uses the complex frequencies f 1, n and f 2, n obtained in this way.

Figure 2007240779
Figure 2007240779

を求めるが、距離を求めるにあたり、複素周波数f1,nとf2,nの順番付けを、それぞれの実部の小さい方から順に並べるという形にするものとする。ここで、複素周波数f1,nとf2,nは、実部が負となるものを除外して並べてもよい。複素周波数f1,nとf2,nは、伝達関数の係数αが実数である場合、必ず複素共役なペアを持つからである。mは2とするのが標準的である。距離算出部106で算出された距離Lを用い、スコアリング部108でスコアS=dexp(−cL)(c>0)を算出し、出力部110に渡す。ここで、スコアは、最高点を1とする場合はd=1とし、最高点を100とする場合にはd=100とするなどすればよい。cの値は、類似度の評価を甘くしたい場合には小さく、厳しくしたい場合は大きくすればよいが、通常はナイキスト周波数fNyの逆数を用いて、c=fNy −m程度にとるのがよい。 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.

図5を参照して、200は入力部、202は複素周波数算出部、204は距離算出部、206はスコアリング部、208は出力部である。   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.

入力部200で時系列s(t)とs(t)を取得し、サンプリング間隔Δtでサンプリングし、複素周波数算出部202で特許文献3記載の方法に従って複素周波数f1,n=x1,n+iy1,n,f2,n=x2,n+iy2,n(n=1..N)を時系列s(t)とs(t)のそれぞれに対して算出する。こうして算出される複素周波数f1,nとf2,nを用いて距離算出部204で距離 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.

Figure 2007240779
Figure 2007240779

を算出するが、距離を算出するにあたり、複素周波数f1,nとf2,nの順番付けを、全ての可能な組み合わせ(順列組み合わせ)を用いてLを算出し、そうして得られるLのうち、最も小さなものを距離Lとして選ぶ。距離算出部204で算出された距離Lを用い、スコアリング部206でスコアS=dexp(−cL)(c>0)を算出し、出力部208に渡す。ここで、スコアは、最高点を1とする場合はd=1とし、最高点を100とする場合にはd=100とするなどすればよい。cの値は、類似度の評価を甘くしたい場合には小さく、厳しくしたい場合には大きくとればよいが、通常はナイキスト周波数fNyの逆数を用いてc=fNy −m程度にとるのがよい。 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.

図6を参照して、300は入力部、302は極解析部、304複素周波数算出部、306は距離計算部、308はスコアリング部、310は出力部である。   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.

入力部300で時系列s(t),s(t)を取得し、サンプリング間隔Δtでサンプリングし、極解析部302で、全極モデル、零・極モデル、線形予測モデル等のモデルに従って極解析を行い、αとβn”をパラメーターとする伝達関数 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

Figure 2007240779
Figure 2007240779

を時系列s(t),s(t)のそれぞれに対して求める。ここで、全極モデル、線形予測モデルであれば、N”=0となる。例えば線形予測モデルを用いるものとすれば、Mを1以上の整数とし、次の式 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

Figure 2007240779
Figure 2007240779

により与えられるEを最小とするような係数a,n=1..Nの組を、連立方程式 Coefficients a n , n = 1. . N sets of simultaneous equations

Figure 2007240779
Figure 2007240779

を解くことによって得る。こうして得られるα=−aを用い、複素周波数算出部304で複素周波数f1,n=x1,n+iy1,n,f2,n=x2,n+iy2,n(n=1..N)を算出する。これらの複素周波数は、上記伝達関数の分母を因数分解して得られる式 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.

Figure 2007240779
Figure 2007240779

によって得られる。こうして得られる複素周波数f1,nとf2,nのうち、以下の条件を満たすものを用いて距離算出部306で距離を求める。
(a)|x|>b|y|(b>0):複素周波数の実部が、その虚部のb倍より大きい
(b)|y|<b’(b’>0):複素周波数の虚部が、ある一定値b’より小さい
条件成立とみなす方法としては、(a)のみ、(b)のみ、(a)and(b)、(a)or(b)の4通りがある。b,b’の選び方としては、例えばbについては1とし、b’についてはナイキスト周波数を目安とする方法がある。
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 ′.

