Abstract
High temperature targets (temperature above 500 K), are the special on the surface of the earth such as forest fire, prairie fire, oil well torches, heap coking, volcanic eruptions, significantly different from those of normal surfaces at lower temperatures. Identification of high-temperature targets plays an important role in environmental monitoring, disaster warning, and resource investigation. In remote sensing data, high-temperature target pixels and bands are studied. And they are deemed samples and variables, respectively, in multivariate analysis. And classification of samples for identification of high-temperature targets is necessary. To classify samples, feature analysis of spectrum needs to be done first. In feature analysis of spectrum, feature bands that can be used to distinguish samples need to be selected. Correspondence analysis is the method that can project samples and variables into the same factor space in the meantime. It can realize the classification of samples and variables synchronously, and the results can be interpreted by each other. First, the correspondence analysis is conducted on Landsat8/OLI remote sensing imagery to build the relationship between samples and variables. After that the correspondence relationship between identification results of high-temperature targets and feature bands can be built in the physical theory of remote sensing and factors which have indicative significance on fire are confirmed. Finally, the single band threshold method is adopted to realize high temperature target recognition by using factor scores. In the field confirmation, results suggest that the precision of identification of high-temperature targets reaches 92%. And we also get a consistent result with SWIR temperature inversion.
1 Introduction
High temperature targets (temperature above 500 K) [1], are the special on the surface of the earth [2,3,4] such as forest fire, prairie fire, oil well torches, heap coking, volcanic eruptions, significantly different from those of normal surfaces at lower temperatures [5,6,7,8].
Identification research of high-temperature targets is important for environmental protection [9,10,11], the statistics of resource [12,13], and disaster prediction [8,14,15,16]. And it is a basis of temperature retrieval for high-temperature targets. Due to the high temperature, according to Plank’s law, we know that the emission energy is equal to or even higher than the reflection energy of the land cover types with normal temperatures. Therefore, the energy of mixed pixels which are received from a sensor’s detecting unit of the instantaneous field of view (IFOV) includes comprehensive energy of reflection and emission. So, for mixed pixels which contain high temperature and normal temperature, the mixed spectrum is significantly different from other normal temperature surface features. Some scholars are on their way to developing methods for identification [17,18,19,20] and temperature retrieval [21,22,23,24] of high-temperature targets [25,26,27]. However, the methods that they used cannot put bands and pixels together in one coordinate space, which means they cannot show a quantitative relationship in feature bands. While the correspondence analysis method [28,29], a method of multivariate analysis, can build indicative fire factors quantitatively, which has indicative significance for the high-temperature targets. In the coordinate plot, the relationship of samples, variables, and samples–variables can be revealed clearly. By the relationship, high-temperature targets can be well identified.
In multivariate analysis, the spectrum feature of normal temperature background and high-temperature target is analyzed first, after which feature bands are selected. Finally, a recognition index is established. Here is a series of key questions in remote sensing recognition of high-temperature targets. In it, a crucial question is to find feature bands. Correspondence analysis [30,31] is a method which can find feature bands. The method can project samples and variables into the same factor space at one time. In multivariate analysis, variables are bands and samples are pixels. That is to say, bands and pixels can be put into the same coordinate space from where classification results of bands and pixels can be obtained, respectively. And the classification results show a correspondence relationship between feature bands and identification results of high-temperature targets.
2 Methods and data
2.1 Study area
Hongluoxian zhen city lies in the southwest of Liaoning Province, China (Figure 1) (120°45′–121°00′E, 41°00′–41°10′N), and is located in the junction of North China and Northeast China economic cooperative area. It borders Jinzhou in the east, Huludao in the north, Shanhaiguan in the West, and Liaodong Bay in the Bohai Sea in the south. It belongs to a warm temperate sub-humid climate in the northern hemisphere. Agriculture is dominated by annual crops like corn and peanut. The chemical industry, oil refining, shipbuilding, and other industries are relatively developed. There are many industrial and mining enterprises, and a large number of coal mining sites, cement plants, metallurgical plants, etc., are distributed. The forest in the study area covers a large area, and human activities cause forest fires frequently between spring and summer [32,33].
