Time Series Data Analyzer, And A Computer-Readable Recording Medium Recording A Time Series Data Analysis Program

• US 20110246144A1
• Filed: 04/02/2010
• Published: 10/06/2011
• Est. Priority Date: 04/02/2010
• Status: Active Grant

• Current Assignee: Yugen Kaisha Suwa Torasuto
• Original Assignee: Yugen Kaisha Suwa Torasuto
• Inventors: Tanaka, Yukio
• Granted Patent: US 8,296,108 B2
• Time in Patent Office: Days
• US Class Current: 703/2
• CPC Class Codes: A61B 5/316 Modalities, i.e. specific diagnostic methods
• CPC Class Codes: A61B 5/374 Detecting the frequency distribution of signals, e.g. detecting delta, theta, alpha, beta or gamma waves

Abstract

The inventor had proposed to use the value of the overall trend of the spectrum of electroencephalogram data as an indicator of the state of the subject on the basis of the findings that the spectrum of electroencephalogram data is an exponential spectrum and that the gradient changes depending on the state of the subject, but the respective states of a subject could not be identified by referring to the value of the gradient only.

To solve the problem, proposed is a time series data analyzer comprising a segment condition input section, an analysis condition input section, an optimum condition deriving section for analyzing each of all segments on the basis of the segment conditions and analysis conditions inputted in the respective input sections, under all analysis conditions by the maximum entropy method and the nonlinear least squares method, for selecting one appropriate segment and one appropriate analysis condition from all the analysis results, and for deriving the optimum segment length and the optimum lag value in correspondence to the selected results, and an analysis execution section for executing analysis by the maximum entropy method by setting the optimum analysis conditions derived as described above.

Claims

1. A time series data analyzer for analyzing the segments obtained from time series data, comprising

a segment condition input section, into which the shortest segment length, the longest segment length, and the total number of obtained segments including the shortest segment, the longest segment and the segments with different lengths ranging from the shortest segment length to the longest segment length, or each time step between the shortest segment and the longest segment are inputted as input items,

an analysis condition input section, into which the minimum lag value, the maximum lag value, and the intervals for setting the series of lag values between the minimum lag value and the maximum lag value are inputted as input items,

an optimum analysis condition deriving section, in which each of all the segments is analyzed on the basis of the segment conditions inputted in the segment condition input section and the analysis conditions inputted in the analysis condition input section, under all the analysis conditions by the maximum entropy method and the nonlinear least squares method, for selecting one appropriate segment and one appropriate analysis condition from all the analysis results and deriving the optimum segment length and the optimum lag value in correspondence to the selected results, and

an analysis execution section, in which the optimum analysis conditions derived by the optimum analysis condition deriving section are set as analysis conditions, for executing the analysis by the maximum entropy method.

2. A time series data analyzer, according to claim 1, wherein the optimum analysis condition deriving section, comprising

a setting processing means for obtaining multiple segments different in length from the time series data on the basis of the conditions inputted in the segment condition input section, to set the segments as sample segments and for reading the analysis conditions inputted in the analysis condition input section, to set the analysis conditions,

a first processing means for calculating the power spectral densities for each of all the sample segments set by the setting processing means, under all analysis conditions using the maximum entropy method,

a second processing means for extracting the dominant spectral peaks for the respective power spectral densities obtained by the first processing means, and calculating the respective quantities of the generalized trigonometric polynomial expressions about the sample segments from the dominant spectral peaks by the nonlinear least squares method, and

a third processing means for determining the validities of the generalized trigonometric polynomial expressions obtained by the second processing means for the sample segment data and the consistencies of the generalized trigonometric polynomial expressions for the power spectral densities, to select one sample segment corresponding to the generalized trigonometric polynomial expression high in validity and consistency, for deriving the segment length and the lag value corresponding to the sample segment as the optimum segment length and the optimum lag value.

