CN105550698B - Novel gray correlation classifier design method - Google Patents

Novel gray correlation classifier design method Download PDF

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CN105550698B
CN105550698B CN201510901370.7A CN201510901370A CN105550698B CN 105550698 B CN105550698 B CN 105550698B CN 201510901370 A CN201510901370 A CN 201510901370A CN 105550698 B CN105550698 B CN 105550698B
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sequence
correlation
resolution
difference
coefficient
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CN105550698A (en
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王生
李靖超
冯云鹤
曹曼琳
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Shanghai Dianji University
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    • G06F18/24—Classification techniques
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Abstract

The invention provides a design method of a novel grey correlation classifier, which comprises the following steps: designing a gray correlation classifier by using a gray correlation algorithm; and normalizing and equalizing the initial value images of each sequence of the behavior of the system, and endowing different resolution coefficients for different signals, so that the constraint capability of the resolution coefficients is enhanced by using the self-adaptive resolution coefficients.

Description

Novel gray correlation classifier design method
Technical Field
The invention relates to the field of electronic countermeasure, signal identification and classifier design, in particular to a novel gray correlation classifier design method.
Background
Nowadays, with the continuous improvement of anti-reconnaissance and anti-interference technologies, the complexity of a communication system and the continuous increase of noise, the individual difference of signals is gradually reduced, and the traditional template comparison method is difficult to complete the individual identification task of a radiation source. How to realize the identification and classification of the radiation source signals under the environment of low unstable signal-to-noise ratio becomes very important for the design and selection of the classifier. The classifier is designed to perform corresponding judgment according to the extracted signal characteristics, so that classification and identification of objects such as signals are realized. The extracted signal features are classified by utilizing a gray correlation classifier, the feature extraction performance of the algorithm is judged by identifying results of different modulation signals under low signal to noise ratio, and the effectiveness of the improved algorithm is verified.
In the traditional grey correlation analysis, uncertain signals with known partial features, unknown partial features and small samples are taken as research objects, favorable information is extracted, and the identification and classification of the signals are realized. On the basis, a batch of novel correlation degree analysis methods are improved. Such as adaptive entropy weight grey correlation degree, generalized absolute correlation degree, T-type correlation degree and grey slope correlation degree.
The novel several typical correlation models are the Duncus correlation, the generalized absolute correlation, the T-type correlation and the gray slope correlation. However, most of the existing models are not ideal, and often do not meet the constraint conditions specified by the four axioms of grey correlation. The Duncus relation and the generalized absolute relation reflect the similarity of development process or magnitude between two sequences by using displacement difference. For the traditional Duncai grey correlation classifier, the anti-noise capability is relatively poor, and the identification effect is difficult to achieve under the condition of a low signal-to-noise ratio; the T-type relevance reflects the development trends of the two sequences by using a speed ratio, the slope relevance reflects the similarity of the development trends or curve shapes of the two sequences by using a speed difference, however, the non-dimensionalization process of the original data actually changes the proportion of the curve, so the slope relevance does not meet the normative; the type B correlation comprehensively utilizes the displacement difference, the speed difference and the acceleration difference to reflect the similarity and the similarity of two sequence curves, and focuses on the overall analysis. And the recognition rate of the above models for the signal loaded with the signal-to-noise ratio is not high.
Disclosure of Invention
The invention aims to solve the technical problem that the defects exist in the prior art, and provides a novel classifier design method based on a gray correlation theory.
In order to achieve the above technical object, according to the present invention, there is provided a novel gray-associated classifier design method, including: the first step is as follows: designing a gray correlation classifier by using a gray correlation algorithm; the second step is as follows: and normalizing and equalizing the initial value images of each sequence of the behavior of the system, and endowing different resolution coefficients for different signals, so that the constraint capability of the resolution coefficients is enhanced by using the self-adaptive resolution coefficients.
Preferably, the first step comprises:
first, the initial image of each sequence of behavior of the system is calculatedx'i：
Figure BDA0000871458350000021
Wherein i is 0,1,2, …, m represents the category of the known signals to be compared in the database, and n represents the number of the signal features;
next, a sequence of difference values is calculated:
Δxi(k)＝x'0(k)-x'i(k),Δxi＝(Δxi(1),Δxi(2),…,Δxi(n)),i＝1,2,…,m
where k is 1,2, …, and n represents the kth characteristic of the signal.
Thirdly, calculating the maximum difference M and the minimum difference M of the difference value sequence:
Figure BDA0000871458350000022
thirdly, a correlation coefficient value gamma is calculated0i(k)：
Figure BDA0000871458350000031
Finally, the correlation value gamma between the sequences is calculated0i：
Figure BDA0000871458350000032
Preferably, the second step includes:
to the primary value like x'iThe following treatments were carried out:
Figure BDA0000871458350000033
wherein the content of the first and second substances,
Figure BDA0000871458350000034
mean value of the sequence, i-0, 1,2, …, m representing the class of known signals to be compared in the database, n representing the signal to be comparedThe number of signal features;
