CN113673355A - Method for classifying echo waveforms of wave spectrometer - Google Patents

Method for classifying echo waveforms of wave spectrometer Download PDF

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CN113673355A
CN113673355A CN202110841340.7A CN202110841340A CN113673355A CN 113673355 A CN113673355 A CN 113673355A CN 202110841340 A CN202110841340 A CN 202110841340A CN 113673355 A CN113673355 A CN 113673355A
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clustering
waveform
matrix
echo
waveforms
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CN113673355B (en
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李秀仲
李高卓
顾经纬
王志雄
何宜军
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Nanjing University of Information Science and Technology
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Abstract

The invention discloses a method for classifying echo waveforms of a wave spectrometer, which comprises the following steps: to be provided withNTaking the echo signals as input signals, and calculating an inverse matrix of an absolute value of a difference between mean values of the echoes and a correlation coefficient matrix between waveforms; performing scale transformation on the reciprocal matrix, performing linear combination on the reciprocal matrix and the correlation coefficient matrix, selecting two waveforms corresponding to maximum value elements in the combined distance matrix as initial clustering centers, and finding out the initial clustering centersKA cluster center; clustering waveforms into cluster categories; selecting the next clustering center for the intra-class sample of each class of the initial clustering by taking the minimum distance sum as a standard; calculate the firstrAnd (3) whether the clustering target error function of the clustering center before and after t +1 times of iteration in each category is larger than a set threshold value or not, if not, obtaining a final classification result, and selecting a clustering index function to determine the optimal clustering number. The invention can accurately divide the echo waveform of the spectrometer so as to screen different typesThe echo type is processed.

Description

Method for classifying echo waveforms of wave spectrometer
Technical Field
The invention relates to a method for classifying echo waveforms of a wave spectrometer, and belongs to the technical field of ocean remote sensing.
Background
With the progress of satellite remote sensing technology, the improvement and change of social demands, and the detection and research on the ocean are more and more. The method can obtain accurate, real-time and large-scale sea condition information and has important significance for ocean forecast, ship navigation, ocean engineering construction, sea-air interface and geophysical science research. Among the many marine dynamic environment parameters, sea waves are one of the most important parameters. For the detection of sea waves, there are many ways or methods, and the common detection methods are ocean buoy, Synthetic Aperture Radar (SAR), and ocean satellite altimeter. However, these detection methods have respective disadvantages, for example, the buoy can only detect one point by one point, the obtained data is point data, and wave data about one sea area or one sea area cannot be obtained, and further, the global wide-range detection cannot be realized. The Synthetic Aperture Radar (SAR) can also obtain the sea wave data, but the coverage area is small, the data is expensive, and the azimuth truncation and the sea wave inversion are complex. Although the satellite altimeter overcomes the weakness that the satellite altimeter and the satellite altimeter cannot realize wide-range observation in the world, the satellite altimeter can only obtain the effective wave height of the sea waves and cannot realize two-dimensional detection of the sea waves, so that a sea wave spectrum cannot be obtained.
The first satellite-borne wave spectrometer CFOSAT swift launch in the world of 10 months in 2018 ascended to the air. The satellite-borne wave spectrometer is the first satellite-borne instrument in the world to measure waves specially. The spectrometer is a real aperture radar, waves are detected in a mode of rotating and scanning 360 degrees by emitting broadband linear frequency modulation signals and adopting small incident angle beams of 0 degree, 2 degrees, 4 degrees, 6 degrees, 8 degrees and 10 degrees, and information extraction of a two-dimensional wave spectrum is achieved. The detection of sea waves by the satellite-borne wave spectrometer mainly depends on the change of a radar backscattering cross section signal caused by the change of sea surface wave inclination. The appearance of the satellite-borne spectrometer can well realize relatively accurate observation of the sea waves, and the sea wave spectrum can be obtained. Therefore, powerful global wave remote sensing data are provided for ocean forecast, ocean scientific research and geophysical development.
