CN106845517B - Spectral tensor dimensionality reduction and classification method based on Tucker decomposition - Google Patents
Spectral tensor dimensionality reduction and classification method based on Tucker decomposition Download PDFInfo
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Abstract
The invention discloses a spectral tensor dimensionality reduction and classification method based on Tucker decomposition, which takes factors influencing the spectral characteristics of ground objects as in-class factors, and respectively takes the in-class factors, the class and a pixel spectrum as a mode to construct a 3-order tensor, and performs dimensionality reduction based on low-rank tensor decomposition on the 3-order tensor; for 3 rd order tensor
Performing low rank tensor decomposition to obtain nuclear tensor
Class space matrix UclassSpace matrix U of factors in classwithin‑classAnd a pixel spectral matrix Upixels(ii) a And classifying the non-category test hyperspectral image d by adopting a supervised classifier. The hyperspectral image classification method can classify the hyperspectral images after the model is established without adjustment, and other tensor modeling methods can achieve the optimal classification effect only by repeatedly setting and adjusting parameters; the invention maps all the pixel spectrums of one class to the same coefficient vector, thereby minimizing the influence of various factors, not only improving the classification precision, but also having stable result.
Description
Technical Field
The invention belongs to the technical field of remote sensing image processing, and particularly relates to a spectral tensor dimensionality reduction and classification method based on Tucker decomposition.
Background
The hyperspectral image provides detailed and rich description of spectral characteristics of the ground objects, greatly improves the classification capability of the ground objects, and is widely applied to the aspects of geological exploration, earth resource investigation, urban remote sensing, planning management, environment and disaster monitoring, fine agriculture, mapping, archaeology and the like.
However, the hyperspectral image is composed of a large amount of waveband data, and the wavebands form a high-dimensional feature space, and a huge amount of calculation is required for processing the hyperspectral image, so that a data disaster is caused. The most effective way to address this problem is to reduce the dimensions. Principal Component Analysis (PCA) is currently the most widely used dimension reduction method due to its simplicity and efficiency. However, PCA requires vectorization of the hyperspectral image and only performs processing in the spectral dimension of the hyperspectral image, ignoring spatial information of the hyperspectral image.
In order to fully utilize the spatial information of the hyperspectral image, researchers have proposed many methods of modeling the hyperspectral image as a tensor. The hyperspectral image may be a set of two-dimensional images and may therefore be represented by multidimensional data, comprising two spatial dimensions and one spectral dimension. Letexier et al model hyperspectral images as third order tensors
Where I1 and I2 are pixel positions and I3 is the number of bands. And carrying out spatial and spectral joint analysis on the hyperspectral image by using a tensor decomposition model. A low rank approximation of the tensor data is generated using the Tucker3 decomposition model, referred to as the LRTA- (k1, k2, k3) method.
Tensor-based low rank approximationNadine Renard et al propose to first perform low rank approximation on the spatial dimension of the hyperspectral data to reduce noise on the spatial dimension; then reduced in the spectral dimension using PCA
A method. The method improves the classification accuracy. However, the method only models the hyperspectral cube as a third-order tensor, and does not consider the real reason influencing the hyperspectral classification precision: the spectral characteristics of the terrain are affected by a variety of factors such as light, mixing, atmospheric scattering, atmospheric radiation, and the like.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a spectral tensor dimension reduction method based on Tucker decomposition, which comprises the following steps:
The invention also provides a hyperspectral image classification method, which comprises the following steps:
step one, the dimension reduction method of claim 1;
step two, judging the class of the pixel spectrum d to be tested:
step 21, setting an initial first mode k and an initial second mode w of the pixel spectrum d to be tested as 1;
Wherein the content of the first and second substances,
in the step (formula 1), the reaction mixture,
is the nuclear tensor; u shapeclassIs a space-like matrix; u shapewithin-classIs an intra-class factor spatial matrix; u shapepixelsIs a pixel spectrum matrix; for 3 rd order tensor
Performing low rank tensor decomposition to obtain nuclear tensor
Class space matrix UclassSpace matrix U of factors in classwithin-classAnd a pixel spectral matrix Upixels；
Step 23, mixing
Flattening along the first mode results in Bw(class)；
Step 24, obtaining coefficient c by (formula 2)w，
Step 25, w is w + 1;
step 26, repeating the steps 22 to 25 until W is more than W, and executing the step 27;
in a step 27, the process is carried out,
step 28, k is k + 1;
step 29, repeating the step 22 to the step 28 until k is more than C, and executing the step 210;
step 210, if ckSatisfy the requirement of
The test pixel spectrum d belongs to class k in class C, k is less than or equal to C;
wherein, ck＝Uclass(k,:)T。
Compared with the prior art, the invention has the following technical effects:
(1) according to the method, the factors influencing the hyperspectral image are modeled into tensors for the first time, so that the problem of modeling the factors influencing the hyperspectral image is solved;
(2) the hyperspectral image classification method can classify the hyperspectral images after the model is established without adjustment, and other tensor modeling methods can achieve the optimal classification effect only by repeatedly setting and adjusting parameters;
(3) the invention maps all the pixel spectrums of one class to the same coefficient vector, thereby minimizing the influence of various factors, not only improving the classification precision, but also having stable result.
