CN100456319C

CN100456319C - High spectrum image repeated selection weighing classification method

Info

Publication number: CN100456319C
Application number: CNB2007101443011A
Authority: CN
Inventors: 王立国; 赵春晖; 乔玉龙
Original assignee: Harbin Engineering University
Current assignee: Harbin Engineering University
Priority date: 2007-09-12
Filing date: 2007-09-12
Publication date: 2009-01-28
Anticipated expiration: 2027-09-12
Also published as: CN101127086A

Abstract

The utility model provides a classification method of hyper-spectral image reselection weighting, comprising at least one of treatment processes of sample weighting, feature weighting and category weighting; wherein, the sample weighting is completed through non-linearly mapping the distance into corresponding weight value according to the relationship between sample abnormal degree and the distance of sample deviation from class center; the feature weighting is completed through extension into classification problem of least square SVM according to the weighting characteristic of separation problem of divergence matrix in the class to linear spectrum; and the category weighting is completed through setting of different values embodying class importance according to special meaning of unit matrix diagonal elements in linear equations of least square SVM.

Description

Hyperspectral image check weighting classification method

(I) technical field

The invention relates to a hyperspectral image classification method, in particular to a hyperspectral image check (multiple) weighting classification method based on a least square support vector machine (least square SVM), and belongs to the field of pattern recognition.

(II) background of the invention

With the development of remote sensing technology, hyperspectral images (HSI) are increasingly widely used. The basic pixels in the hyperspectral images are high-dimensional data vectors, and the correct classification of the high-dimensional data vectors is the most basic and important content of the hyperspectral data analysis. Among the numerous hyperspectral image classification methods, a Support Vector Machine (SVM) is widely favored and used with its excellent classification performance. SVMs have emerged in a number of structural styles during development. Of these types of architectures, least squares SVM is popular, the main reason for which is that the cost function of least squares SVM is an optimization problem with only equality constraints, the solution of which can be done in a linear system. Although the least square SVM shows good performance in the hyperspectral image classification, how to further improve the classification performance is still a content worthy of research. In the process of hyperspectral image classification, the generalization performance of the least squares SVM is sensitive to outlier points and noise interference pixels (generally referred to as abnormal pixels) in the training process, and the outlier points and the noise interference pixels inevitably and widely exist in hyperspectral data, so that the accuracy of the model is influenced. The least square modeling method is too dependent on training samples and is sensitive to the existence of abnormal pixels, and the generalization performance of the model can be completely destroyed by introducing a small amount of abnormal pixels.

In 2002, J.A.K.SUYKENS provides a weighting method of a least square SVM, so that pixels and outliers which are seriously interfered by noise in a hyperspectral image are effectively controlled, and better robust characteristics and popularization capability are obtained. This method of weighting involves a preliminary training. It is known that the amount of computation required for a training is generally large, and especially when there are many training samples, the method becomes very time-consuming. For this reason, this method has not been effectively generalized.

The above weighting method and other existing SVM-based hyperspectral image classification weighting methods are implemented for training samples, and few documents are considered for the following two cases. Firstly, different features (or called bands, spectral bands) of the hyperspectral images have different influences on the separability of the categories, namely, the hyperspectral images have different functions on the categories, so that the hyperspectral images are not treated equally in the design of a classifier; secondly, in practical application, the remote sensing data categories are numerous, and the meaning of different categories for hyperspectral data analysis is often different, or the degree of interest of researchers to the hyperspectral data analysis is different, so that the categories also need to be considered in the design of the classifier. The traditional feature selection method can extract features which have large influence on the category separability, but the method obviously lacks flexibility and influences the analysis effect.

Disclosure of the invention

The invention aims to provide a hyperspectral image checkability weighting classification method based on a least square SVM (support vector machine) for carrying out multiple weighting processing on pixels, characteristics and categories.