The L1A product of the SWIM spectrometer is mainly a small incident angle oblique beam echo waveform, and during observation, a satellite substellar point may experience various ground types such as sea, island, oil spill, sea ice, lake, desert, vegetation and the like. Therefore, in different ground types, a plurality of different echo waveforms exist, and even in the sky of a normal sea, due to occasional abnormality of the instrument and the like, the echo also appears abnormally. When echo data is processed, if abnormal echoes are not distinguished and screened, and finally the echo information enters the two-dimensional sea wave spectrum information extraction process, the inversion error of the two-dimensional sea wave spectrum is obviously increased, and even the sea wave spectrum information cannot be applied. Therefore, in order to process spectrometer echo data with high quality and obtain two-dimensional wave spectrum information with high accuracy, it is particularly important to classify spectrometer echoes.
Disclosure of Invention
The invention provides a method for classifying the echo waveform of a wave spectrometer according to the echo characteristics of the wave spectrometer in order to solve the problem that the echo waveform of the existing wave spectrometer is not effectively classified, and the method is a method for classifying the echo waveform of the wave spectrometer without any prior information.
The invention specifically adopts the following technical scheme to solve the technical problems:
a method for classifying an echo waveform of a wave spectrometer comprises the following steps:
step one, aiming at one-orbit satellite data, for a wave beam with a certain radar incidence angle theta, N echo signals received by a sea wave spectrometer are used as input signals, and an inverse matrix T of an absolute value of a mean value difference between sea wave spectrometer echoes is calculated0And a correlation coefficient matrix R between the waveforms;
step two, obtaining the reciprocal matrix T of the mean difference absolute value between the echoes of the wave spectrometer obtained in the step one0Carrying out scale transformation to make the distribution of the matrix be the same as the distribution of a correlation coefficient matrix R among waveforms, and obtaining a matrix T after the scale transformation;
step three, carrying out linear combination according to the matrix T after the scale transformation obtained in the step two and a correlation coefficient matrix R between waveforms to obtain a combined distance matrix d 0;
step four, selecting two waveforms corresponding to the maximum value elements in the combined distance matrix d0 as initial clustering centers, finding a third waveform with the maximum distance sum of the two clustering centers in other waveforms as a third clustering center, and so on, and finally finding K clustering centers;
step five, clustering the waveforms into various clustering categories according to the principle that a certain waveform is closest to K clustering centers;
step six, selecting the next clustering center in the class by taking the minimum distance sum as a standard for the in-class sample of each class of the initial clustering;
step seven, calculating whether a clustering target error function E of a clustering center in the r category before and after t +1 iterations is greater than a set threshold value, finishing the clustering process when the calculated clustering target error function E is not greater than the set threshold value, and obtaining a final classification result, otherwise, returning to the step five;
and step eight, taking the linear combination of the intra-class compactness and the inter-class separation degree as a clustering index function to determine the optimal clustering number, and finally outputting a class index to finish clustering.
Further, as a preferred technical solution of the present invention, in the first step, a reciprocal matrix T of an absolute value of a difference between mean values between echoes of the wave spectrometer is calculated0And a correlation coefficient matrix R between the waveforms, comprising the steps of:
step 1-1, for N echo signals, an absolute value matrix of the mean difference between echoes of a wave spectrometer
Figure BDA0003177683770000021
The calculation formula is as follows:
Figure BDA0003177683770000031
wherein n _ swap is the number of points included in the echo collected by the beam with the radar incident angle theta, Ai，mAnd Aj，mNormalized backscattering coefficients for the mth and the jth waveforms, respectively;
Figure BDA0003177683770000032
is the absolute value of the difference between the means between the ith and jth waveforms;
step 1-2, an absolute value matrix of the mean difference between echoes of the wave spectrometer
Figure BDA0003177683770000033
Taking reciprocal to obtain reciprocal matrix T0：
Figure BDA0003177683770000034
Step 1-3, calculating a correlation coefficient matrix R between echoes:
Figure BDA0003177683770000035
wherein m is the normalized backscattering coefficient number, AiIs the ith waveform; a. thejIs the jth waveform.