Drawings
FIG. 1 is an exploded view of the integrated dimension reduction of the spectral tensor;
FIG. 2(a) is a pseudo color composite of the HYDICE data set bands 60, 27 and 17;
FIG. 2(b) is a true tag diagram of the HYDICE dataset;
FIG. 3 is a plot of spectra for each class of HYDICE dataset;
FIG. 4(a) shows 7 classes in the HYDICE dataset and corresponding spectral curves;
FIG. 4(b) is a spectral plot of different samples in turf categories;
FIG. 4(c) is a graph showing the formation of a 3-order spectral tensor;
FIG. 5(a) is a SVM classification chart for PCA; FIG. 5(b) is a SVM classification chart of LRTA- (60,60, 7); FIG. 5(c) shows LRTAdr-(60,60,7) an SVM classification map; FIG. 5(d) is a SVM classification chart of the present invention;
FIG. 6(a) is the relationship between the overall classification rate (OA) of LRTA- (60,60,7) and the number of iterations of the Alternating Least Squares (ALS); FIG. 6(b) shows LRTAdr-(60,60,7) a global classification rate (OA) versus a number of Alternating Least Squares (ALS) iterations; FIG. 6(c) is thisThe relationship between the overall classification rate (OA) and the number of iterations of the Alternating Least Squares (ALS) of the invention;
FIG. 7(a) is the relation of overall classification rate (OA) of LRTA- (k1, k2,7) to spatial rank; FIG. 7(b) shows LRTAdr-Overall classification rate (OA) of (k1, k2,7) versus spatial rank.
Detailed Description
The invention is further illustrated by the following examples and figures.
Example 1
The embodiment provides a spectral tensor dimension reduction method based on Tucker decomposition, which takes a randomly selected pixel spectrum as an in-class factor, and takes bands of the in-class factor, the class and the pixel spectrum as modes respectively to construct a 3-order tensor, and dimension reduction based on low-rank tensor decomposition is carried out on the 3-order tensor;
because the spectral characteristics of the ground objects are susceptible to various factors such as illumination, mixing, atmospheric scattering, atmospheric radiation and the like, the spectral characteristics of the ground objects are used as intra-class factors for modeling, and the classification accuracy of the hyperspectral images is improved.
The low rank approximation of the tensor data is generated by using the Tucker3 decomposition model, and the classification precision of the hyperspectral image is improved.
Example 2
In this embodiment, the pixel spectrum of the hyperspectral image selected in embodiment 1 is used as a training set, and any unclassified pixel spectrum in Washington DC Mall of hybrid is input as a test pixel spectrum d.
Wherein d is (0.4012, 0.3909, 0.3885, 0.4026, 0.4004, 0.3967, 0.3778, 0.3441, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.5005, 0.501, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3096, 0.3792, 0.2951, 0.3792, 0.268, 0.3792, 0.3792, 0.3792, 0.231, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.206, 0.3792, 0.3792, 0.3792, 0.3792, 0.175, 0.3792, 0.1809, 0.17, 0.3792, 0.3792, 0.3792, 0.3792, 36145, 0.3792, 0.3792, 0.3792, 0.3792, 360672, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 360.0.0.68, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 0.3792, 3672,0.0.0.0.68, 3672,0.0.68, 3672,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72, 0.035, 0.0293, 0.024, 0.0171, 0.0107, 0.0036, 0.0006, 0.0012, 0.0025, 0.0075, 0.0126, 0.0132, 0.0061, 0.0042, 0.0094, 0.0166, 0.0168, 0.0125, 0.0119, 0.0137, 0.0168, 0.0181, 0.0187, 0.0186, 0.0187, 0.0191, 0.0187, 0.0174, 0.0163, 0.0158, 0.015, 0.0149, 0.0146, 0.0153, 0.0155, 0.0148, 0.0136, 0.0123, 0.0106, 0.0094, 0.009, 0.0086, 0.00486, 0.0050.0050, 005008, 0.0050.0062, 0.0061, 0.0065, 0.0061, 0.0025, 0.0065, 0.0025, 0.1, 0.0025, 0.1, 0.4, 0.8;
in this embodiment, the determining the class of the pixel spectrum d to be tested based on embodiment 1 includes the following steps:
in this embodiment, k is a natural number from 1 to 7, and represents a Roof (Roof), a street (street), a lawn (Grass), a Tree (Tree), a Path (Path), a Water body (Water), and a Shadow (Shadow), respectively.