The purpose of the invention is realized as follows:

the invention at least comprises one of sample weighting, feature weighting or category weighting processing;

1) the sample weighting process comprises:

is the pixel x of each training sample_iCalculate its corresponding distance D (x)_i，x₀) The calculation formula is as follows:

D(x_i，x₀)＝(K(x_i，x_i)+K(x₀，x₀)-2K(x_i，x₀))^1/21, 2, …, n. (1) wherein x₀Is a sample x_iThe corresponding class center (i.e. the average value of all samples of the class), and the function K (·,) is the kernel function in the SVM;

② to distance D (x)_i，x₀) Carrying out normalization processing, wherein a formula selected by the normalization processing is as follows:

wherein,

D_{\max} = \max_{i} (D (x_{i}, x_{0}));

normalized distance

Converting into corresponding weight, wherein the conversion formula is as follows:

wherein,

D_{\min} = \min_{i} (D (x_{i}, x_{0}));

fourthly, optimizing error terms { e) in the expression of least square SVM classification_i}_i＝1 ⁿSubstituted by its weighted form { v_ie_i}_i＝1 ⁿAnd obtaining a least square SVM classification optimization expression of sample weighting:

i＝1，2，…，n，γ＞0. (4)

s.t.y_i＝<w，φ(x_i)>+b+e_i

2) the characteristic weighting process comprises the following steps:

calculating various average vectors mu for all n training sample pixels_j(j＝1，2，…，n)：

<math> <mrow> <msub> <mi>μ</mi> <mi>j</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>n</mi> <mi>j</mi> </msub> </mfrac> <munder> <mi>Σ</mi> <mrow> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>&Element;</mo> <msub> <mi>C</mi> <mi>j</mi> </msub> </mrow> </munder> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> </math>

Wherein, C_j、n_jRespectively representing a jth sample set and the number of samples thereof;

② calculating the within-class divergence matrix S_WThe formula is as follows:

<math> <mrow> <msub> <mi>S</mi> <mi>W</mi> </msub> <mo>=</mo> <munderover> <mi>Σ</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>P</mi> </munderover> <munder> <mi>Σ</mi> <mrow> <mi>r</mi> <mo>&Element;</mo> <msub> <mi>C</mi> <mi>j</mi> </msub> </mrow> </munder> <mrow> <mo>(</mo> <mi>r</mi> <mo>-</mo> <msub> <mi>μ</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <mi>r</mi> <mo>-</mo> <msub> <mi>μ</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow> </math>

utilizing properOrthogonal matrix U and diagonalization B, real symmetric matrix S_WConverted into the following form:

S_{W}^{- 1} = {({UBU}^{T})}^{- 1} = ({UB}^{- 1 / 2}) {(U B^{- 1 / 2})}^{T} - - - (7)

then the matrix G ═ UB^-1/2)^TCan be used as a weighting matrix to perform left multiplication on all the hyperspectral data to complete wave band weighting;

3) the category weighting process comprises:

after the arrangement sequence of all n training samples is specified, different weighted values are specified for each category according to different analytical meanings;

② constructing an n multiplied by n diagonal matrix

Diagonal elements such that

The diagonal elements correspond to weights of classes to which corresponding sequence training samples belong;

using the constructed diagonal matrix

Replacing an identity matrix I in a linear equation set corresponding to the least square SVM to obtain a new classification equation set with class weighting property:

wherein y ═ y₁，y₂，…，y_n]^TFor the class attribute value corresponding to the training sample, 1_v＝[1，1，…，1]^T(ii) a And solving the weighted equation set to obtain a classification discriminant function so as to realize the class weighted classification of the hyperspectral images.

The present invention may further comprise:

for each training sample pixel x_iCalculate its corresponding distance D (x)_i，x₀) The selected calculation formula is as follows:

D(x_i，x₀)＝(K(x_i，x_i)+K(x₀，x₀)-2K(x_i，x₀))^1/2-r，i＝1，2，…，n.

(1)

wherein r is x₀And the minimum circle radius of the sample pixel with the specified proportion is contained as the circle center. Here, r may be set to 0 without calculation, and has only a small influence on the weighting effect.