processing the resolution coefficient rho as follows:
calculating the mean value Delta of all the absolute values of the differencesV：
Figure BDA0000871458350000035
Δmax＝max|x′0(k)-x′i(k)|
Note the book
Figure BDA0000871458350000036
Obtaining:
Figure BDA0000871458350000037
the value of the resolution coefficient rho is obtained as follows:
Figure BDA0000871458350000038
then, the resolution coefficients ρ are averaged:
Figure BDA0000871458350000039
then substituting the resolution coefficient rho into the following formula, and combining the Lagrange median theorem to stably solve the correlation coefficient to obtain a new correlation coefficient gamma0i(k) Solving:
Figure BDA0000871458350000041
from this, a correlation value gamma between the sequences is calculated0i。
In summary, in view of the above disadvantages in the related research in the past, the present invention provides a novel adaptive gray-scale correlation classifier design algorithm for signals generated under different signal-to-noise ratios, which utilizes the equalization of the initial value image to enhance the signal normalization of the loaded signal-to-noise ratio, and enhances the constraint and rationalization of the discrimination coefficient, thereby changing the correlation coefficient, improving the adaptive capacity of the classifier, and achieving the purpose of accurately identifying the signals under different signal-to-noise ratios.
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A more complete understanding of the present invention, and the attendant advantages and features thereof, will be more readily understood by reference to the following detailed description when considered in conjunction with the accompanying drawings wherein:
FIG. 1 schematically illustrates a flow diagram of a novel gray-associated classifier design method in accordance with a preferred embodiment of the present invention.
Fig. 2 schematically shows the recognition rate of a grey correlation algorithm according to the prior art.
Fig. 3 schematically shows the recognition rate of an improved gray correlation algorithm according to a preferred embodiment of the present invention.
It is to be noted, however, that the appended drawings illustrate rather than limit the invention. It is noted that the drawings representing structures may not be drawn to scale. Also, in the drawings, the same or similar elements are denoted by the same or similar reference numerals.
Detailed Description
In order that the present disclosure may be more clearly and readily understood, reference will now be made in detail to the present disclosure as illustrated in the accompanying drawings.
The invention strengthens the standardization and self-adaption capability of the grey correlation classifier, and firstly provides a design method of a common grey correlation classifier. And then, normalizing and equalizing the initial value image, and enhancing the constraint capability of the resolution coefficient. Finally, the self-adaptive capacity of the gray correlation classifier can be improved by utilizing an entropy weight algorithm, and a technical method of the novel gray correlation classifier is provided.
The basic idea of the grey correlation theory is a method for quantitatively describing and comparing the change and development situation of a system. Assume that the row sequence of the system is:
X0＝(x0(1),x0(2),…,x0(n))
X1＝(x1(1),x1(2),…,x1(n))
……
Xi＝(xi(1),xi(2),…,xi(n))
……
Xm＝(xm(1),xm(2),…,xm(n)) (1)
wherein, X0Representing a reference sequence, i.e. a signal to be identified, X1,X2,…,XmRepresents a comparison sequence, wherein i is 0,1,2, …, m represents the class of known signals to be compared in the database, and n represents the number of signal features.
Order:
Figure BDA0000871458350000051
Figure BDA0000871458350000052
where ρ ∈ (0,1) is defined as the resolution factor, usually 0.5. γ (X)0,Xi) Is referred to as X0And XiGray correlation of (2), often abbreviated as γ0iK-point correlation coefficient γ (x)0(k),xi(k) Abbreviated as γ)0i(k)。
Due to the complexity of the communication environment and the presence of various noises, the extracted features have large fluctuation and are difficult to express by a uniform correlation coefficient. It is difficult to classify with the common gray correlation algorithm and therefore the present invention proposes to use a new type of gray correlation for identification.
Compared with a common gray correlation algorithm, the method can accurately determine an initial value image. The invention utilizes the comprehensive equalized initial value image and the self-adaptive resolution coefficient, thereby improving the self-adaptive capacity and the constraint capacity of the correlation coefficient and improving the self-adaptive capacity of the classifier. The method has better identification capability on signals with fluctuation under different signal-to-noise ratios. Meanwhile, the method has obvious effect on solving the grey correlation degree by applying the correlation coefficient.
FIG. 1 schematically illustrates a flow diagram of a novel gray-associated classifier design method in accordance with a preferred embodiment of the present invention.
As shown in fig. 1, the method for designing a novel gray-associated classifier according to the preferred embodiment of the present invention includes:
first step S1: designing a gray correlation classifier by using a gray correlation algorithm; here a common grey correlation algorithm is used.
The specific calculation process is as follows:
1. first, the primary values of the sequences of behavior of the system are computed as x'iNamely:
Figure BDA0000871458350000061
where i is 0,1,2, …, m indicates the class of the known signals to be compared in the database, and n indicates the number of signal features.
2. Next, a sequence of difference values is calculated, namely:
Δxi(k)＝x'0(k)-x'i(k),Δxi＝(Δxi(1),Δxi(2),…,Δxi(n)),i＝1,2,…,m(5)
k is 1,2, …, and n represents the kth characteristic of the signal.
3. Thirdly, calculating the maximum difference M and the minimum difference M of the difference value sequence, namely:
Figure BDA0000871458350000062
4. thirdly, a correlation coefficient value gamma is calculated0i(k) Namely:
Figure BDA0000871458350000063
5. finally, the correlation value gamma between the sequences is calculated0iNamely:
Figure BDA0000871458350000064
then gamma is0iThe degree of association between the sequences, i.e., the degree of similarity between the sequences, is indicated.