Wherein the content of the first and second substances,
in the step (formula 1), the reaction mixture,
is the nuclear tensor; u shapeclassIs a space-like matrix; u shapewithin-classIs an intra-class factor spatial matrix; u shapepixelsIs a pixel spectrum matrix; for 3 rd order tensor
Performing low rank tensor decomposition to obtain nuclear tensor
Class space matrix UclassSpace matrix U of factors in classwithin-classAnd a pixel spectral matrix Upixels；
Step 3, mixing
Flattening along the first mode results in Bw(class)；
The flattening is to rearrange the N-order tensor into a matrix form. E.g. tensor
N-mode flattened matrix A(n)Is defined as
Wherein M isn＝In+1In+2…INI1I2…In-1。
Step 4, by (formula 2), obtaining
Wherein, cwIs a coefficient;
step 5, w is w + 1;
in the step 7, the step of,
step 9, repeating the step 2 to the step 8 until k is more than C and executing the step 10;
wherein, ck＝Uclass(k,:)T。
k is a natural number from 1 to 7, and represents a Roof (Roof), a street (street), a lawn (Grass), a Tree (Tree), a Path (Path), a Water body (Water), and a Shadow (Shadow), respectively.
And (3) comparison test:
in order to test the classification efficiency of the invention, a hyperspectral image of Washington DC Mall of HYDICE is selected, and the size of an original image is 1280 multiplied by 307. From visible to infrared spectrum of 0.4 ~ 2.4 um total 210 wave bands, due to the opaque atmosphere, 0.9 ~ 1.4um area of the wave band is abandoned, the remaining 191 wave bands. In this experiment, the inventors cut the size of the image to 250 × 307.
Pseudo color composition maps and real label maps of bands 60, 27 and 17 of the Washington DC Mall hyperspectral image are shown in FIGS. 2(a) and 2 (b). The hyperspectral image comprises 7 types of samples which are respectively as follows: roof (Roof), street (street), lawn (Grass), Tree (Tree), Path (Path), Water (Water) and Shadow (Shadow).
The spectral curves for each sample are shown in fig. 3, and are very similar because streets, roads and roofs are constructed from similar materials, and the spectral curves are simpler because the streets are flatter and broader. Trees and grassland are similar, so spectral curves are highly similar, resulting in increased classification difficulty. The shadow and the water body are uniform and consistent integrally, so that the spectral curve is simple, the information amount is less, and the identification is difficult.
In the commonly used prior art methods of LRTA- (k1, k2, k3) and LRTAdr- (k1, k2, p), the spectra of pixels in the training set are represented as a 3 < rd > order tensor
In the invention, the pixel spectrum in the training set is constructed into 3-order tensor
As shown in fig. 4. Fig. 4(a) is a 7-class ground object and its corresponding spectrum curve in the hyperspectral image, and fig. 4(b) is a spectrum curve of different samples in the lawn class, and it is seen from the graph that although the same class of ground object is, its spectrum curves are slightly different, which indicates that the same class of ground object shows different spectrums when influenced by different factors, which increases the difficulty of identification. FIG. 4(c) is a 3 rd order tensor
The process of construction of (1).
Both training and test samples were randomly extracted from the dataset, with the number of samples shown in table 1.
TABLE 1 number of training and testing samples for classification in dataset
The present invention performed three experiments. The first is a classification experiment of four methods, the second is an ALS performance experiment based on three tensor methods, and the third is a parameter adjustment experiment based on three tensor methods. The experiment uses the Overall classification rate (OA) and Kappa coefficient as indexes, and the classifiers used are Support Vector Machine (SVM) and Mahalanobis Distance (MD).
Since the dimensionality of the method is reduced to 307 multiplied by 250 multiplied by 7, for comparison, the number of principal components of PCA is set to 7, and k1, k2 and k3 of LRTA- (k1, k2 and k3) are selected to be 60,60 and 7; k1, k2, p of LRTAdr- (k1, k2, p) are selected to be 60,60, 7.
Using the SVM classifier, the classification chart of the four methods is shown in fig. 5, and the experimental results are shown in table 2. It can be seen from fig. 5 and table 2 that our proposed method of the invention achieves the best results in both classification plots, OA and Kappa coefficients. From these classification maps, it can be seen that there are pixels of the Roof class among pixels of the Street class, of which FIG. 5(c) is most apparent. Among the pixels of the Water class are some pixels of the Shadow class, of which fig. 5(b) is the worst and fig. 5(d) is the best. This is because the LRTA- (k1, k2, k3) method is only a result of filtering in the spatial and spectral dimensions, and not spectral dimensionality reduction. With Roof class pixels mixed in Path class pixels, FIG. 5(b) is most apparent, while FIG. 5(d) is much cleaner than the others. These phenomena all indicate that: in the categories with higher resolution difficulty (Water category and Shadow category, rofof category and Path category), the classification effect of fig. 5(d) is obviously better than that of the other three methods.