3. A time series data analyzer, according to claim 2, wherein

the second processing means extracts the number of the dominant spectral peaks, and the respective peak frequencies and peak powers of the dominant spectral peaks from the power spectral densities calculated by the first processing means, to calculate the respective quantities of the generalized trigonometric polynomial expressions by calculation of the nonlinear least squares method for minimizing the sum of squares of residuals, with the abovementioned number as the number of terms, and with the inverse numbers of the respective peak frequencies as the initial values of the periods of respective trigonometric terms, and

the third processing means has

a first selection function for comparing the standard deviations of the residuals in the respective quantities of the generalized trigonometric polynomial expressions concerning the respective sample segments, with a set value, to reject the generalized trigonometric polynomial expressions, the standard deviations of which are not lower than the set value and to retain the other generalized trigonometric polynomial expressions as selection candidates,

a second selection function for comparing the periods of the respective terms of the polynomials decided by the nonlinear least squares method, with the initial values of the periods set from the inverse numbers of the peak frequencies of power spectral densities, to reject the generalized trigonometric polynomial expressions, for which the differences obtained as results of the comparison are not lower than a set value, and to retain the other generalized trigonometric polynomial expressions as selection candidates, and

a third selection function for comparing the powers obtained from the amplitudes of the respective terms of the polynomials decided by the nonlinear least squares method, with the powers of the peaks corresponding to power spectral densities pair by pair, to reject the generalized trigonometric polynomial expressions having the amplitudes, the differences of which obtained as results of the comparison are not lower than a set value, and to retain the other generalized trigonometric polynomial expressions as selection candidates, wherein

the processings by the first, second and third selection functions are performed one after another for selecting the generalized trigonometric polynomial expression(s) high in validity and consistency.

4. A time series data analyzer, according to claim 3, wherein the third processing means has a fourth selection function for selecting the generalized trigonometric polynomial expression smallest in the standard deviation of residuals in the case where multiple generalized trigonometric polynomial expressions remain as selection candidates after performing the processings by the first, second and third selection functions one after another.

5. A time series data analyzer, according to claim 3, wherein the third processing means has a fifth selection function for selecting the longest sample segment as the optimum sample segment in the case where multiple sample segments having the selected generalized trigonometric polynomial expression remain after performing the processings by the first, second and third selection functions to ensure that the sample segment selected by the fifth selection function can be selected as the optimum segment and that the lag value used for calculating the power spectral densities in correspondence to the selected generalized trigonometric polynomial expression can be selected as the optimum lag value for the sample segment.

6. A time series data analyzer, according to claim 4, wherein the third processing means has a fifth selection function for selecting the longest sample segment as the optimum sample segment in the case where multiple sample segments having the selected generalized trigonometric polynomial expression remain after performing the processings by the first, second, third and fourth selection functions, to ensure that the sample segment selected by the fifth selection function can be selected as the optimum segment and that the lag value used for calculating the power spectral densities in correspondence to the selected generalized trigonometric polynomial expression can be selected as the optimum lag value for the sample segment.

7. A time series data analyzer, according to claims 1, wherein the analysis execution section comprises

a segment preparation means for obtaining segments from the time series data on the basis of the optimum segment length derived by the optimum analysis condition deriving section and set in the analysis condition setting means,

a power spectral density calculation means for calculating the power spectral densities for the prepared segments by the maximum entropy method using the optimum lag value derived by the optimum analysis condition deriving section and set in the analysis condition setting means,

a peak extraction means for extracting the number of dominant peaks of the calculated power spectral densities, and the center frequencies and peak powers of the respective peaks, and

a characteristic quantity extraction means for extracting characteristic quantities from the extracted peak string.

8. A time series data analyzer, according to claim 7, wherein the peak extraction means extracts dominant peaks by a first processing of obtaining a locally prominent peak in each range as wide as several times the average interval between peaks obtained from all the peaks of power spectral densities, and fusing the obtained prominent peak with any adjacent peak within each interval shorter than the average interval, for forming a fused peak, and by a second processing of fusing all the peaks other than the prominent peaks and the fused peaks with the nearest prominent peak or fused peak respectively, wherein in the case where multiple peaks are fused, the peak powers prevailing before and after the fusion are conserved, and the center frequency of each fused peak is obtained in proportion to the peak powers of the multiple peaks existing before the fusion.

9. A time series data analyzer, according to claims 7, wherein the characteristic quantity extraction means comprises

a trend line calculation means for obtaining the gradient and y-intercept of the trend line of the so-called exponential spectrum by the linear least squares method for a set of the logarithmic peak power values and peak frequencies of the multiple dominant peaks extracted by the peak extraction means,

a relative power calculation means for obtaining relative power by dividing the peak power values of all the peaks obtained by the power spectral density calculation means, by the power values shown by the trend line, for normalization, and

a characteristic quantity calculation means for calculating characteristic quantities of the relative peak power distribution from the peaks discretely arranged on the frequency axis and the relative peak powers thereof.

