Method for classifying a time series, that includes a prescribable plurality of samples, with a computer

• US 6,226,549 B1
• Filed: 07/12/1999
• Issued: 05/01/2001
• Est. Priority Date: 06/21/1996
• Status: Expired due to Fees

• Current Assignee: Siemens AG
• Original Assignee: Siemens AG
• Inventors: Deco, Gustavo, Schittenkopf, Christian
• Primary Examiner(s): LAYNO, CARL HERNANDZ
• Application Number:
  US09/202,649
• Time in Patent Office: 659 Days
• Field of Search: 600/515, 600/516, 600/544
• US Class Current: 600/518
• CPC Class Codes: G06F 18/00 Pattern recognition
• CPC Class Codes: G06F 2218/12 Classification; Matching

Abstract

A method for classifying a time series, that includes a prescribable plurality of samples, with a computer wherein generalized correlation integral is determined for at least a part of samples of a time series. A functions family of an entropy function is determined from the values of the generalized correlation integral. A plurality of considered future samples is thereby employed as a family parameter of the functions family. The time series is classified into various types of characteristic processes from the curve of the functions family of the entropy function.

Claims

1. A method for the classification of a time series, comprising the steps of:

generating a signal representing a dynamic process;

sampling, using a sampler, the generated signal, producing a prescribable plurality of samples;

determining, using a computer, values c_t<sup>n,τ

,p,{circumflex over (N)},ε</sup>

of a generalized correlation integral for at least a part of the samples;

determining the value c_t<sup>n,τ

,p,{circumflex over (N)},ε</sup>

of the generalized correlation integral upon employment of preceding samples and future samples;

determining a functions family of an entropy function h(p, ε

) from the values c_t<sup>n,τ

,p,{circumflex over (N)},ε</sup>

of the generalized correlation integral, wherein the preceding samples and the future samples are respectively past and future samples in time with reference to the sample for which the value c_t<sup>n,τ

,p,{circumflex over (N)},ε</sup>

of the generalized correlation integral is respectively determined;

employing a plurality (p) of the steps to the future considered sample as family parameter of the functions family of the entropy function h(p,ε

);

employing a partition interval quantity (ε

) of a data space in which the samples can be located as a running variable of the functions family of the entropy function h(p,ε

); and

classifying the time series on the basis of the curve of the functions family of the entropy function h(p,ε

).

2. A method as claimed in claim 1, wherein the value c_t^n,τ

,p,{circumflex over (N)},ε

of the generalized correlation integral is respectively derived from a medium plurality of samples that are located in an environment of predetermined size around the sample for which the value c_t<sup>n,τ

,p,{circumflex over (N)},ε</sup>

of the generalized correlation integral is respectively determined.

3. A method as claimed in claim 2, wherein the size of the environment is dependent on the partition interval quantity (ε

).

4. A method as claimed in claim 1, wherein the respective value c_t^n,τ

,p,{circumflex over (N)},ε

of the generalized correlation integral is formed according to one of the following rules;

$\begin{array}{cc}\text{ <br><br> <br><br> <br><br> <br><br> <br><br> <br><br> <br><br> <br><br> <br><br>}<br><br>c_t^{n,\mathrm{\tau <br><br>},p,\hat{N},\mathrm{\varepsilon <br><br>}}=\frac{1}{\hat{N}}<br><br>\underset{\hat{t}=1}{\overset{\hat{N}}{\sum <br><br>}}<br><br>\mathrm{\Theta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(\frac{\mathrm{\varepsilon <br><br>}}{f}-<br><br>{\underset{\_}{x}}_t^{n,\mathrm{\tau <br><br>},p}-{\underset{\_}{x}}_{\hat{t}}^{n,\mathrm{\tau <br><br>},p}<br><br>\right),<br><br>\text{with}<br><br><br><br>\text{ <br><br> <br><br> <br><br> <br><br> <br><br> <br><br> <br><br> <br><br>}<br><br>{\underset{\_}{x}}_t^{n,\mathrm{\tau <br><br>},p}=\left(x_t,x_{t+\mathrm{\tau <br><br>}},\mathrm{\cdots <br><br>},x_{t+\left(n-1\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\tau <br><br>}},x_{t+\left(n-1+p\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\tau <br><br>}}\right),<br><br>\text{with <br><br> <br><br>}<br><br><br><br>\text{ <br><br> <br><br> <br><br> <br><br> <br><br> <br><br> <br><br> <br><br> <br><br> <br><br> <br><br> <br><br>}<br><br>\mathrm{\Theta <br><br>}<br><br>\left(z\right)=\{\begin{array}{cc}0<br><br>\text{;<br><br>}& z\le <br><br>0\\ 1<br><br>\text{;<br><br>}& z><br><br>0\end{array}<br><br>\text{, <br><br> <br><br>whereby}& \left(1\right)\end{array}$