Imagery of study area in Landsat8/OLI (753RGB).
2.2 SWIR physical model
One Landsat-8 OLI scene acquired on May 30, 2013 is selected in this study. A series of imagery processing steps, such as radiometric calibration, atmospheric correction, and clipping, have been performed first. Through processes mentioned above, for high-temperature pixels of remote sensing imagery, their radiant energy is the sum of reflected and emitted energies due to high-temperature targets in them. We call the reflectivity of pixels as the visual reflectivity [34] and the physical expression is on the basis of law of energy conservation (Figure 2) [35].
where ρ 0 is the visual reflectivity of a mixed pixel; M 1 is the emission flux density of high-temperature targets in it; M 2 is the reflectance flux density of high-temperature targets in it; M 3 is the emission flux density of normal temperature land cover types in it; M 4 is the reflectance flux density of normal temperature land cover types in it; S is the percentage of the area of high-temperature targets for mixed pixel ( S can be valued by the actual situation); θ is the sun zenith angle; E 0 is the solar irradiance for upper bound of the atmosphere; and T θ is the transmittance of the atmosphere.
The sketch of the physical model of a mixed pixel on the basis of law of energy conservation in SWIR for high-temperature targets.
2.3 Correspondence analysis method
Correspondence analysis, known as correspondence factor analysis, is also a type of R–Q mode factor analysis. The method is mainly used for revealing the relationship among samples, variables, and samples–variables. R-mode factor analysis is mainly used for studying the relationship among variables to realize the classification of samples; Q-mode factor analysis is mainly studied for the relationship among samples to realize the classification of variables. Both of them separate variables and samples, respectively, thus the relationship between multiple variables and multiple samples cannot be found easily. However, correspondence analysis is a useful method to address the problem. In correspondence analysis, the scale units between variables and samples are not uniform, therefore the scale between them has to be standardized to unify into the same coordinate space. Correspondence analysis can compress m dimension variables and n dimension samples into the same p dimension factor space. After that, variables and samples can be classified and plotted into the same coordinate space at the same time. Based on the expression in the coordinate space, factors can be explained easily. Correspondence analysis starts from matrix W, which is converted from the original matrix X that is built from original remote sensing data.
The principle is that matrix WW T (Q-mode) contains information of samples and matrix W T W (R-mode) contains information of variables. In multivariate analysis, matrix WW T and matrix W T W have the same eigenvalue and eigenvector. Correspondence analysis contains both row and column conversion first. That is the essential difference. And the other steps are similar to that of R-mode factor analysis (Q-mode factor analysis). Q-mode factor score is equivalent to R-mode factor loading, and Q-mode factor loading is equivalent to R-mode factor score. Because of allelism, we can do one type to obtain both types’ results. Compared to Q-mode analysis, fewer jobs are needed for R-mode factor analysis. So, for other steps, we consider the R-mode factor analysis. In the analysis, the factor loading matrix A represents information about variables and the factor score matrix F represents information of samples. Factor loading represents m dimension variable points in p dimension factor space, and factor score represents n dimension sample points in p dimension factor space. Factor loading has exactly the same variance with factor score, that is, variable points and sample points have the same degree of dispersion, and they are located in the same p dimension factor space. Thus, the relationship of samples, variables, and samples–variables can be studied in the same space.
The calculation of correspondence analysis is as follows:
Row and column standardization processing of original data matrix X:
where X is an n × m order original data matrix; n is the number of samples/pixels; m is the number of variables/bands; R is a matrix of row conversion, n × 1; C is a matrix of column conversion, 1 × m ; and W is a standardization matrix.
Calculation of similarity matrix H:
Calculation of eigenvalue Λ and eigenvector U of H (we ignore eigenvalue 1 and its eigenvector. It is a trivial solution which does not make sense).