Further, as a preferred technical solution of the present invention, the matrix T obtained in the second step after the scale transformation specifically includes:
T(i，j)＝a*T0+b，i，j＝1，2，...，N
wherein, T (i, j) is a matrix after inverse scale transformation of the absolute value of the difference between the mean values of the ith echo and the jth echo, a is a multiplicative coefficient, and b is an additive coefficient.
Further, as a preferred technical solution of the present invention, the step three obtains a combined distance matrix d0, specifically:
d0(i，j)＝T(i，j)+R(i，j)，i，j＝1，2，...，N
where d0(i, j) is the combined distance matrix.
Further, as a preferred technical solution of the present invention, K clustering centers are found in the fourth step, and the recurrence formula is as follows:
Figure BDA0003177683770000036
wherein the content of the first and second substances,
Figure BDA0003177683770000037
the distance from the new initial clustering center to the previous n-1 clustering centers is the sum, n is the serial number of the clustering centers, and K clustering centers can be finally found on the basis;
Figure BDA0003177683770000038
is the nth cluster center to be found,
Figure BDA0003177683770000041
is the distance from the jth waveform to the r cluster center, AjIs the jth waveform, CrIs the r-th category of the image,
Figure BDA0003177683770000042
is the r-th cluster center.
Further, as a preferred technical solution of the present invention, a calculation formula of a minimum distance from the ith waveform used for clustering in the step five to the center distances of the K clusters is:
Figure BDA0003177683770000047
wherein d2(i) is the minimum distance between the ith waveform and the K cluster centers, i is from 1 to N, when the ith waveform belongs to the r-th initial cluster center, AiFor the (i) th waveform, the waveform,
Figure BDA0003177683770000048
is the r-th cluster center.
Further, as a preferred technical solution of the present invention, the new cluster center discriminant function used in the sixth step is as follows:
Figure BDA0003177683770000043
wherein d3(A) is the function value of the discrimination of the cluster center, A is the newly selected cluster center in the cluster, AiIs the ith waveform, AjIs the jth waveform, d0 (A)i，Aj) Is the distance between two waveforms, NrIs the number of samples within this class.
Further, as a preferred technical solution of the present invention, the calculating of the clustering target error function in the seventh step adopts a formula:
Figure BDA0003177683770000044
where E is the value of the clustering target error, i.e., all K clustering centers
Figure BDA0003177683770000045
And (4) the sum of the distances of the centers of the two clusters after t times of updating and t +1 times of updating. .
Further, as a preferred technical solution of the present invention, the clustering index function adopted in the step eight specifically includes:
Q(CK)＝S(CK)+F(CK)
wherein, Q (C)K) As a function of a clustering index, CK＝{C1，C2，...，CKDividing a classification sample set, wherein K is the number of clustering centers; cKClass K centers; s (C)K) Is the similar internal compactness; f (C)K) The inter-class separation degree is the average value of the distance between the inter-class sample pairs; the calculation formulas of the two are as follows:
Figure BDA0003177683770000046
Figure BDA0003177683770000051
in the above two formulae, d0(A, A ') is the distance between two echoes, A and A' are CiTwo echoes within a class; ci，CjThe number of samples in the two classes is Ni，Nj。
By adopting the technical scheme, the invention can produce the following technical effects:
the method for classifying the echo waveforms of the wave spectrometer distinguishes whether the waveforms are abnormal or not by calculating the correlation coefficient among the echo waveforms of the wave spectrometer. Since the satellite-borne spectrometer operates at a small incidence angle, the normalized backscattering coefficient thereof decreases with increasing incidence angle, so that theoretically the normal sea echoes are similar in shape, while the echoes of different ground types are quite different in shape. The correlation coefficient method can accurately distinguish abnormal echoes aiming at the characteristic echo of the spectrometer, thereby screening normal sea surface echoes.