x_t references the sample x_t of the time series at the time t,

τ

references the time interval that respectively lies between two samples x_t, x_t+1,

x_t+τ

references a sample of the time series at a time t+τ

,

n references a plurality of preceding samples taken into consideration,

p references the plurality of steps (time intervals) to the future sample taken into consideration,

x_t<sup>n,τ

,p</sup> references the sample vector,

f references an arbitrary number,

{circumflex over (t)} references a running index with which all sample vectors x_t<sup>n,τ

,p</sup> that are taken into consideration in the respectively employed, generalized correlation integral at the times {circumflex over (t)},

{circumflex over (N)} references a plurality of sample vectors x_t<sup>n,τ

,p</sup> that are taken into consideration in the respectively employed, generalized correlation integral,

ε

references the partition interval quantity of a data space in which the samples can be located,

Θ

(z) references a heavy side function, $\begin{array}{cc}{c}_t^{n,\mathrm{\tau <br><br>},p,\hat{N},\mathrm{\varepsilon <br><br>}}=\frac{1}{\hat{N}}<br><br>\underset{\hat{t}=1}{\overset{\hat{N}}{\sum <br><br>}}<br><br>\mathrm{\Theta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(\frac{\mathrm{\varepsilon <br><br>}}{f}-{<br><br>{\underset{\_}{x}}_t^{n,\mathrm{\tau <br><br>},p}-{\underset{\_}{x}}_{\hat{t}}^{n,\mathrm{\tau <br><br>},p}<br><br>}^m\right),& \left(2\right)\end{array}$

wherein m references an arbitrary number.

5. A method as claimed in claim 1, wherein the functions family of the entropy function h(p, ε

) is formed according to the following rule;

$\begin{array}{cc}h<br><br>\left(p,\mathrm{\varepsilon <br><br>}\right)=\frac{1}{\mathrm{\tau <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{n\to <br><br>\mathrm{\infty <br><br>}}{\lim }<br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{\hat{N}\to <br><br>\mathrm{\infty <br><br>}}{\lim }<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{1}{\hat{N}}<br><br>\underset{t=1}{\overset{\hat{N}}{\sum <br><br>}}<br><br>\log <br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{c_t^{n,\mathrm{\tau <br><br>},p,\hat{N},\mathrm{\varepsilon <br><br>}}}{c_t^{n-1,\mathrm{\tau <br><br>},l,\hat{N},\mathrm{\varepsilon <br><br>}}}.& \left(3\right)\end{array}$

6. A method as claimed in claim 1, wherein, in the classification, the time series is classified into one of a first time series type and a second time series type.

7. A method as claimed in claim 1, wherein the first time series type describes a time series in which a stochastic structure exists between the samples of the time series, and the second time series type describes a time series in which no stochastic structure exists between the samples of the time series.

8. A method as claimed in claim 1, wherein the partition interval quantity (ε

) with logarithmized scale is employed as a running variable of the functions family.

9. A method as claimed in claim 8, wherein the classification of the time series occurs according to at least one of the following criteria with respect to the curve of the functions family of the entropy function h(p, ε

);

when the curve is characterized by a substantially horizontal family of straight lines, then the time series is classified into a first time series type;

when the curve is characterized by a functions family that, for smaller partition interval quantities (ε

), exhibits a substantially horizontal family of straight lines and, with increasing partition interval quantities (ε

), exhibits a family of straight lines with positive slope after kink partition interval quantities (ε

′

), then the time series is classified into a second time series type;

when the curve for all future samples (p) is essentially characterized by a straight line with positive slope, then the time series is classified into a third time series type;

when the curve is essentially characterized by a family of straight lines with shifted straight lines with positive slope lying substantially parallel to one another, then the time series is classified into a fourth time series type.

10. A method as claimed in claim 1, wherein the step of generating the signal comprises the step of producing a measured electrocardiogram signal (ECG) which is used as the signal.

11. A method as claimed in claim 1, wherein the step of generating the signal comprises them step of producing a measured electroencephalogram signal (EEG) which is used as the signal.

12. A method as claimed in claim 1, wherein the step of generating the signal comprises the steps of:

producing a voltage curve representing a brain pressure; and

producing a measured signal from the voltage curve which is used as the signal.

13. A method as claimed in claim 1, wherein the step of generating the signal comprises the step of producing a measured signal proportional to rate curves of a financial market which is used as the signal.