Calculation of factor loading matrix A:
where A is an m × p order matrix called a loading matrix that represents the correlation between variables and factors; and p is the number of factors.
Calculation of factor score matrix F:
where F is an n × p order matrix called factor score matrix that represents the correlation between samples and factors.
2.3.1 Professional explanation
For data processing of target identification in remote sensing, the factor loading matrix A represents the linear combination of bands and these combinations of bands have certain indicative meanings, whose combination weight can direct the selection of feature bands. Factor score matrix F represents the clustering relationship of pixels, which has certain significance in the classification and identification of target objects and represents the correlation between samples and factors.
3 Results
Based on spectral analysis, 30 representative pixels for various types of land cover types, including forest land (sunny slope), forest land (shady slope), cultivated land, cultivated land (greenhouse), water, high-temperature targets, residential area, road, burned area, and uncultivated land, are selected, respectively, from remote sensing imagery (Table 1). There are 300 samples in total.
Introduction of ten types of land cover in the study area
| Types of land cover | Introduction 753 (RGB) |
|---|---|
| Forest land (sunny slope) | The forest land on the sunny slope in the remote sensing image has reflectivity which is much larger and the green color is much lighter |
| Forest land (shady slope) | The forest land on the shady slope in the remote sensing image has reflectivity which is much smaller and the green color is much darker |
| Cultivated land | It appears bright green in the remote sensing images and it is planted in large areas from March to July every year |
| Cultivated land (greenhouse) | It shows light green in the remote sensing image. Cucumbers and tomatoes are usually planted inside |
| Water | The water in the study area is river and small ponds with dark blue color |
| High-temperature targets | It shows red with generally small area in the remote sensing image |
| Residential area | It is generally located near roads and rivers, presenting a mauve, faceted distribution |
| Road | Linear distribution, white or lavender |
| Burned area | It shows dark red in the remote sensing image, planar distribution and small area |
| Uncultivated land | It is generally pink and distributed in large area, but it is green in August and September |
In correspondence analysis of the study area, representative samples, eigenvalues, and information quantity as shown in Table 2 are selected. And factor loading matrix as shown in Table 3 is achieved (Cirrus band has been ignored.).
Similar matrix eigenvalues and information quantity calculated by the representative samples
| Factor | Eigenvalue | Information quantity % | Accumulated information quantity % |
|---|---|---|---|
| Factor 1 | 0.147179 | 67.69 | 67.69 |
| Factor 2 | 0.061659 | 28.36 | 96.05 |
| Factor 3 | 0.006169 | 2.84 | 98.89 |
| Factor 4 | 0.001915 | 0.88 | 99.77 |
| Factor 5 | 0.000404 | 0.19 | 99.96 |
| Factor 6 | 0.000092 | 0.04 | 100.000 |
Factor loading matrix calculated by the representative samples
| Factor 1 | Factor 2 | Factor 3 | |
|---|---|---|---|
| Band 1 | −0.007094 | 0.019189 | −0.005692 |
| Band 2 | −0.006666 | 0.022112 | −0.004440 |
| Band 3 | −0.010611 | 0.016439 | −0.001937 |
| Band 4 | −0.006538 | 0.022599 | 0.003813 |
| Band 5 | −0.025345 | −0.016640 | −0.002437 |
| Band 6 | 0.001184 | −0.003179 | 0.007697 |
| Band 7 | 0.037609 | −0.006585 | −0.002525 |
As the accumulated information quantity of the first three factors has reached 98.89%, and it satisfies the requirements with little information loss, this study will concentrate on the first three factors with large amounts of information and give detailed explanation of their analysis.