In order to achieve the object of the present invention, when establishing a classification model: training samples with different abnormal degrees are controlled differently; the characteristics with different classification and separability are embodied differently; the data types with different analytical meanings are treated differently, and finally, a better data analysis effect is achieved.

According to the relation between the sample abnormal degree and the distance of the sample deviating from the class center, the distance is nonlinearly mapped into a corresponding weight to complete sample weighting; according to the weighting characteristic of the in-class divergence matrix to the linear spectrum separation problem, the method is popularized to the least square SVM classification problem to complete feature weighting; and according to the special meaning of the diagonal elements of the unit matrix in the least square SVM linear equation set, setting the diagonal elements into different numerical values reflecting the importance of the category to complete the category weighting.

In the above three weighting methods, sample weighting is a means applied exclusively to training samples, the second is an operation performed on all data, and class weighting is a reset of diagonal elements of a matrix during training. They can be used alone or in any combination of check ways.

(IV) description of the drawings

Fig. 1 to fig. 2 are graphs showing mapping relationships from distances to weights in a sample weighting process.

FIG. 3 is a schematic diagram of a least squares SVM check weighting operation interface.

FIGS. 3 a-3-e are comparisons of classification results for a first set of different weighting cases, where: FIG. 3-a) is a graph of the classification results using unweighted least squares SVM; FIG. 3-b) is a graph of the classification results of the least squares SVM under application of sample weighting; FIG. 3-c) is a graph of the classification results of the least squares SVM under feature weighting; FIG. 3-d) is a graph of the classification results of least squares SVM under class weighting; 3-e) is a graph of least squares SVM classification results under a combination of three weighting methods.

FIGS. 4 a-4-e are comparisons of classification results for a first set of different weighting cases, where: FIG. 4-a) is a graph of the classification results using unweighted least squares SVM; FIG. 4-b) is a graph of the classification results of the least squares SVM under application of sample weighting; FIG. 4-c) is a graph of the classification results of the least squares SVM under feature weighting; FIG. 4-d) is a graph of the classification results of least squares SVM under class weighting; 4-e) is a graph of least squares SVM classification results under a combination of three weighting methods.

(V) detailed description of the preferred embodiments

The invention will now be described in more detail by way of example with reference to the accompanying drawings in which:

the invention relates to a method for improving analysis effect when a least square SVM is applied to hyperspectral image classification, which is completed by adopting a triple weight mode capable of checking. The basic process of sample weighting is as follows: 1) calculating a distance D (x) to its corresponding class center for each training sample pel_i，x₀) (ii) a 2) Will be at a distance D (x)_i，x₀) Performing normalization processing(ii) a 3) Further, the normalized distance

Converting into corresponding weight; 4) finally, the least square SVM classification is optimized to obtain an error term { e ] in the expression_i}_i＝1 ⁿSubstituted by its weighted form { v_ie_i}_i＝1 ⁿA least squares SVM classification optimization expression of the sample weights is obtained. The feature weighting process steps are as follows: 1) calculating various types of average vectors mu for all n training sample pixels_j(j ═ 1, 2, …, n); 2) using the mean vector mu_jCalculating an intra-class divergence matrix S_W(ii) a 3) Using intra-class divergence matrices S_WAnd calculating a weighting matrix to complete the band weighting. The class weighting process steps are as follows: 1) specify all n trainsAfter the arrangement sequence of the samples, defining different weighted values for each category according to different analytical meanings; 2) constructing an n x n diagonal matrix

Diagonal elements such that

The diagonal elements correspond to weights of classes to which corresponding sequence training samples belong; 3) with diagonal matrices constructed

And replacing the unit matrix I in the linear equation set corresponding to the least square SVM to obtain a new classification equation set with class weighting property. A detailed description of the construction of the process of the invention is given first:

1) with respect to sample weighting. The mathematical model of the least squares SVM is an optimization problem with only the sum of squares of the error cost functions constrained by equality, the solution of which can be done in a linear system. The optimization problem expression is as follows:

i＝1，2，…，n，γ＞0.(1)

s.t.y_i＝<w，φ(x_i)>+b+e_i，

in order to obtain a weighted training model of the least squares SVM, the error variables in equation (1) are weighted, i.e. e_iCorresponding to the weight v_iThus, this formula becomes

i＝1，2，…，n，γ＞0.(2)

s.t.y_i＝<w，φ(x_i)>+b+e_i

Thus, how to reasonably determine the weight v_iBecomes a key issue in sample weighting. Due to the fact that in the training sampleThe anomaly samples are relatively far from their respective class centers, so their degree of "anomaly" can be measured by a distance scale. Fig. 1 shows the sorting distance corresponding to a group of similar real hyperspectral data samples, and the situation of mapping the distance to the corresponding weight.

On the other hand, due to the spectral variability within a class, even a pure sample cannot be concentrated in the corresponding class center, but there is a relatively small deviation. In view of this, in calculating the distance, we can subtract a correction constant from the previously determined distance. For this purpose, the minimum radius including the sample points of the class at the predetermined ratio around the class center is determined, and the radius is set as the correction constant.

Let sample x_iThe corresponding class center is x₀And with x₀The circle with the radius r as the center of the circle is the smallest circle containing the samples with the specified proportion. By using

Represents a sample x_iTo x₀Uncorrected distance, then

The calculation formula of (a) is as follows:

so that x can be specified_iTo its class center x₀Corrected distance D (x)_i，x₀) Is composed of

D (x_{i} {, x}_{0}) = \hat{D} (x_{i}, x_{0}) - r,

i＝1，2，…，n.(4)

Note the book

D_{\max} = \max_{i} (D (x_{i}, x_{0})) - - - (5)

D_{\min} = \min_{i} (D (x_{i}, x_{0}))

In combination withTo representThe normalized form of (a), namely:

the weight factor can be obtained by the following formula:

easy to verify 0 < v_iLess than or equal to 1. Now will be the error term { e } in equation (1)_i}_i＝1 ⁿSubstituted by its weighted form { v_ie_i}_i＝1 ⁿA novel weighted least squares SVM is obtained, the mathematical model being:

i＝1，2，…，n，γ＞0.(8)

s.t.y_i＝<w，φ(x_i)>+b+e_i

2) with respect to feature weighting. The key to feature weighting is to find a suitable weighting matrix that can strengthen the effective features and weaken the relatively less effective features. A weighting matrix determination method based on Fisher linear discriminant analysis, a widely used pattern classification technique, is given below. With n training sample vectors for classification, mu_jIs the average of the jth class of samples (j ═ 1, 2, …, n), i.e.

<math> <mrow> <msub> <mi>μ</mi> <mi>j</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>n</mi> <mi>j</mi> </msub> </mfrac> <munder> <mi>Σ</mi> <mrow> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>&Element;</mo> <msub> <mi>C</mi> <mi>j</mi> </msub> </mrow> </munder> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow> </math>

C_j、n_jRespectively representing the jth class sample set and the number of samples thereof, thereby defining a divergence matrix S in the class_WThe following were used:

here, the

<math> <mrow> <msub> <mi>S</mi> <mi>j</mi> </msub> <mo>=</mo> <munder> <mi>Σ</mi> <mrow> <mi>r</mi> <mo>&Element;</mo> <msub> <mi>C</mi> <mi>j</mi> </msub> </mrow> </munder> <mrow> <mo>(</mo> <mi>r</mi> <mo>-</mo> <msub> <mi>μ</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <mi>r</mi> <mo>-</mo> <msub> <mi>μ</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow> </math>

