CN108446599B - Hyperspectral image band rapid selection method of p-value statistical modeling independence - Google Patents
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Abstract
The invention relates to a hyperspectral image band fast selection method based on p-value statistical modeling independence. Image importing: and importing the hyperspectral images of the to-be-selected wave bands. p-value statistical calculation: and acquiring a p-value statistic of Pearson linear correlation between wave bands of the hyperspectral images. Calculating an objective function: and (4) counting the sum of p values between each wave band of the hyperspectral image and other wave bands, namely the independence of the wave bands. Selecting wave bands: and sequencing the independence of each wave band, and selecting the wave bands. The invention selects the wave band of the hyperspectral image, has low algorithm complexity and high efficiency, and can achieve the effect of real-time or even real-time.
Description
Technical Field
The invention relates to the field of remote sensing, and particularly provides a hyperspectral image band fast selection method of p-value statistical modeling independence, which is used for hyperspectral dimension reduction and image classification.
Background
Due to the characteristics of large data volume and high redundancy, the hyperspectral image is not easy to realize typical applications such as unmixing, classification, target detection, physical quantity inversion and the like with high efficiency and high precision, and dimension reduction is one of the main means for effectively solving the problem. As one of two main implementations of dimension reduction, band selection seeks a "large information amount and strong independence" characteristic band to achieve simplification of the feature space. Although some methods and software can effectively select the bands with large information amount and strong independence, the method often needs to consume a large amount of time and needs a strong hardware system as a support.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: the defects of the prior art are overcome, and a high-efficiency high-spectrum image wave band quick selection method is provided. The method mainly comprises the steps of image importing, Pearson linear correlation coefficient calculating, p value statistic calculating, band independence index calculating, band selecting and the like, and is simple in calculation and strong in real-time performance.
The technical scheme adopted by the invention is as follows: a hyperspectral image band rapid selection method of p-value statistical modeling independence comprises the following steps:
the method comprises the following steps of (1) importing hyperspectral images of wave bands to be selected, and carrying out the same standardization processing on each wave band;
step (2), according to the result obtained in the step (1), calculating a Pearson linear correlation coefficient r between every two wave bands to finally obtain an r value matrix of the full wave band;
step (3) according to the result obtained in the step (2), calculating the statistical quantity of the correlation analysis p values between every two wave bands to finally obtain a p value matrix of the full wave band;
step (4), according to the result obtained in the step (3), performing descending order arrangement on each row of the p value matrix to obtain a descending order p value matrix and a corresponding wave band sequence number matrix;
step (5), according to the result obtained in the step (4), taking the descending p value matrix and the front k rows of the corresponding wave band sequence number matrix, and counting the sum of p values in the descending p value matrix corresponding to each wave band number in the wave band sequence number matrix, namely the independence index of each wave band when k wave bands are selected;
and (6) according to the result obtained in the step (5), performing descending order arrangement on the independence indexes of the wave bands, and taking k wave bands which are ranked at the top, namely the result of wave band selection.
Further, the calculation process of the Pearson linear correlation coefficient r value between every two wave bands and the full-wave band r value matrix in the step (2) is as follows:
step (21) decentralization: subtracting the average value of each wave band;
step (22) calculating covariance between bands;
step (23) normalizes the covariance: the covariance between the wave bands is divided by the standard deviation of the covariance to obtain the Pearson linear correlation coefficient r value between every two wave bands;
and (24) carrying out the operations of the steps (21) to (23) on any two wave bands of the full wave bands to obtain a full wave band r value matrix.
Further, the linear correlation p-value statistics and the full-band p-value matrix between every two wave bands in the step (3) are calculated as follows:
step (31) constructing a t statistic with degree of freedom upsilon; preferably, v is set to N-2, where N is the total number of samples in the correlation analysis.
Step (32) calculating an alpha function A (t | ν);
step (33), calculating a p-value statistic, namely a linear correlation p-value statistic between every two wave bands;
and (34) carrying out the operations of the steps (31) to (33) on any two wave bands of the full wave bands to obtain a full wave band p value matrix.
Further, the process of acquiring the descending p-value matrix and the corresponding band sequence number matrix in step (4) is as follows:
step (41) performing descending order arrangement on each column of the p value matrix to obtain a descending order p value matrix;
and (42) acquiring the p-value column in the descending order, and simultaneously acquiring the wave band serial number corresponding to the p value of the column to acquire a corresponding wave band serial number matrix.