4 Discussion
In correspondence analysis, we do row and column conversion first and the other steps are similar to R-mode factor analysis. At the end, we can get the results of both the R-mode and Q-mode. The factor loading matrix reflects the relationship between variables and factors, that is, each factor can be considered as a linear combination of each variable. The thematic significance of factors is determined based on the understanding of physical meaning of variables of each band. Element a ij in the factor loading matrix shows an important degree of variable i to factor j. The greater the absolute value of a ij is, the more important variable i is to factor j. That is to say, the thematic meaning of factor can be described by variables with a larger absolute value of a ij . In the light of the factor loading matrix, absolute values of factor loading at fifth and seventh band variables are larger in factor 1 (i.e., f 1). That is to say, f 1 mainly represents information about band 5 and band 7. The result of f 1 is equal to the difference value of the combination of band 7 and band 5.
The approximate expression of f 1 is:
where ρ 5 is the visual reflectivity of band 5, and ρ 7 is the visual reflectivity of band 7.
f 1 is on the basis of b5 and b7, and they are SWIR bands. That means SWIR bands are more suitable for study of high-temperature targets. So temperature of high-temperature targets can be obtained by the formula (7) which is constructed on the basis of Plank’s law using SWIR bands (Figure 3) [7]:
where ρ is the reflectance of surface features at normal temperature; ε is the emissivity of high-temperature targets; h is the Planck’s constant (h = 6.63 × 10−34 Js); c is the speed of light in vacuum (c = 3 × 108 m/s); and k is the Boltzmann constant (k = 1.38 × 10−23 J/K); λ is the wavelength; E is the solar irradiance of earth’s surface; and the other parameters are the same as of formula (1).
![Figure 3
Radiation flux density of blackbody in different temperatures (Based on the law we know that thermal infrared remote sensor [TIRS] bands are more suitable for studying normal temperature features at temperature of 300 K.).](/document/doi/10.1515/geo-2022-0353/asset/graphic/j_geo-2022-0353_fig_003.jpg)
Radiation flux density of blackbody in different temperatures (Based on the law we know that thermal infrared remote sensor [TIRS] bands are more suitable for studying normal temperature features at temperature of 300 K.).
The main difference between high-temperature targets and other land cover types is that for targets with high temperature, ρ
7 and ρ
5 are much larger. For pixels, the greater the value of f1 is, the more likely there are high-temperature targets in them. At the same time, f1 is similar to Normalized Difference Fire Index (NDFI) [35,36,37,38] (
In correspondence analysis, the factor score matrix reflects the relationship between samples and factors. The digital number value of a pixel in each factor score image (Figure 4) represents the weight of the composition of the lightness of river, vegetation, and fire factors. In score imagery of f 1, the reflectivity of fire is very high, and it shows a high brightness value. In score imagery of f 2, the reflectivity of the river is very high, and it shows a high brightness value, while in score imagery of invert result for f 2, the reflectivity of forest land and cultivated land shows high brightness value. In score imagery of f 3, the reflectivity of uncultivated land is very high, and it also shows a high brightness value.
(a) Factor score of false color image, (b) factor score of f 1, (c) factor score of f 2, and (d) factor score of f 3.
Factor loading matrix reflects the relationship between variables and factors. In correspondence analysis, variables and samples are put into the same factor space, and two of f 1, f 2, and f 3 are selected to construct two-dimension scatter plots (Figure 5). In a scatter plot, all representative pixel samples show different clustering characteristics of points. Based on the scatter plot, pixel samples can be classified and targets can be recognized. Consider the meaning of factor loading, seven variables (bands 1–7, expressed as b1, b2…, b7) are divided into three groups, and they represent three factors, respectively. f 1 mainly represents the relationship between b5 and b7, and it is the fire factor. f 2 mainly represents differences between b1, b2, b3, b4, and the other bands. In plots 2a and 2c, water samples are distributed at the positive axis direction of f 2, and vegetation samples are distributed at the negative axis direction of f 2. So, f 2 can be called a vegetation–water factor. f 3 mainly represents differences between b6 and the other bands. In plots 2b and 2c, the uncultivated land samples are distributed at the positive axis direction of f 2, so f 3 can be called as an uncultivated land factor. In the factor loading matrix, each variable has itself contribution in Table 4. In Table 4, we can see the absolute and relative contributions of each variable to the factor. Based on the absolute and relative contribution of variables that we can get the band combination of factor. The contribution of f 1 is consistent between absolute and relative, while f 2 and f 3 are not uniform in absolute and relative contribution, respectively. Absolute contribution and the relative contribution can deal with the problem of short distance in two-dimensional projection in visual, while they can deal with the problem of long distance in p-dimensional in reality. So, we can be sure of the thematic meaning of f 1 explicitly.