In the method for classifying the echo waveform of the wave spectrometer, the reciprocal of the absolute value of the difference of the mean values of the echo waveforms is used as a factor in the distance between the two waveforms to represent the size of the waveform difference. Therefore, two echoes with large waveform mean difference but different shapes can be distinguished in actual data processing.
The method for standardizing the standard correlation coefficient by the reciprocal of the absolute value of the difference of the echo waveform mean values, which is provided by the method, can distinguish some special echo waveforms, and the echoes can not be distinguished by two echoes with similar waveforms due to the correlation coefficient method, and obviously do not belong to the same category. The method can obtain a comprehensive distance matrix which comprises two kinds of distance information, namely information of approximate degree of waveform shape and information of large difference of waveform mean value, and the standardization method enables two kinds of echo distances to be used coordinately.
Drawings
Fig. 1 is a general flowchart of a method for classifying an echo waveform of a wave spectrometer according to the present invention.
FIG. 2 is a 5000 waveform correlation coefficient histogram of the 6 th beam of a certain trajectory segment of the wave spectrometer.
FIG. 3 is a reciprocal histogram of the absolute value of the difference between the echoes after 5000 waveform scale transformations of the 6 th beam of a certain trajectory segment of the wave spectrometer of the present invention.
Fig. 4 is a variation curve of 5000 waveform clustering indexes Q of the 6 th wave beam in a certain track segment of the wave spectrometer.
FIG. 5 shows the cluster center waveforms of different classes and the number of echoes within the class in 5000 waveforms of the 6 th beam of a certain trajectory segment of the wave spectrometer.
FIG. 6 shows 5000 waveforms of the 6 th beam in a certain track segment of the wave spectrometer in the invention, wherein the 2 nd waveforms are distributed in the neighborhood of North Africa and Italy.
FIG. 7 is a graph showing the distribution of the various footprints of the type 2 waveform of FIG. 6 in accordance with the present invention.
Detailed Description
The following describes embodiments of the present invention with reference to the drawings.
As shown in fig. 1, the present invention relates to a method for classifying an echo waveform of a wave spectrometer, which specifically comprises the following steps:
step one, aiming at one-orbit satellite data, for a wave beam with a certain radar incidence angle theta, N echo signals received by a sea wave spectrometer are used as input signals, and an inverse matrix T of an absolute value of a mean value difference between sea wave spectrometer echoes is calculated0And a correlation coefficient matrix R between the waveforms, the specific steps are as follows:
step 1-1, for N echo signals, an absolute value matrix of the mean difference between echoes of a wave spectrometer
Figure BDA0003177683770000061
The calculation formula is as follows:
Figure BDA0003177683770000062
wherein n _ swap is collected by the beam with radar incidence angle thetaNumber of points included in the echo, Ai，mAnd Aj，mThe m-th normalized backscattering coefficient in the ith and j waveforms respectively, wherein m is the normalized backscattering coefficient sequence number.
Figure BDA0003177683770000063
Is the absolute value of the difference between the means between the ith and jth waveforms.
Step 1-2, an absolute value matrix of the mean difference between echoes of the wave spectrometer
Figure BDA0003177683770000064
Taking reciprocal to obtain reciprocal matrix T0：
Figure BDA0003177683770000065
Step 1-3, calculating a correlation coefficient matrix R between echoes:
Figure BDA0003177683770000066
wherein n _ swap is the number of points included in the echo collected by the beam with the radar incident angle theta, Ai，mAnd Aj，mThe m-th normalized backscattering coefficient in the ith and j waveforms respectively, wherein m is the normalized backscattering coefficient sequence number. A. theiIs the ith waveform; a. thejIs the jth waveform.
FIG. 2 shows a 5000 waveform correlation coefficient histogram of the 6 th beam of a certain trajectory segment of the wave spectrometer; as shown in FIG. 3, it is a reciprocal histogram T of the absolute value of the difference between the echoes after 5000 waveform scale transformations of the 6 th beam in a certain track segment of the wave spectrometer0。
Step two, obtaining the reciprocal matrix T of the mean difference absolute value between the echoes of the wave spectrometer obtained in the step one0Carrying out scale transformation to make the distribution of the matrix be the same as the distribution of a correlation coefficient matrix R among waveforms to obtain a matrix T after the scale transformation, which specifically comprises the following steps:
T(i，j)＝a*T0(i，j)+b，i，j＝1，2，...，N
wherein, T (i, j) is a matrix after inverse scale transformation of the absolute value of the difference between the mean values of the ith echo and the jth echo, a is a multiplicative coefficient, and b is an additive coefficient.