Compared with the prior art, the invention has the advantages that:
(1) the invention belongs to an unsupervised dimension reduction method, and self-adaptively and automatically completes resolving from a data end to a result end without setting a threshold;
(2) the algorithm complexity of the method provided by the invention is lower, and the lower space complexity has lower requirements on the system hardware level;
(3) the invention can select the wave band of the hyperspectral image in real time or even in real time so as to effectively classify the image, secondarily select the target characteristic wave band and the like.
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FIG. 1 is a flow chart of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments. The invention provides a hyperspectral image band rapid selection method of p-value statistical modeling independence, as shown in figure 1, comprising the following main steps:
step (1), importing data and initializing: and importing hyperspectral images of the wave bands to be selected, and carrying out the same standardization processing on each wave band.
The starting end of the hyperspectral image band selection method is used for importing hyperspectral image data, and then preprocessing such as standardization and the like is needed to be carried out on the data.
One waveband B in the hyperspectral image is normalized to be BnormThe normalization process can be expressed as formula (1):
Bnorm＝(B-Bmin)/(Bmax-Bmin) (1)
wherein, Bmax、BminThe maximum and minimum values of B, respectively.
The normalized hyperspectral image Mi,j,nEach wave band image is converted into a column vector to obtain a matrix Mij,n: wherein, i, j, n are Mi,j,nThe total number of rows, columns and bands of (i) is Mij,nThe number of rows of (c).
Step (2), calculating a wave band correlation coefficient r and a full wave band r value matrix: and (3) calculating a Pearson linear correlation coefficient r between every two wave bands according to the result obtained in the step (1).
Hyperspectral image M based on initializationij,nRespectively calculating Pearson correlation coefficient between any two wave bands by using a formula (2) which comprises dataDecentralization, covariance calculation, etc.:
wherein N is the total number of samples, i.e., N ═ ij ═ i × j; binary sequences
Represents Mij,nAny two of the column vectors in (a),
and
are respectively as
And
is measured.
And (3) repeating the step (2) to calculate the correlation coefficient r between any two wave bands of the full wave band, and finally obtaining the r value matrix of the full wave band.
Step (3), calculating a p value statistic and a full-band p value matrix of the band correlation coefficient r: and (3) according to the result obtained in the step (2), performing linear correlation analysis p-value statistics between every two wave bands and calculating a full-wave band p-value matrix.
The p-value is set forth by the statistician Sir Ronald Aylmer Fisher, expressing the probability of the same or more extreme case occurring when the original hypothesis (or null hypothesis) is true as the current observation. In hypothesis testing for correlation analysis, the original hypothesis is no correlation (no correlation), and in this case, the p value is a statistic of the sample, and the magnitude of the p value is solved by constructing a t statistic with a degree of freedom v:
p＝1-A(t|ν) (3)
ν＝N-2 (6)
wherein the beta function
Alternatively, the beta function may be indirectly solved by the gamma function Γ. Respectively calculating P values between every two wave bands through a correlation coefficient r matrix to obtain a correlation coefficient P value matrix Pnxn。
And (4) repeating the step (3) to calculate the p value between any two wave bands of the full wave band, and finally obtaining the p value matrix of the full wave band.
Step four, processing the correlation coefficient p value matrix among the bands in a descending order: and (4) according to the result obtained in the step (3), performing descending order arrangement on each row of the p-value matrix to obtain a descending order p-value matrix and a corresponding wave band sequence number matrix.
Removing the P-value matrix Pn×nObtaining P after the P value of the middle wave band and the P value of the middle wave band(n-1)×n(ii) a To P(n-1)×nThe columns are arranged in descending order, and the first k rows are selected to form a matrix PSk×nAnd the corresponding wave band numbers are combined into a matrix Bk×n；
Step five, calculating an objective function, wherein the objective function is used for expressing independence indexes of a certain waveband when k wavebands are selected: according to the result obtained in the step (4), taking the descending p value matrix and the first k rows of the corresponding wave band sequence number matrix, and counting the sum of p values in the descending p value matrix corresponding to each wave band number in the wave band sequence number matrix, namely the independence index of each wave band when k wave bands are selected;
constructing a band-selected reference value objective function fk(i)：
Wherein f isk(i) Is the element i in BThe sum of the p values at the corresponding positions of PS represents a selection reference value of the i-th band when k bands are selected.
