CN112417188B - Hyperspectral image classification method based on graph model - Google Patents
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Abstract
The invention discloses a hyperspectral image classification method based on a graph model, which is characterized by comprising the following steps of: 1) modeling a graph; 2) resolving an optimization problem; 3) decomposing a Hessian matrix; 4) an approximation of newton step size; 5) carrying out iterative solution; 6) distributed solving; 7) and solving the classification result. The method has low calculation complexity under large-scale data and can finish classification with higher precision.
Description
Technical Field
The invention relates to the technical field of hyperspectral images, graph models and machine learning, in particular to a hyperspectral image classification method based on a graph model.
Background
The hyperspectral image data is a special image, is firstly applied to the satellite remote sensing technology, and is widely applied to the fields of military affairs, medicine, geology, agriculture and the like. The common image is subjected to broadband imaging during imaging, the imaging result hardly has spectral characteristics, and the related research is extremely dependent on the spatial resolution of the image. The hyperspectral image is the result of imaging of multiple narrow bands, and compared with a common image, the hyperspectral image carries abundant spectrum information. The research on the hyperspectral data is very extensive, and classification is an important item. The hyperspectral image classification aims at marking pixel points, and the marking result can well reflect the relevant characteristics of the target to be detected. However, the hyperspectral image classification has the problems of small known sample size, high data dimensionality and the like.
The diagram is a common data structure, and is commonly used in wireless sensor networks, social networks and other scenarios. In addition, graphs are also commonly used for dimensionality reduction of data with higher feature dimensions.
Machine learning is a general term for a type of task solution method, which mathematically models a related task and then uses a computer or other tool to solve the modeled optimization problem to obtain a result. Machine learning has been widely used in industry, traffic, IC design, etc. through decades of development.
Disclosure of Invention
The invention aims to provide a hyperspectral image classification method based on a graph model, aiming at the problems of large data size, high data dimensionality, small known sample size and the like in a hyperspectral image classification task. The method has low calculation complexity under large-scale data and can finish classification with higher precision.
The technical scheme for realizing the purpose of the invention is as follows:
a hyperspectral image classification method based on a graph model comprises the following steps:
1) graph modeling: suppose the hyperspectral image data is X ═ X1,x2,...,xm×n]∈Rm×n×dTotal of m × n pixel points, xi∈RdIs the feature vector of the ith pixel,labels on pixels in the data are all from L ═ L 1,l2,...,lcAnd all the types of the C are replaced by C,is a tag of a known moiety in X,is an unknown tag, has a value of 0, andfeature vector x of different pixel points of hyperspectral image dataiThe graph G is constructed as { V, E, W }, where V is a node set of the graph, corresponding to each pixel in the data and connected by an edge, E is an edge set, the edge is used to describe similarity and adjacency relation between nodes, W is a weight matrix, and an internal element represents a similarity degree corresponding to two nodes and is defined as formula (1):
2) the optimization problem is summarized as follows: the one-hot encoding matrix Y of the label Y is defined as shown in formula (2):
yiis the ith element in tag y. From Y, the classification problem of hyperspectral images can be summarized as shown in equation (3):
and (3) solving the formula (3) to obtain a one-hot coding matrix F for classification, wherein in the formula (3), alpha is a weight factor, and L isn=I-D-1/2WD-1/2Is a normalized graph Laplace matrix, I is a unit matrix, yjAnd fjThe j-th columns of Y and F respectively,is fjD is a degree matrix, defined as shown in formula (4):
will D-1/2WD-1/2Is marked as WnThe problem in the formula (3) is composed of c optimization problems, which are independent from each other and similar in solving process, and only one of the optimization problems is analyzed, so that f is equal to f jThe method comprises the following steps:
3) decomposition of the Hessian matrix: the problem in the formula (5) is solved by using a Newton method, and the information of the first order and the second order gradient of the problem is respectively shown in formulas (6) and (7):
thus obtaining the Hessian matrix H ═ alpha I + L of the objective functionnLet Wn=Wnd+WnuWherein W isnd=diag(Wn) From Ln=I-WnThe method comprises the following steps:
A=αI+(1+θ)(I-Wnd) (8),
B=Wnu+θ(I-Wnd) (9),
wherein theta is a parameter for controlling decomposition, and the Hessian matrix can be decomposed into a combination of A and B as shown in formula (10):
H=A-B (10);
4) approximation of newton step size: when solving by the Newton method, the Newton step length of the k step is represented by the formula (10):
let P equal Wn-αI,Q=(I-P)-1Q ≈ I + P by Taylor expansion, the Newton step size of equation (11) is approximated by equation (12):
5) and (3) iterative solution: equation (5) is solved according to equation (13) using the approximate newton step size in equation (12):
in equation (13), k in the upper right corner of the variable is the number of iterations, and f0=0,f1When 1 is equal toWhen the result is true, terminating the iteration;
6) distributed solution: the matching terms in the formula (5) are respectively expressed asThe first order gradient information at the ith node is shown in equation (14):
wijis WnThe element in the ith row and j column corresponds to the weight value between the node i and the node j on the graph, so that for the node i, the following elements exist:
6-8) on all nodesAre spliced into fk+1Judging the termination conditionWhether or not: if the condition is terminatedIf it is true, fk+1Setting a corresponding column in the one-hot matrix, and starting to solve the next column of the one-hot matrix; if the condition is terminatedIf not, f is usedk+1Performing the next iteration with the initial value;
7) solving a classification result: obtaining a one-hot coding matrix F through the step 6), and finally obtaining a classification result through a formula (15)
The technical scheme includes that a graph model is adopted to carry out dimensionality reduction on hyperspectral image data, then a learning task is subjected to problem regression, then a Hessian matrix is approximated through matrix decomposition, and the approximated Hessian matrix is used for solving through a quasi-Newton method.