TABLE 2 Classification accuracy of four methods
ALS provides a solid foundation for the spatial and spectral combination treatment of LRTA- (k1, k2, k3), LRTAdr- (k1, k2, p) and the method of the invention. To illustrate the performance of the ALS algorithm, fig. 6 is a graph of the number of OA and ALS iterations, using SVM and MD classifiers. In this experiment k1, k2, k3, p were set to 60,60,7, respectively.
The OA values at iteration 0 represent the classification results at the initial value of ALS. As can be seen from fig. 6(a) & (b), the LRTA- (k1, k2, k3) and LRTAdr- (k1, k2, p) methods require at least 2 iterations to achieve a good classification result. And the classification results of both methods are somewhat oscillatory at different iteration numbers.
As can be seen from fig. 6(c), the method of the present invention achieves the best classification result using only the initial values of ALS. In addition, the method of the invention has higher classification precision under both classifiers than the LRTA- (k1, k2, k3) and LRTAdr- (k1, k2, p) methods, and the result is stable.
In this experiment, 200 samples were selected for training for each class, with the 200 samples representing various factors. The method of the present invention represents each class with a 7-dimensional coefficient vector, and thus features 7 in the spectral domain. And no parameter adjustment is required.
Also based on tensor method, LRTA- (k1, k2, k3) and LRTAdr- (k1, k2, p) methods need to adjust the spatial rank (k1, k2) correspondingly, so as to reach higher overall recognition rate. As shown in fig. 7. Ranks of modes 1, 2 with k1 and k2, OA being a function of k1 and k 2. Experiments were performed using SVM classifiers, k1 and k2 varying from 1 to 150, k3 and p set to 7.
As can be seen from fig. 7, for the LRTA- (k1, k2, k3) method, k1 and k2 should be at least greater than 10 to obtain better classification effect; for the LRTAdr- (k1, k2, p) method, k1 and k2 should be at least more than 20 to obtain better classification effect; and, if a stable OA value is desired, it should be at least 80-100. This is why k1 and k2 are generally chosen to be at least greater than 20 in practical applications, but k1 and k2 should be chosen to be as small as possible because the smaller the rank of the tensor is, the more sparse the data is, and the more favorable it is to store and process.
In the invention, a new dimension reduction method for a hyperspectral image is provided, and the method has the following advantages: 1) the factors that affect the hyperspectral image are modeled as tensors for the first time. 2) The model can be used after being built without adjustment, and the other tensor modeling methods can achieve the optimal classification effect only by repeatedly setting and adjusting parameters. 3) The method has the greatest advantage that all pixel spectrums of one class are mapped to the same coefficient vector, so that the influence of various factors is minimized, the classification precision is improved, and the result is stable. A series of experiments prove that the classification precision of the method is improved compared with other three methods.
Claims (1)
1. A hyperspectral image classification method is characterized by comprising the following steps:
the method comprises the following steps:
step 11, randomly selecting a pixel spectrum in a hyperspectral image as a training set, wherein the selected pixel spectrum has L wave bands and C samples, and randomly selecting W pixel spectra in each of the C samples as an intra-class factor, wherein C is a natural number which is more than or equal to 1, and W is a natural number which is more than or equal to 1;
step 12, constructing 3-order tensor
Wherein C is a first mode, W is a second mode, L is a third mode, wherein L is a natural number greater than or equal to 1, and then for a 3 rd order tensor
Performing low rank decomposition to obtain nuclear tensor
Class space matrix UclassSpace matrix U of factors in classwithin-classAnd a pixel spectral matrix Upixels；
Step two, judging the class of the pixel spectrum d to be tested:
step 21, setting an initial first mode k and an initial second mode w of the pixel spectrum d to be tested as 1;
step 22, calculating the basis tensor
Replacing W of the basic tensor B of the pixel spectrum of the training set by W to obtain the sub-tensor
Step 23, mixing
Flattening along the first mode results in Bw(class)；
Step 24, obtaining coefficient c by (formula 2)w，
Step 25, w is w + 1;
step 26, repeating the steps 22 to 25 until W is more than W, and executing the step 27;
in a step 27, the process is carried out,
step 28, k is k + 1;
step 29, repeating the step 22 to the step 28 until k is more than C, and executing the step 210;
step 210, if ckSatisfy the requirement of
The test pixel spectrum d belongs to class k in class C, k is less than or equal to C;
wherein, ck＝Uclass(k,:)T。
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