10. A time series data analyzer, according to claim 7, wherein the time series data is electroencephalogram data, and the characteristic quantities extracted by the characteristic quantity extraction means include three frequencies at which the integrated value obtained by integrating the relative peak powers from the low frequency side in the frequency band of interest of the electroencephalogram spectrum usually ranging from 1 to 30 Hz or 0.5 to 30 Hz corresponds to 25%, 50% or 75% of the total relative peak power of the frequency band of interest.

11. A computer-readable recording medium recording a time series data analysis program, for analyzing the segments obtained from time series data, comprising

a step of inputting the shortest segment length, the longest segment length, and the total number of obtained segments including the shortest segment, the longest segment and the segments with different lengths ranging from the shortest segment length to the longest segment length, or each time step between the shortest segment and the longest segment, as input items,

a step of inputting the minimum lag value, the maximum lag value, and the intervals for setting the series of lag values between the minimum lag value and the maximum lag value, as input items,

a step of analyzing each of all the segments on the basis of the inputted segment conditions and the inputted analysis conditions, under all the analysis conditions by the maximum entropy method and the nonlinear least squares method, for selecting one appropriate segment and one appropriate analysis condition from all the analysis results and deriving the analysis conditions consisting of the optimum segment length and the optimum lag value in correspondence to the selected results, and

a step of setting the derived optimum analysis conditions as analysis conditions for executing the analysis by the maximum entropy method.

12. A computer-readable recording medium recording a time series data analyzing program, according to claim 11, wherein the step of deriving analysis conditions, comprising

a step of obtaining multiple segments different in length from the time series data on the basis of the inputted segment conditions and setting them as sample segments,

a step of setting analysis conditions,

a first processing step of calculating power spectral densities for each of all the set sample segments under all the set analysis conditions using the maximum entropy method,

a second processing step of extracting dominant spectral peaks for the respective power spectral densities obtained by the first processing step, and calculating the respective quantities of the generalized trigonometric polynomial expressions for the sample segments from the dominant spectral peaks by the nonlinear least squares method, and

a third processing step of determining the validities of the generalized trigonometric polynomial expressions obtained by the second processing step for the sample segment data and the consistencies of the generalized trigonometric polynomial expressions for the power spectral densities, to select one sample segment corresponding to the generalized trigonometric polynomial expression high in validity and consistency, and for deriving the segment length and the lag value corresponding to the selected sample segment, as the optimum segment length and the optimum lag value.

13. A compute-readable recording medium recording a time series data analysis program, according to claim 12, wherein

the second processing step has

a step of extracting the number of the dominant spectral peaks, and the peak frequencies and peak powers of the dominant spectral peaks from the power spectral densities calculated by the first processing step, and

a step of calculating the respective quantities of the generalized trigonometric polynomial expressions by calculation of the nonlinear least squares method for minimizing the sum of squares of residuals, with the abovementioned number as the number of terms, and with the inverse numbers of the respective peak frequencies as the initial values of the periods of respective trigonometric terms, and

the third processing step has

a first selection step of comparing the standard deviations of the residuals in the respective quantities of the generalized trigonometric polynomial expressions concerning the respective sample segments, with a set value, to reject the generalized trigonometric polynomial expressions, the standard deviations of which are not lower than the set value and to retain the other generalized trigonometric polynomial expressions as selection candidates,

a second selection step of comparing the periods of the respective terms of the polynomials decided by the nonlinear least squares method, with the initial values of the periods set from the inverse numbers of the peak frequencies of power spectral densities, to reject the generalized trigonometric polynomial expressions, for which the differences obtained as results of the comparison are not lower than a set value, and to retain the other generalized trigonometric polynomial expressions as selection candidates, and

a third selection step of comparing the powers obtained from the amplitudes of the respective terms of the polynomials decided by the nonlinear least squares method, with the powers of the peaks corresponding to power spectral densities pair by pair, to reject the generalized trigonometric polynomial expressions having the amplitudes, the differences of which obtained as results of the comparison are not lower than a set value, and to retain the other generalized trigonometric polynomial expressions as selection candidates, wherein

the processings by the first, second and third selection steps are performed one after another for selecting the generalized trigonometric polynomial expression(s) high in validity and consistency.