Scatter plot of factors 1, 2, and 3: (a) scatter plot of factors 1 and 2, (b) scatter plot of factors 1–3, and (c) scatter plot of factors 2 and 3.
Factor loading matrix with the absolute contribution and the relative contribution
| The absolute contribution | The relative contribution | |||||
|---|---|---|---|---|---|---|
| f 1 | f 2 | f 3 | f 1 | f 2 | f 3 | |
| b1 | 0.006994 | 0.122159 | 0.107416 | 0.105836 | 0.774442 | 0.068136 |
| b2 | 0.005708 | 0.149944 | 0.060424 | 0.078055 | 0.859012 | 0.034636 |
| b3 | 0.019579 | 0.112183 | 0.015565 | 0.282836 | 0.678924 | 0.009425 |
| b4 | 0.008060 | 0.229851 | 0.065397 | 0.071129 | 0.849738 | 0.024190 |
| b5 | 0.319374 | 0.328605 | 0.070438 | 0.693777 | 0.299053 | 0.0064148 |
| b6 | 0.000607 | 0.010446 | 0.611996 | 0.0185439 | 0.133799 | 0.784344 |
| b7 | 0.639678 | 0.046812 | 0.068765 | 0.965651 | 0.029605 | 0.004351 |
Bold values are the bigger values in each factor.
The final identification and extraction are accomplished through the threshold setting. In the light of the R-mode factor score, we took the known high-temperature pixels as the end-element sample for statistics. In statistics of fire factor, the mean value is 0.001246 and the standard deviation is 0.000250. The threshold of fire is obtained as 0.000746 by calculating the difference of mean value and two times standard deviation. Then, threshold was applied and we found that there are 89 high-temperature pixels (Figure 6). Resulting pixels are noted by red in the remote sensing image. They are verified one by one in the field through burned area, among which are seven error pixels. All error pixels are color bonds. Seven error pixels are distributed in six different positions in the study area (Table 5). The reason for this misjudgment is that they have higher values than other surface features in curves of all bands, and they have high similarity on the spectrum with high-temperature targets (Figure 7), while they are different from other land cover types. The identification precision reaches 92%. The results were checked by field validation on July 27, 2013. The results were also compared with burned area imagery.
Identification result of high-temperature targets.
The coordinates of seven misjudged pixels of color bond in the study area
| Latitude | Longitude | Notes | |
|---|---|---|---|
| Position 1 | 41°4′43″N | 120°56′10″E | 1 Pixel |
| Position 2 | 41°4′21″N | 120°47′18″E | 1 Pixel |
| Position 3 | 41°4′10″N | 120°46′2″E | 1 Pixel |
| Position 4 | 41°3′17″N | 120°58′22″E | 2 Pixels (extra pixel is on the east) |
| 41°3′17″N,120°58′23″E | |||
| Position 5 | 41°1′32″N | 120°53′8″E | 1 Pixel |
| Position 6 | 41°1′11″N | 120°52′34″E | 1 Pixel |
Spectral curves of (a) color bond (7 pixels of misjudgment), (b) high-temperature targets (7 random pixels with high temperature in the right 82), and (c) all kinds of land cover types in the study area.
In order to compare the identification results of correspondence analysis, we adopted four other methods to identify high-temperature targets. They are Mahalanobis distance multiple truncation method, Mahalanobis distance multiple discriminant analysis method, variance analysis, and factor analysis.
The principle of Mahalanobis distance multiple truncation method is shown in Figure 8. And the parameters and results are shown in Table 6. m is the number of bands. n is the number of samples. α is the credibility. D α is the Mahalanobis distance [5]. The method obtained too many result pixels as shown in Table 6, and there are too many misjudgment pixels in this method.