In Fisher Linear Spectroscopy mixture analysis, S_W ^-1Have been successfully used as weighting matrices in the mixed-pixel spectral separation problem:

wherein r is a mixed spectrum vector to be analyzed, α is a mixed proportion vector to be solved, and M is a spectrum matrix with spectrum end members as column vectors. From the analysis, S_WIs a real symmetric matrix, so that there is an orthogonal matrix U that diagonalizes it as a matrix B:

U^TS_WU＝B (13)

further, it can be inferred that:

S_{W}^{- 1} = {({UBU}^{T})}^{- 1} = {({UB}^{- 1 / 2}) ({UB}^{- 1 / 2})}^{T} - - - (14)

remember G ═ G (UB)^-1/2)^TThen (12) is converted into

Comparing the original spectral separation problem:

it is understood that formula (9) corresponds to the conversion of G ═ UB^-1/2)^TUsed as a sample weighting matrix. It is known from the relationship between spectral separation and the data classification problem (spectral separation into more accurate soft classifications) that G can be used as a sample weighting matrix in the classification problem.

3) With respect to category weighting. In the least squares SVM algorithm, the corresponding dual problem is:

the optimal KKT condition is as follows:

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mi>L</mi> </mrow> <mrow> <mo>&PartialD;</mo> <mi>w</mi> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> <mo>&RightArrow;</mo> <mi>w</mi> <mo>=</mo> <munderover> <mi>Σ</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>α</mi> <mi>k</mi> </msub> <mi>φ</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mi>L</mi> </mrow> <mrow> <mo>&PartialD;</mo> <mi>b</mi> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> <mo>&RightArrow;</mo> <munderover> <mi>Σ</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>α</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mi>L</mi> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>e</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> <mo>&RightArrow;</mo> <msub> <mi>α</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>γe</mi> <mi>i</mi> </msub> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>·</mo> <mo>·</mo> <mo>·</mo> <mo>,</mo> <mi>n</mi> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mi>L</mi> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>α</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> <mo>&RightArrow;</mo> <mo><</mo> <mi>w</mi> <mo>,</mo> <mi>φ</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>></mo> <mo>+</mo> <mi>b</mi> <mo>+</mo> <msub> <mi>e</mi> <mi>k</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>·</mo> <mo>·</mo> <mo>·</mo> <mo>,</mo> <mi>n</mi> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow> </math>

the above formula can be further represented by the elimination of w and e by the elimination method:

wherein y ═ y₁，y₂，…，y_n]^T，1_v＝[1，1，…，1]^T，α＝[α₁，α₂，…，α_n]^TK is a kernel function matrix of the training samples, I is an n x n identity matrix, and n is the number of the training samples. When I is an identity matrix, the representation is trainedThe routine considers equally for each training sample. The category weighting means that the importance degree of each category is changed by changing the diagonal element value of the corresponding position of some category samples in the I instead of the original 1, so that the interested categories are protected, and the non-important categories are restrained.

According to theoretical analysis and simulation tests, the diagonal element value of the I can reflect the attention degree of each training sample. The larger a certain weight of I is, the less importance of the training process on the corresponding sample is, and vice versa. Therefore, the weight corresponding to the training sample of the interested category is properly reduced, and the weight corresponding to the training sample of the non-interested category is properly increased, so that the classification precision of the interested category can be effectively improved.

FIG. 2 is a schematic diagram of an operation interface of the least squares SVM check weighting.

According to the method, the performance of the real remote sensing image is evaluated. The remote sensing image is taken from a part of Indian agriculture and forestry hyperspectral remote sensing test area in northwest of Indiana in 1992, and the image size is 144 multiplied by 144, 220 spectral range (characteristic). Raw surveillance data defines the image into a total of 16 terrain categories, in addition to background.