時系列s(t),s(t)とについて、上記の条件を満たす複素周波数の数をN’,N’と表記することにする。一般に両者は異なる値となるが、距離の算出には、両者の可能な全ての組み合わせを用い、対を作らない|N’−N’|個の複素周波数については、距離の計算に用いないものとして、N=min(N’,N’)として、 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 ′)

Figure 2007240779
Figure 2007240779

を計算し、そのうち最も小さい値をとるものを、距離Lとして採用するものとする。距離算出部306で算出された距離Lを用い、スコアリング部308でS=dexp(−cL)(c>0)を算出し、出力部310に渡す。ここで、スコアは、最高点を1とする場合はd=1とし、最高点を100とする場合にはd=100とするなどすればよい。cの値は、類似度の評価を甘くしたい場合には小さく、厳しくしたい場合は大きくすればよいが、通常はナイキスト周波数fNyの逆数を用いてc=fNy −m程度にとるのがよい。 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. .

パワースペクトルの差分を積分して類似度を評価する従来の手法を説明するための図である。It is a figure for demonstrating the conventional method of integrating the difference of a power spectrum and evaluating similarity. 本発明における類似度を評価する方法を説明するための図である。It is a figure for demonstrating the method to evaluate the similarity in this invention. 時系列のスペクトル表現と複素周波数表現の対応関係を示す図である。It is a figure which shows the correspondence of the time-series spectrum expression and complex frequency expression. 本発明の第1の実施例による時系列の類似度を評価する処理ブロックを示す図である。It is a figure which shows the processing block which evaluates the similarity of a time series by 1st Example of this invention. 本発明の第2の実施例による時系列の類似度を評価する処理ブロックを示す図である。It is a figure which shows the processing block which evaluates the similarity of a time series by the 2nd Example of this invention. 本発明の第3の実施例による時系列の類似度を評価する処理ブロックを示す図である。It is a figure which shows the processing block which evaluates the similarity of a time series by the 3rd Example of this invention.

符号の説明Explanation of symbols

100,200,300 入力部
102,302 極解析部
104,202,304 複素周波数算出部
106,204,306 距離算出部
108,206,308 スコアリング部
110,208,310 出力部
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)

時系列s(t)とs(t)の時系列類似度の評価において、それぞれの時系列について複素周波数の組f1,n=x1,n+iy1,n,(n=1..N),N≧1とf2,n’=x2,n’+iy2,n’,(n’=1..N’),N’≧1とを算出し、それら複素周波数の組を用いて時系列類似度の評価を行うことを特徴とする時系列類似度スコアリング方法。 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. 請求項1記載の複素周波数の組の算出に極解析を用いることを特徴とする時系列類似度スコアリング方法。   2. A time series similarity scoring method, wherein polar analysis is used to calculate a set of complex frequencies according to claim 1. 請求項2記載の極解析に全極モデルまたは零・極モデルを用いることを特徴とする時系列類似度スコアリング方法。   3. A time series similarity scoring method using an all-pole model or a zero / pole model for pole analysis according to claim 2. 請求項1記載の複素周波数の組の導出に特開2005−249967号記載の複素周波数導出方法を用いることを特徴とする時系列類似度スコアリング方法。   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. 請求項1記載の複素周波数の組の要素である一群の複素周波数のうち、(a)|x|>b|y|(b>0)なる条件を満たす複素周波数のみを用いてスコアリングを行う、または(b)|y|<b’(b’>0)なる条件を満たす複素周波数のみを用いてスコアリングを行う、または(a),(b)両条件を同時に満たす複素周波数のみを用いてスコアリングを行う、または(a),(b)どちらかの条件を満たす複素周波数のみを用いてスコアリングを行うことを特徴とする時系列類似度スコアリング方法。   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). 請求項1記載の複素周波数の組を用い、N=min(N,N’)とし、時系列間の距離Lを、
Figure 2007240779
もしくはこの定数倍をもって与えることを特徴とする時系列類似度スコアリング方法。
Using the set of complex frequencies according to claim 1, N 0 = min (N, N ′), and the distance L between the time series is
Figure 2007240779
Or the time series similarity scoring method characterized by giving with this constant multiple.
請求項6記載の距離Lを用い、時系列類似度のスコアSをS=exp(−cL)(c>0)、もしくはこの定数倍として与えることを特徴とする時系列類似度スコアリング方法。   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. 請求項1記載のf1,n,f2,n’の順番付けを、それぞれの実部の小さい順で行うことを特徴とする時系列類似度スコアリング方法。 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. 請求項1記載のf1,n,f2,n’の順番付けを、すべての可能な組み合わせによって行い、それぞれの組み合わせに応じて請求項6記載の方法によって得られる時系列間の距離Lのうち、最も小さなものを時系列間の距離Lとして採用することを特徴とする時系列類似度スコアリング方法。
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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