The principle of mahalanobis distance multiple truncation method is showed in Figure 8. And the parameters and results are showed in Table 6. m is the numbers of bands. n is the numbers of samples. α is credibility. D α is mahalanobis distance [5]. The method got too many result pixels in Table 6, and there are too many misjudgment pixels in this method.
The principle of Mahalanobis distance multiple discriminant analysis method is showed in Figure 9. There are 9 times’ operations, and we only show the ninth operation in the Table 7. There are total 531 results pixels at the end of operation, and there are also too many misjudgment pixels in this method.
Separable measure method is based on variance analysis, where value is the inter-group variance divided by intra-group variance that shows the relationship of systematic error and random error. Separable measure of all types of features in the study area is shown in Figure 10, and separable measure of high-temperature targets with the other types of features in the study area is shown in Figure 11. On the basis of Figures 10 and 11, we can get equation 8. There are a total of 705 result pixels, and there are too many misjudgment pixels in this method as well.
(8)where v is the separable measure; ρ 5 is the visual reflectivity of band 5; ρ 6 is the visual reflectivity of band 6; and ρ 7 is the visual reflectivity of band 7.
Factor analysis [36] is similar to correspondence analysis. And the difference is at the conversion for matrix X. Factor analysis only does column conversion, while correspondence analysis does both row and column conversions. Another difference is at the relationship. Factor analysis (R-mode) reveals the relationships between bands and factors, while correspondence analysis reveals the relationships among bands, sample, and factors. There are a total of 121 result pixels in the factor analysis. It has a great advantage than the first three methods, but it also has misjudgment pixels.
The principle of Mahalanobis distance multiple truncation method.
Parameters and results of Mahalanobis distance multiple truncation method
| m | N | α | F |
|
Pixels |
|---|---|---|---|---|---|
| 7 | 453,310 | 0.05 | 2.01 | 14.070 | 490 |
| 7 | 452,820 | 0.05 | 2.01 | 14.070 | 154 |
| 7 | 452,666 | 0.05 | 2.01 | 14.070 | 26 |
| 7 | 452,640 | 0.05 | 2.01 | 14.070 | 2 |
The principle of Mahalanobis distance multiple discriminant analysis method.
Separable measure of all types of features in the study area.
Separable measure of high-temperature targets with the other types of features in the study area.
Identification results of high-temperature targets with five methods. (a) Mahalanobis distance multiple discriminant analysis method, (b) mahalanobis distance multiple discriminant analysis method, (c) separable measure method, (d) factor analysis, (e) correspondence analysis.
Parameters and results of Mahalanobis distance multiple discriminant analysis method (the ninth operation)
| Types of land cover | M | N | A | F |
|
|---|---|---|---|---|---|
| Forest land (sunny slope) | 7 | 61,384 | 0.05 | 2.01 | 14.072 |
| Forest land (shady slope) | 7 | 41,751 | 0.05 | 2.01 | 14.072 |
| Cultivated land | 7 | 37,029 | 0.05 | 2.01 | 14.073 |
| Cultivated land (greenhouse) | 7 | 22,376 | 0.05 | 2.01 | 14.074 |
| Water | 7 | 7,934 | 0.05 | 2.01 | 14.082 |
| Residential area | 7 | 37,172 | 0.05 | 2.01 | 14.073 |
| Road | 7 | 70,023 | 0.05 | 2.01 | 14.071 |
| Burned area | 7 | 12,695 | 0.05 | 2.01 | 14.078 |
| Uncultivated land | 7 | 162,415 | 0.05 | 2.01 | 14.071 |
Identification results of high-temperature targets are shown in Figure 12. The figures shown in Figure 12 are the subset of the study area. Result pixels are noted by red in the remote sensing image, which explicitly reveals the results of identification for the above methods.