Step three, performing linear combination according to the matrix T after the scale transformation obtained in the step two and the correlation coefficient matrix R between the waveforms to obtain a combined distance matrix d0, which specifically comprises the following steps:
d0(i，j)＝T(i，j)+R(i，j)，i，j＝1，2，...，N
where d0(i, j) is the combined distance matrix.
Step four, selecting two waveforms corresponding to the maximum value elements in the combined distance matrix d0 as initial clustering centers, finding a third waveform with the maximum distance sum of the two clustering centers from other waveforms as a third clustering center, and so on, and finally finding K clustering centers, wherein the adopted recursion formula is as follows:
Figure BDA0003177683770000071
wherein the content of the first and second substances,
Figure BDA0003177683770000072
the distance from the new initial clustering center to the previous n-1 clustering centers is the sum, n is the serial number of the clustering centers, and K clustering centers can be finally found on the basis;
Figure BDA0003177683770000073
is the nth cluster center to be found,
Figure BDA0003177683770000074
is the distance from the jth waveform to the r cluster center, AjIs the jth waveform, CrIs the r-th category of the image,
Figure BDA0003177683770000075
is the r-th clusterA center.
Step five, clustering the waveforms into various clustering categories according to the principle that a certain waveform is closest to K clustering centers, wherein the adopted minimum distance formula in the distance from the ith waveform to the K clustering centers is specifically as follows:
Figure BDA0003177683770000076
wherein d2(i) is the minimum distance between the ith waveform and the K cluster centers, i is from 1 to N, when the ith waveform belongs to the r-th initial cluster center, AiFor the (i) th waveform, the waveform,
Figure BDA0003177683770000077
the r-th cluster center.
And step six, selecting the next clustering center in the class by taking the minimum distance sum as a standard for the in-class sample of each class of the initial clustering, wherein a new clustering center discrimination function is adopted as follows:
Figure BDA0003177683770000081
wherein d3(A) is the function value of the discrimination of the cluster center, A is the newly selected cluster center in the cluster, AiIs the ith waveform, AjThe j-th waveform, d0 (A)i，Aj) Is the distance between two waveforms, NrIs the number of samples within this class.
Step seven, calculating whether a clustering target error function E of a clustering center in the r category before and after t +1 iterations is greater than a set threshold value, finishing the clustering process when the calculated clustering target error function E is not greater than the set threshold value, and obtaining a final classification result, otherwise returning to the step 5 for classification and the step 6 for recalculating the clustering center; the clustering target error function used is specifically as follows:
Figure BDA0003177683770000082
where E is the value of the clustering target error, i.e., all K clustering centers
Figure BDA0003177683770000083
And (4) the sum of the distances of the centers of the two clusters after t times of updating and t +1 times of updating.