Step six, selecting a wave band: and (5) according to the result obtained in the step (5), performing descending arrangement on the independence indexes of the wave bands when the k wave bands are selected, and taking the k wave bands which are ranked at the top, namely the wave band selection result.
To fk(i) (i is 1,2, …, n) and selecting the wave band corresponding to the first k values.
The above description is only an embodiment of a method for quickly selecting a hyperspectral image band according to the invention. The present invention is not limited to the above-described embodiments. The description of the invention is intended to be illustrative, and not to limit the scope of the claims. Many alternatives, modifications, and variations will be apparent to those skilled in the art. All technical solutions formed by adopting equivalent substitutions or equivalent transformations fall within the protection scope of the claims of the present invention.
Claims (4)
1. A hyperspectral image band rapid selection method of p-value statistical modeling independence is characterized in that: the method comprises the following steps:
the method comprises the following steps of (1) importing hyperspectral images of wave bands to be selected, and carrying out the same standardization processing on each wave band;
step (2), according to the result obtained in the step (1), calculating a Pearson linear correlation coefficient r between every two wave bands to finally obtain an r value matrix of the full wave band;
step (3) according to the result obtained in the step (2), calculating linear correlation analysis p-value statistics between every two wave bands to finally obtain a p-value matrix of the full wave band;
and (4) according to the result obtained in the step (3), performing descending order arrangement on each column of the p-value matrix to obtain a descending order p-value matrix and a corresponding wave band sequence number matrix, specifically: removing the P-value matrix Pn×nObtaining P after the P value of the middle wave band and the P value of the middle wave band(n-1)×n(ii) a To P(n-1)×nThe columns are arranged in descending order, and the first k rows are selected to form a matrix PSk×nAnd the corresponding wave band numbers are combined into a matrix Bk×n；
Step (5), according to the result obtained in the step (4), taking the descending p value matrix and the front k rows of the corresponding wave band sequence number matrix, and counting the sum of p values in the descending p value matrix corresponding to each wave band number in the wave band sequence number matrix, namely the independence index of each wave band when k wave bands are selected;
and (6) according to the result obtained in the step (5), performing descending order arrangement on the independence indexes of the wave bands when the k wave bands are selected, and taking the k wave bands which are ranked at the top, namely the wave band selection result.
2. The method for quickly selecting the hyperspectral image bands of p-value statistical modeling independence according to claim 1, characterized in that: the calculation process of the Pearson linear correlation coefficient r value between every two wave bands in the step (2) and the full-wave band r value matrix is as follows:
step (21) decentralization: subtracting the average value of each wave band;
step (22) calculating covariance between bands;
step (23) normalizes the covariance: the covariance between the wave bands is divided by the standard deviation of the covariance to obtain the Pearson linear correlation coefficient r value between every two wave bands;
and (24) carrying out the operations of the steps (21) to (23) on any two wave bands of the full wave bands to obtain a full wave band r value matrix.
3. The method for quickly selecting the hyperspectral image bands of p-value statistical modeling independence according to claim 1, characterized in that: the linear correlation p-value statistics between every two wave bands and the calculation process of the full-wave band p-value matrix in the step (3) are as follows:
constructing a t statistic with degree of freedom upsilon, and calculating a p value statistic by adopting p as 1-A (t | v);
step (32) of calculating an alpha function a (t | ν):
ν＝N-2；
wherein the beta function
Step (33) respectively calculating P values between every two wave bands through a correlation coefficient r matrix to obtain a correlation coefficient P value matrix PnxnThe linear correlation p value statistic of the wave bands is obtained;
and (34) carrying out the operations of the steps (31) to (33) on any two wave bands of the full wave bands to obtain a full wave band p value matrix.
4. The method for quickly selecting the hyperspectral image bands of p-value statistical modeling independence according to claim 1, characterized in that: the process for acquiring the descending p-value matrix and the corresponding band sequence number matrix in the step (4) is as follows:
step (41) performing descending order arrangement on each column of the p value matrix to obtain a descending order p value matrix;
and (42) acquiring the p-value column in the descending order, and simultaneously acquiring the wave band serial number corresponding to the p value of the column to acquire a corresponding wave band serial number matrix.
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