Second step S2: normalizing and equalizing initial value images of each sequence of the behavior of the system, and endowing different resolution coefficients for different signals, so that the constraint capability of the resolution coefficients is enhanced by using self-adaptive resolution coefficients;
the specific treatment is as follows:
for the primary value defined in formula (4) like x'iThe following treatments were carried out:
Figure BDA0000871458350000071
wherein the content of the first and second substances,
Figure BDA0000871458350000072
the mean value of the sequence is represented, i is 0,1,2, …, m represents the class of known signals to be compared in the database, and n represents the number of signal features.
The resolution coefficient ρ defined in equation (7) is processed as follows:
calculating the mean value Delta of all the absolute values of the differencesVNamely:
Figure BDA0000871458350000073
Δmax＝max|x′0(k)-x′i(k)| (11)
note the book
Figure BDA0000871458350000074
Namely:
Figure BDA0000871458350000075
the value of the resolution coefficient ρ is:
Figure BDA0000871458350000076
then, taking the mean value of the resolution coefficient rho:
Figure BDA0000871458350000077
substituting the resolution coefficient rho into a formula (15) and stably solving the correlation coefficient by combining the Lagrange median theorem to obtain a new correlation coefficient gamma0i(k) Solving:
Figure BDA0000871458350000078
finally, calculating the correlation value gamma between the sequences0i。
The selection of the resolution factor has a great influence on the correlation degree, and the selection of the resolution factor accords with the following principle: the integrity of the correlation degree is fully embodied, namely the correlation degree is not only related to the two groups of sequences of the reference sequence and the comparison sequence, but also related to other comparison sequences; the method has the anti-interference effect, namely, when an abnormal value occurs in the observation sequence of the system factor, the influence of the abnormal value on the correlation degree can be weakened and inhibited. Since the resolution coefficient ρ is uniformly set to 0.5 in the solution of the correlation degree of the common gray, the difficulty of identification increases for different signals. Different signals are therefore given different resolution coefficients p, so that the adaptivity of the correlation coefficients is improved.
< specific examples >
First, 100 samples are reconstructed for 6 different analog and digital modulation signals, and six different intensity signal-to-noise ratios are applied. The novel self-adaptive gray correlation classifier design method provided by the invention is utilized to identify signals under different signal-to-noise ratios, and is compared with the identification results of the self-adaptive entropy weight gray correlation classifier and the common gray correlation algorithm, and the results are shown in table 1.
TABLE 1 recognition rates of 3 classifier design algorithms at different SNR
Figure BDA0000871458350000081
As can be seen from the identification results of Table 1 and FIGS. 2 and 3, the improved gray correlation algorithm provided by the present invention has a significant identification effect at a signal-to-noise ratio of 20 dB; when the signal-to-noise ratio is gradually reduced, the recognition rates of the adaptive entropy weight gray correlation classifier and the common gray correlation algorithm are reduced quickly, and compared with the novel gray correlation algorithm provided by the invention, the recognition rates of the adaptive entropy weight gray correlation classifier and the common gray correlation algorithm are higher under different signal-to-noise ratios.
In summary, the prior art method generally directly performs an initial value image on a signal, and has large curve proportion change and low normalization degree. And because the resolution coefficient rho is generally set to be 0.5, noise generates a volatility to signals, and the signals loaded with different signal-to-noise ratios are difficult to achieve better discrimination. Aiming at the defect of the prior art, the technical scheme provided by the invention utilizes an improved self-adaptive gray correlation classifier design algorithm to identify the signal characteristics under noise, and improves the resolution coefficient and the correlation coefficient through initial value image equalization. Therefore, the self-adaptive capacity of the signal recognition device is improved, and the aim of recognizing signals under different signal to noise ratios is fulfilled.
The invention provides a novel self-adaptive gray correlation classifier method, which has the advantages that the identification and the distinction of signals under the signal-to-noise ratio can be improved, common signals have a plurality of characteristics, and the plurality of characteristics jointly determine the dynamic trend of one signal, so the relationship among the characteristics needs to be distinguished. The invention selects the primary and secondary degrees of the signal characteristics by averaging the initial value image and improving the resolution coefficient and the correlation coefficient, improves the self-adaptive capacity of the self-adaptive gray correlation classifier, and has obvious effect on the environment with complicated communication and low signal-to-noise ratio. The classifier method has a great application value in the identification and classification of signals. And is suitable for various calculations for solving gray correlation by using the resolution coefficient.
In addition, it should be noted that the terms "first", "second", "third", and the like in the specification are used for distinguishing various components, elements, steps, and the like in the specification, and are not used for indicating a logical relationship or a sequential relationship between the various components, elements, steps, and the like, unless otherwise specified or indicated.
It is to be understood that while the present invention has been described in conjunction with the preferred embodiments thereof, it is not intended to limit the invention to those embodiments. It will be apparent to those skilled in the art from this disclosure that many changes and modifications can be made, or equivalents modified, in the embodiments of the invention without departing from the scope of the invention. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention are still within the scope of the protection of the technical solution of the present invention, unless the contents of the technical solution of the present invention are departed.