And step eight, taking the linear combination of the intra-class compactness and the inter-class separation degree as a clustering index function to determine the optimal clustering number, and finally outputting a class index to finish clustering. The clustering index function used is as follows:
Q(CK)＝S(CK)+F(CK)
in the formula, Q (C)K) As a function of a clustering index, CK＝{C1，C2，...，CKAnd K is the number of clustering centers. CKClass K centers. S (C)K) For intra-class compactness, the sum of the mean of the distances from each sample in the set to itself among all samples in the class to which it belongs (including the sample) is used as a measure. F (C)K) The inter-class separation is the average of the distances between pairs of inter-class samples. The calculation formulas of the two are as follows;
Figure BDA0003177683770000084
Figure BDA0003177683770000085
in the above two formulae, d0(A, A ') is the distance between two echoes, A, A' are CiTwo echoes within the class. Ci，CjThe number of samples in the two classes is Ni，Nj。
As shown in fig. 4, a change curve of 5000 waveform clustering indexes Q of the 6 th wave beam in a certain track segment of the wave spectrometer is shown; after screening, as shown in fig. 5, the number of the cluster center waveforms of different categories and the number of various echoes thereof in 5000 waveforms of the 6 th beam in a certain track section of the wave spectrometer are shown; in order to show the overall effect of the classification method, fig. 6 shows that the 2 nd type waveforms in 5000 wave beams of the 6 th wave beam in a certain track section of the wave spectrometer are distributed near north africa and italy and are marked by black gray; (ii) a Since the spectrometer consists of 6 beams, each of which can actually produce a continuous echo, the present invention uses figure 7 to show the classification details for the distribution of the various footprints of the type 2 waveform of figure 6.
Therefore, the method of the present invention uses the reciprocal of the absolute value of the difference between the mean values of the echo waveforms as a factor in the distance between the two waveforms to represent the magnitude of the waveform difference. In the actual data processing, two echoes with larger waveform mean value difference but different shapes can be distinguished; and the correlation coefficient among the echo waveforms is calculated to distinguish whether the waveforms are abnormal or not, so that abnormal echoes can be distinguished more accurately, and normal sea surface echoes are screened. The method can obtain a comprehensive distance matrix which comprises two kinds of distance information, namely information of approximate degree of waveform shape and information of large difference of waveform mean value, and the standardization method enables two kinds of echo distances to be used coordinately.
While the invention has been described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention.

Claims (9)

1. A method for classifying an echo waveform of a wave spectrometer is characterized by comprising the following steps:
step one, aiming at one-orbit satellite data, for a wave beam with a certain radar incidence angle theta, N echo signals received by a sea wave spectrometer are used as input signals, and an inverse matrix T of an absolute value of a mean value difference between sea wave spectrometer echoes is calculated0And a correlation coefficient matrix R between the waveforms;
step two, averaging the echoes of the wave spectrometer obtained in the step oneInverse matrix T of the absolute values of the differences of the values0Carrying out scale transformation to make the distribution of the matrix be the same as the distribution of a correlation coefficient matrix R among waveforms, and obtaining a matrix T after the scale transformation;
step three, carrying out linear combination according to the matrix T after the scale transformation obtained in the step two and a correlation coefficient matrix R between waveforms to obtain a combined distance matrix d 0;
step four, selecting two waveforms corresponding to the maximum value elements in the combined distance matrix d0 as initial clustering centers, finding a third waveform with the maximum distance sum of the two clustering centers in other waveforms as a third clustering center, and so on, and finally finding K clustering centers;
step five, clustering the waveforms into various clustering categories according to the principle that a certain waveform is closest to K clustering centers;
step six, selecting the next clustering center in the class by taking the minimum distance sum as a standard for the in-class sample of each class of the initial clustering;
step seven, calculating whether a clustering target error function E of a clustering center in the r category before and after t +1 iterations is greater than a set threshold value, finishing the clustering process when the calculated clustering target error function E is not greater than the set threshold value, and obtaining a final classification result, otherwise, returning to the step five;
and step eight, taking the linear combination of the intra-class compactness and the inter-class separation degree as a clustering index function to determine the optimal clustering number, and finally outputting a class index to finish clustering.
2. A method of classifying the waveform of an echo from a wave spectrometer according to claim 1, wherein in step one an inverse matrix T of the absolute value of the difference in mean values between echoes of the wave spectrometer is calculated0And a correlation coefficient matrix R between the waveforms, comprising the steps of:
step 1-1, for N echo signals, an absolute value matrix of the mean difference between echoes of a wave spectrometer
Figure FDA0003177683760000011
The calculation formula is as follows:
Figure FDA0003177683760000012
wherein n _ swap is the number of points included in the echo collected by the beam with the radar incident angle theta, Ai，mAnd Aj，mNormalized backscattering coefficients for the mth and the jth waveforms, respectively;
Figure FDA0003177683760000013
is the absolute value of the difference between the means between the ith and jth waveforms;
step 1-2, an absolute value matrix of the mean difference between echoes of the wave spectrometer
Figure FDA0003177683760000021
Taking reciprocal to obtain reciprocal matrix T0：
Figure FDA0003177683760000022
Step 1-3, calculating a correlation coefficient matrix R between echoes:
Figure FDA0003177683760000023
wherein m is the normalized backscattering coefficient number, AiIs the ith waveform; a. thejIs the jth waveform.