The first group of experimental samples is formed by combining data of three types of ground objects, namely 3, 8 and 11 in the image. And (4) extracting spectral characteristics of part of pixels as training samples, and using the whole data as test samples. The effect test is performed by sequentially adopting unweighted, sample weighted, feature weighted and category weighted modes (three categories sequentially correspond to weights 1, 5 and 10), and triple weighted modes, and the classification results are sequentially shown in fig. 2a) to e). In the classification result, the above three categories are labeled as blue, pink and green in turn. Pixels with wrong classification in the image are displayed by white dots. Experimental results show that the overall classification precision can be improved to different degrees by using the sample weighting method and the feature weighting method, the category weighting method can improve the analysis effect of the category corresponding to the relatively small weight (simultaneously reduce the analysis effect of the category corresponding to the relatively large weight), and the three weighting methods can achieve better analysis effect on the whole by using the three weighting methods simultaneously.

In the second set of experiments, three types of ground objects 2, 10 and 6 were selected, and the experimental method was the same as above, and the classification results are shown in fig. 3. The objective evaluation indexes of the above two experiments are shown in tables 1 and 2, respectively.

TABLE 1 number of misclassified samples in the first group of surface feature classifications

TABLE 2 number of misclassified samples in the second set of ground object classifications

Claims

1. A hyperspectral image checkability weighting classification method at least comprises one of sample weighting, feature weighting or category weighting processing procedures, and is characterized in that:

1) the sample weighting process comprises:

D(x_i，x₀)＝(K(x_i，x_i)+K(x₀，x₀)-2K(x_i，x₀))^1/2，i＝1，2，…，n.

wherein x is₀Is a sample x_iCorresponding class center, wherein the function K (·,) is a kernel function in the SVM;

wherein,

D_{\max} = \max_{i} (D (x_{i}, x_{0}));

normalized distance

wherein,

D_{\min} = \min_{i} (D (x_{i}, x_{0}));

s.t. y_i＝<w，φ(x_i)>+b+e_i

2) the characteristic weighting process comprises the following steps:

calculating various average vectors mu for all n training sample pixels_j，j＝1，2，…，n：

<math> <mrow> <msub> <mi>μ</mi> <mi>j</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>n</mi> <mi>j</mi> </msub> </mfrac> <munder> <mi>Σ</mi> <mrow> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>&Element;</mo> <msub> <mi>C</mi> <mi>j</mi> </msub> </mrow> </munder> <msub> <mi>r</mi> <mi>i</mi> </msub> </mrow> </math>

<math> <mrow> <msub> <mi>S</mi> <mi>W</mi> </msub> <mo>=</mo> <munderover> <mi>Σ</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>P</mi> </munderover> <munder> <mi>Σ</mi> <mrow> <mi>r</mi> <mo>&Element;</mo> <msub> <mi>C</mi> <mi>j</mi> </msub> </mrow> </munder> <mrow> <mo>(</mo> <mi>r</mi> <mo>-</mo> <msub> <mi>μ</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <mi>r</mi> <mo>-</mo> <msub> <mi>μ</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mi>T</mi> </msup> </mrow> </math>

③ using appropriate orthogonal matrix U and diagonalization B, the real symmetric matrix S_WConverted into the following form:

S_{W}^{- 1} = {({UBU}^{T})}^{- 1} = ({UB}^{- 1 / 2}) {({UB}^{- 1 / 2})}^{T}

3) the category weighting process comprises:

② constructing an n multiplied by n diagonal matrix

Diagonal elements such thatThe diagonal elements correspond to weights of classes to which corresponding sequence training samples belong;

using the constructed diagonal matrixReplacing an identity matrix I in a linear equation set corresponding to the least square SVM to obtain a new classification equation set with class weighting property:

wherein y ═ y₁，y₂，…，y_n]^TIs the class attribute value corresponding to the training sample, l_v＝[l，l，…，l]^T(ii) a And solving the weighted equation set to obtain a classification discriminant function so as to realize the class weighted classification of the hyperspectral images.

2. The checking weighted classification method of spectral images according to claim 1, wherein:

wherein r is x₀And the minimum circle radius of the sample pixel with the specified proportion is contained as the circle center.

3. The spectral image checkability weighting classification method according to claim 1 or 2, characterized by: it is a combination of sample weighting, feature weighting and class weighting processes.