Claims (2)

1. A novel gray correlation classifier design method is characterized by comprising the following steps:
the first step is as follows: designing a gray correlation classifier by using a gray correlation algorithm;
the second step is as follows: normalizing and equalizing initial value images of the behavior sequence of the system, endowing different resolution coefficients aiming at different signals, thereby utilizing the self-adaptive resolution coefficients to strengthen the constraint capability on the resolution coefficients, bringing the different resolution coefficients into a new association coefficient formula, and combining the Lagrange median theorem to stably solve the association coefficients to obtain new association coefficients; wherein the system refers to an object to be classified;
the second step includes:
and processing the initial value image as follows:
Figure FDA0002480252920000011
wherein the content of the first and second substances,
Figure FDA0002480252920000012
the mean value of the sequence is represented, i is 0,1,2, …, m represents the class of known signals to be compared in the database, and n represents the number of signal features; xiRepresenting said sequence of behaviors, Xi＝(xi(1),xi(2),…,xi(n))；X'iRepresenting the initial value image;
the resolution coefficient is processed as follows:
calculating the mean value Delta of all the absolute values of the differencesV：
Figure FDA0002480252920000013
Δmax＝max|x′0(k)-x′i(k)|
Note the book
Figure FDA0002480252920000014
Obtaining:
Figure FDA0002480252920000015
the value of the resolution coefficient rho is obtained as follows:
Figure FDA0002480252920000016
then, the resolution coefficients ρ are averaged:
Figure FDA0002480252920000021
then, the mean value of the resolution coefficient rho is substituted into the following formula, and the Lagrange median theorem is combined to stably solve the correlation coefficient to obtain a new correlation coefficient gamma0i(k) Solving:
Figure FDA0002480252920000022
from this, a correlation value gamma between the sequences is calculated0iM represents the maximum difference of the difference sequence, M' represents the minimum difference of the difference sequence, △ xi(k) Representing a sequence of difference values.
2. The novel gray-associated classifier design method as claimed in claim 1, wherein said first step comprises:
first, an initial image of a sequence of behaviors of a system is computed, the system referring to the objects to be classified:
Figure FDA0002480252920000023
wherein i is 0,1,2, …, m represents the category of the known signals to be compared in the database, and n represents the number of the signal features; x'iRepresenting the initial value image; xiRepresenting the sequence of behaviors;
next, a sequence of difference values is calculated:
Δxi(k)＝x'0(k)-x'i(k),Δxi＝(Δxi(1),Δxi(2),…,Δxi(n)),i＝1,2,…,m
where k is 1,2, …, n represents the kth characteristic of the signal, △ xi(k) Representing a sequence of difference values;
again, the maximum difference M and the minimum difference M' of the sequence of difference values are calculated:
Figure FDA0002480252920000024
thirdly, a correlation coefficient value gamma is calculated0i(k)：
Figure FDA0002480252920000025
Finally, the correlation value gamma between the sequences is calculated0i：
Figure FDA0002480252920000026
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