Surgery – Diagnostic testing – Cardiovascular
Reexamination Certificate
1999-07-12
2001-05-01
Layno, Carl H. (Department: 3762)
Surgery
Diagnostic testing
Cardiovascular
C600S544000
Reexamination Certificate
active
06226549
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method wherein it is possible to distinguish between a process characterized by a time series that describes a white noise and a Markov process, and wherein it is also possible to distinguish between a chaotic process and a chaotic process with underlying noise.
2. Description of the Prior Art
Technical fields in which it is of interest to draw conclusions about the future behavior of a time series from a measured time series can be seen, for example, in various areas of medicine. The prediction of a future course of a time series usually occurs given the assumption that the time series exhibits non-linear correlations between the samples of the time series. For example, a specific area of application within medicine is cardiology. Specifically in the problem area of sudden cardiac death, it is critical to recognize the early warning signs of sudden cardiac death in order to initiate counter-measures against the occurrence of sudden cardiac death as early as possible.
It generally represents a considerable problem to classify a measured signal, particularly an electrical signal, and its samples, for example, in a purely chaotic process, a chaotic process with underlying noise, a process with white noise or a Markov process.
For example, document [1] discloses the determination of what is referred to as a Kolmogorov entropy. Further, this document discloses that a correlation function, that is explained in greater detail later, be formed.
It is known from documents [2], [3] to classify the time series into different types of time series on the basis of correlation integrals of the samples of the time series.
In these methods, however, the problem occurs that certain types of processes and, thus, types of time series cannot be discriminated. For example, it is not possible to distinguish with these methods between a process that is characterized by a time series that describes a white noise and a Markov process.
With this method, further, it also is not possible to distinguish between a chaotic process and a chaotic process with underlying noise.
SUMMARY OF THE INVENTION
The present invention is thus directed to a method for classifying a time series with which the above-described types of time series that cannot be classified with the known methods also can be correctly distinguished and classified.
According to the method of the present invention, an electrical signal is sampled and a generalized correlation integral is determined for an arbitrary plurality of samples upon employment of preceding samples and future samples. The preceding samples and future samples relate to the sample for which the correlation integral is respectively currently intended. A functions family of an entropy function is determined from the plurality of identified values of the generalized correlation integral for the various samples. Given the functions family, an arbitrary plurality of considered, future samples is employed as a family parameter of the functions family. A partition interval quantity of a data space in which the samples can be located is employed as a run variable of the functions family. The time series is classified on the basis of the characteristic course of the functions family of the entropy function.
This method now makes it possible to also distinguish a process having [. . . ] a time series with underlying white noise from a process having a time series with the characteristics of a Markov process. A discrimination between time series with which a chaotic process is described from time series with which a chaotic process with noise is described is also possible.
A very simple and fast determination of the values of the generalized correlation integral given the consideration of a respectively medium plurality of samples that are located around the sample in an environment having a prescribable size.
A further simplification of the method occurs when the size of the environment is selected dependent on the partition interval quantity.
Further, it is advantageous in a development of the method to accelerate the classification wherein the time series is only classified into a first time series type and into a second time series type. This development of the method makes it possible to merely investigate whether, for example, the time series describes a chaotic process or a chaotic process with noise. This development leads to a considerable saving of calculating time since other specific instances of time series need not be taken into further consideration in the investigation of the time series.
The method can be employed advantageously in various technical fields; for example, when the time series is a measured cardiogram signal, a measured electroencephalogram signal or, a measured signal with which a voltage curve of brain pressure is described [sic]. A very simple and dependable classification of the individual time series and their conclusions for characteristic properties of the signals is possible for these cases.
In an further embodiment of the method, it is provided that stochastic correlations in rate curves of a financial market be determined when the time series is established by such a rate curve. In this way, it is possible to make statements about possible future rate curves of a financial market.
Additional features and advantages of the present invention are described in, and will be apparent from, the Detailed Description of the Preferred Embodiments and the Drawings.
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Deco Gustavo
Schittenkopf Christian
Bell Boyd & Lloyd LLC
Layno Carl H.
Siemens Aktiengesellschaft
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