14. A computer-readable recording medium recording a time series data analysis program, according to claim 13, wherein the third processing step has a fourth selection step of selecting the generalized trigonometric polynomial expression smallest in the standard deviation of residuals in the case where multiple generalized trigonometric polynomial expressions remain as selection candidates after performing the processings by the first, second and third selection steps one after another.

15. A computer-readable recording medium recording a time series data analysis program, according to claim 13, wherein the third processing step has a fifth selection step of selecting the longest sample segment as the optimum sample segment in the case where multiple sample segments having the selected generalized trigonometric polynomial expression remain as selection candidates after performing the processings by the first, second and third selection steps, to ensure that the sample segment selected by the fifth selection step can be selected as the optimum segment and that the lag value used for calculating the power spectral densities in correspondence to the selected generalized trigonometric polynomial expression can be selected as the optimum lag value for the sample segment.

16. A computer-readable recording medium recording a time series data analysis program, according to claim 14, wherein the third processing step has a fifth selection step of selecting the longest sample segment as the optimum sample segment in the case where multiple sample segments having the selected generalized trigonometric polynomial expression remain as selection candidates after performing the processings by the first, second, third and fourth selection steps, to ensure that the sample segment selected by the fifth selection step can be selected as the optimum segment and that the lag value used for calculating the power spectral densities in correspondence to the selected generalized trigonometric polynomial expression can be selected as the optimum lag value for the sample segment.

17. A computer-readable recording medium recording a time series data analysis program, according to any one of claims 11, wherein the analysis execution step comprises

a segment preparation step of obtaining segments from the time series data on 45 the basis of the optimum segment length derived by the optimum analysis condition deriving step and set in the analysis condition setting means,

a power spectral density calculation step of calculating the power spectral densities for the prepared segments by the maximum entropy method using the optimum lag value derived by the optimum analysis condition deriving step and set in the analysis condition setting means,

a peak extraction step of extracting the number of dominant peaks of the calculated power spectral densities, and the center frequencies and peak powers of the respective peaks, and

a characteristic quantity extraction step of extracting characteristic quantities from the extracted peak string.

18. A computer-readable recording medium recording a time series data analysis program, according to claim 17, wherein the peak extraction step comprises

a first processing step comprising

a step of obtaining the average interval between peaks from all the peaks of power spectral densities,

a step of obtaining a locally prominent peak in each range as wide as several times the obtained average interval and

a step of fusing the obtained prominent peak with any adjacent peak within each interval shorter than the average interval for forming a fused peak, and

a second processing step of fusing all the peaks other than the prominent peaks and the fused peaks with the nearest prominent peak or fused peak respectively, wherein

in the first processing step and the second processing step, in the case where multiple peaks are fused, the peak powers prevailing before and after the fusion are conserved, and the center frequency of each fused peak is obtained in proportion to the peak powers of the multiple peaks existing before the fusion.

19. A computer-readable recording medium recording a time series data analysis program, according to any one of claims 17, wherein the characteristic quantity extraction step comprises

a trend line calculation step of obtaining the gradient and y-intercept of the trend line of the so-called exponential spectrum by the linear least squares method for a set of the logarithmic peak power values and peak frequencies of the multiple dominant peaks extracted by the peak extraction step,

a relative power calculation step of obtaining relative power by dividing the peak power values of all the peaks obtained by the power spectral density calculation means, by the power values shown by the trend line, for normalization, and

a characteristic quantity calculation step of calculating characteristic quantities of the relative peak power distribution from the peaks discretely arranged on the frequency axis and the relative peak powers thereof.

20. A computer-readable recording medium recording a time series data analysis program, according to claim 17, wherein the time series data is electroencephalogram data, and the characteristic quantities extracted by the characteristic quantity extraction step include three frequencies at which the integrated value obtained by integrating the relative peak powers from the low frequency side in the frequency band of interest of the electroencephalogram spectrum usually ranging from 1 to 30 Hz or 0.5 to 30 Hz corresponds to 25%, 50% or 75% of the total relative peak power of the frequency band of interest.