3. A method for classifying an echo waveform of a wave spectrometer according to claim 1, wherein the matrix T after the scaling is obtained in the second step is specifically:
T(i，j)＝a*T0+b，i，j＝1，2，...，N
wherein, T (i, j) is a matrix after inverse scale transformation of the absolute value of the difference between the mean values of the ith echo and the jth echo, a is a multiplicative coefficient, and b is an additive coefficient.
4. A method for classifying an echo waveform of a wave spectrometer according to claim 1, characterized in that the step three is performed to obtain a combined distance matrix d0, specifically:
d0(i，j)＝T(i，j)+R(i，j)，i，j＝1，2，...，N
where d0(i, j) is the combined distance matrix.
5. A method of classifying an echo waveform from a wave spectrometer according to claim 1, wherein K cluster centers are found in the fourth step using the following recursion formula:
Figure FDA0003177683760000024
wherein the content of the first and second substances,
Figure FDA0003177683760000025
the distance from the new initial clustering center to the previous n-1 clustering centers is the sum, n is the serial number of the clustering centers, and K clustering centers can be finally found on the basis;
Figure FDA0003177683760000026
is the nth cluster center to be found,
Figure FDA0003177683760000027
is the distance from the jth waveform to the r cluster center, AjIs the jth waveform, CrIs the r-th category of the image,
Figure FDA0003177683760000028
is the r-th cluster center.
6. A wave spectrometer echo waveform classification method according to claim 1, characterized in that the smallest distance from the ith waveform used for clustering in the fifth step to the center distance of K clusters is calculated by the formula:
Figure FDA0003177683760000029
wherein d2(i) is the minimum distance between the ith waveform and the K cluster centers, i is from 1 to N, when the ith waveform belongs to the r-th initial cluster center, AiFor the (i) th waveform, the waveform,
Figure FDA0003177683760000031
is the r-th cluster center.
7. A method of classifying an echo waveform from a wave spectrometer according to claim 1, wherein the new cluster center discriminant function used in step six is as follows:
Figure FDA0003177683760000032
wherein d3(A) is the function value of the discrimination of the cluster center, A is the newly selected cluster center in the cluster, AiIs the ith waveform, AjThe j-th waveform, d0 (A)i，Aj) Is the distance between two waveforms, NrIs the number of samples within this class.
8. A wave spectrometer echo waveform classification method according to claim 1, characterized in that the formula for calculating the clustering target error function in the seventh step is:
Figure FDA0003177683760000033
where E is the value of the clustering target error, i.e., all K clustering centers
Figure FDA0003177683760000034
And (4) the sum of the distances of the centers of the two clusters after t times of updating and t +1 times of updating.
9. A method for classifying an echo waveform of a wave spectrometer according to claim 1, wherein the clustering index function used in the step eight is specifically:
Q(CK)＝S(CK)+F(CK)
wherein, Q (C)K) As a function of a clustering index, CK＝{C1，C2，...，CKDividing a classification sample set, wherein K is the number of clustering centers; cKClass K centers; s (C)K) Is the similar internal compactness; f (C)K) The inter-class separation degree is the average value of the distance between the inter-class sample pairs; the calculation formulas of the two are as follows:
Figure FDA0003177683760000035
Figure FDA0003177683760000036
in the above two formulae, d0(A, A ') is the distance between two echoes, A and A' are CiTwo echoes within a class; ci，CjThe number of samples in the two classes is Ni，Nj。
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