Furthermore, the temperature has been inversed with the TIRS imagery (Lansat8 TIRS 10 band) by using the method of radiative transfer equation [39] in the same time phase of the study area. Pixels in thermal imagery that match positions of the right 82 pixels mentioned above serve as thermal infrared abnormal areas. And the other areas are taken as normal temperature background in the process of statistical analysis of temperature. Results are listed in Tables 8 and 9. Results show that the values of normal temperature background and high-temperature targets are rather close, which makes it difficult to distinguish targets from background. Moreover, the target with the highest temperature in inversion results is 338.32 K, which is quite different from its actual temperature (500+ K). And the temperature of high-temperature targets inversed with the shortwave infrared bands (Table 10) based on blackbody radiation characteristics is relatively consistent with the actual temperature (i.e., formula (7), because of the large area of forest fire, S = 1 is set in formula (7). If it is a small area fire, b5 and b7 are both needed to be calculate in the formula (7) to get parameter S) [40]. That is to say, TIRS data fail to reflect features of high-temperature targets properly. The main reason for this is that the radiance energy increase in SWIR bands is larger than TIR (Plank function), so SWIR bands can be used to identify high-temperature targets whose area is much smaller. And high-temperature targets with the same temperature and area will have much weaker energy in TIR rather than SWIR.
Inversion temperature of thermal infrared high targets in the study area
| Min | Max | Mean | Std dev | Mode | Median | |
|---|---|---|---|---|---|---|
| T (K) | 322.13 | 338.32 | 331.22 | 5.11 | 335.40 | 326.68 |
Inversion temperature of thermal infrared normal temperature background in the study area
| Min | Max | Mean | Std dev | Mode | Median | |
|---|---|---|---|---|---|---|
| T (K) | 304.75 | 332.25 | 320.00 | 8.21 | 319.22 | 318.50 |
Inversion temperature of shortwave infrared high targets in the study area
| Min | Max | Mean | Std dev | Mode | Median | |
|---|---|---|---|---|---|---|
| T (K) | 491.28 | 569.63 | 542.61 | 18.44 | 560.55 | 546.25 |
5 Conclusion
Compared with additional identification methods, correspondence analysis can put variables and samples into the same factor coordinate system so that relationships among them can be revealed clearly. Thus, information extraction of high-temperature targets can be realized. In the scatter plot, the clustering relationship of pixel samples indicates the significance of factors. And factor expressions can be built by band variables. With the row and column conversion first and then with factor loading matrix and factor score matrix, the relationship among variables, samples, and factors can be obtained. Factor loading matrix reflects the relationship between variables and factors. So, each factor can be considered as a linear combination of some variables. Factor score matrix reflects the relationship between samples and factors. In the result of correspondence analysis, the factor score matrix represents the factor composition weight of pixel samples, and it can be used to classify pixel samples and recognize targets. By fire f 1, high-temperature targets can be obtained. By the expression f 1, we know that SWIR bands are suitable for the better identification of high-temperature targets than TIR bands (f 1 consists of b5 and b7, and they are SWIR bands). The correspondence analysis approach can be used to identify other types of land cover in some other study areas. It can be used to analyze thematic significance of objects in the research. And it can also be used in the research of other fields. Actually, we have used it for the exam score evaluation of the students.
Acknowledgments
This research was funded by the National Natural Science Foundation of China, grant number 41871022 and 41977411. The research was funded by Scientific Research Foundation for the doctor, grant number 2018021.
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Author contributions: Conceptualization: P.J. and L.J.P.; methodology: Y.Y.F.; software: F.J.; validation: Y.Y.F, F.J., and D.H.S.; formal analysis: Y.Y.F.; investigation: Y.Y.F.; resources: D.H.S; data curation: P.J.; writing – original draft preparation: Y.Y.F.; writing – review and editing: D.H.S.; visualization: F.J.; supervision: L.J.F.; project administration: D.H.S.; funding acquisition: D.H.S. All authors have read and agreed to the published version of the manuscript.
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Conflicts of Interest: The authors declare no conflict of interest.
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