The method has the advantages of low calculation complexity and high classification precision, and is more suitable for the large-scale hyperspectral image classification problem.
Drawings
FIG. 1 is a schematic diagram of iterative convergence in KSC data for implementing the method;
fig. 2 is a schematic diagram of iterative convergence in IndianPines data by the implementation method.
Detailed Description
The invention will be further described with reference to the following drawings and examples, but is not limited thereto.
Example (b):
a hyperspectral image classification method based on a graph model comprises the following steps:
1) graph modeling: suppose the hyperspectral image data is X ═ X1,x2,...,xm×n]∈Rm×n×dTotal of m × n pixel points, xi∈RdIs the feature vector of the ith pixel,labels on pixels in the data are all from L ═ L1,l2,...,lcAnd all the types of the C are replaced by C,is a tag of a known moiety in X,is an unknown tag, has a value of 0, andfeature vector x of different pixel points of hyperspectral image dataiThe graph G is constructed as { V, E, W }, where V is a node set of the graph, corresponding to each pixel in the data and connected by an edge, E is an edge set, the edge is used to describe similarity and adjacency relation between nodes, W is a weight matrix, and an internal element represents a similarity degree corresponding to two nodes and is defined as formula (1):
2) the optimization problem is summarized as follows: the one-hot encoding matrix Y of the label Y is defined as shown in formula (2):
yiIs the ith element in tag y. From Y, the classification problem of hyperspectral images can be summarized as shown in equation (3):
and (3) solving the formula (3) to obtain a one-hot coding matrix F for classification, wherein in the formula (3), alpha is a weight factor, and L isn=I-D-1/2WD-1/2Is a normalized graph Laplace matrix, I is a unit matrix, yjAnd fjThe j-th columns of Y and F respectively,is fjD is a degree matrix, defined as shown in formula (4):
will D-1/2WD-1/2Is marked as WnThe problem in the formula (3) is composed of c optimization problems, which are independent from each other and similar in solving process, and only one of the optimization problems is analyzed, so that f is equal to fjThe method comprises the following steps:
3) decomposition of the Hessian matrix: the problem in the formula (5) is solved by using a Newton method, and the information of the first order and the second order gradient of the problem is respectively shown in formulas (6) and (7):
thus obtaining the Hessian matrix H ═ alpha I + L of the objective functionnLet Wn=Wnd+WnuWherein W isnd=diag(Wn) From Ln=I-WnThe method comprises the following steps:
A=αI+(1+θ)(I-Wnd) (8),
B=Wnu+θ(I-Wnd) (9),
wherein theta is a parameter for controlling decomposition, and the Hessian matrix can be decomposed into a combination of A and B as shown in formula (10):
H=A-B (10);
4) approximation of newton step size: when the Newton method is used for solving, the Newton step length of the k step is represented by the formula (10):
let P equal Wn-αI,Q=(I-P)-1Q ≈ I + P by Taylor expansion, the Newton step size of equation (11) is approximated by equation (12):
5) And (3) iterative solution: equation (5) is solved using the approximate newton step size in equation (12) according to equation (13):
in equation (13), k at the upper right corner of the variable is the number of iterations, and f0=0,f1When being equal to 1When the result is true, terminating the iteration;
6) distributed solution: the matching terms in the formula (5) are respectively expressed asThe first order gradient information at the ith node is shown in equation (14):
wijis WnThe element in the ith row and j column corresponds to the weight value between the node i and the node j on the graph, so that for the node i, the following elements exist:
6-8) on all nodesAre spliced into fk+1Judging the termination conditionWhether or not: if the condition is terminatedIf it is true, fk+1Setting a corresponding column in the one-hot matrix, and starting to solve the next column of the one-hot matrix; if the condition is terminated If not, use fk+1Performing the next iteration for the initial value;
7) solving a classification result: obtaining a one-hot coding matrix F by the step 6), and finallyObtaining the classification result through the formula (15)
Simulation example 1:
in the embodiment, KSC data is adopted for simulation, 176 frequency bands are arranged in the KSC data, 5211 pixel points are total after background removal, the pixel points can be divided into 13 classes and are a multi-class learning task, before simulation, tag values are sampled to generate data sets with different known tag numbers, for multi-item comparison, data sets with 5, 10, 15 and 20 known samples in each class are generated, table 1 shows that the classification performance comparison in the KSC data by adopting the method of the embodiment and the centralized method is performed, the OA parameters and the calculation time are included, and the simulation result of table 1 shows that in the KSC data, compared with the centralized method, the classification accuracy by adopting the method of the embodiment and the centralized method is completely consistent, the calculation speed by adopting the method of the embodiment is slightly higher than that by adopting the centralized method, as shown in figure 1, iterative convergence can be performed within limited times by adopting the method of the embodiment, it is demonstrated that the method of the present example produces better results and is less time consuming.
TABLE 1
Number of samples known | 5 | 10 | 15 | 20 |
OA value Using the method of this example | 66.75% | 71.76% | 73.87% | 75.03% |
Using this example method time consuming(s) | 7.476 | 8.181 | 8.057 | 8.153 |
Using centralized approach OA values | 66.5% | 71.78% | 73.87% | 75.03% |
Consuming time using a centralized approach(s) | 35.72 | 34.97 | 35.08 | 35.55 |
Simulation example 2:
in the embodiment, IndanPines data is adopted for simulation, 200 frequency bands exist in the IndanPines data, 10249 pixel points are obtained after background removal, the pixel points can be divided into 16 classes and are also a multi-class learning task, as in simulation example 1, sampling produced datasets of only 5, 10, 15, 20 known samples for each class, and table 2 shows the comparison of classification performance in indianpins data using the method of the present example and the centralized method, which also includes OA parameters and the time consumption of calculation, the simulation results in table 2 show that, in Indian pines data, compared with the centralized method, the classification accuracy of the method is basically consistent with that of the centralized method, in the simulation example, the calculation speed of the method is far better than that of the method adopting a centralized method, and as shown in fig. 2, iterative convergence can be performed within a limited number of times by adopting the method of the example, which shows that the method of the example is more suitable for a hyperspectral image classification task under large-scale data.
TABLE 2
Number of samples known | 5 | 10 | 15 | 20 |
OA value Using the method of this example | 41.98% | 46.69% | 49.71% | 51.67% |
Using this example method time consuming(s) | 37.09 | 38.59 | 39.1 | 39.83 |
Using centralized approach OA values | 42.02% | 46.7% | 49.72% | 51.68% |
Consuming time using a centralized approach(s) | 242.9 | 271 | 242.5 | 299.6 |
。
Claims (1)
1. A hyperspectral image classification method based on a graph model is characterized by comprising the following steps:
1) graph modeling: suppose the hyperspectral image data is X ═ X1,x2,...,xm×n]∈Rm×n×dTotal of m × n pixel points, xi∈RdIs the feature vector of the ith pixel,labels on pixels in the data are all from L ═ L1,l2,...,lcAnd all the types of the C are replaced by C,is a tag of a known moiety in X,is an unknown tag, has a value of 0, andfeature vector x of different pixel points of hyperspectral image dataiAccording to the similar characteristics of the method, a graph G is constructed, wherein the graph G is { V, E, W }, V is a node set of the graph and corresponds to each pixel in the dataThe nodes are connected by edges, E is an edge set, the edges are used for describing similarity and adjacency relations between the nodes, W is a weight matrix, and internal elements represent the similarity degree of the corresponding two nodes and are defined as shown in a formula (1):
2) the optimization problem is summarized as follows: the one-hot encoding matrix Y of the label Y is defined as shown in formula (2):
yiis the ith element in label y; from Y, the classification problem of hyperspectral images can be summarized as shown in equation (3):
and (3) solving the formula (3) to obtain a one-hot coding matrix F for classification, wherein in the formula (3), alpha is a weight factor, and L is n=I-D-1/2WD-1/2Is a normalized graph Laplace matrix, I is a unit matrix, yjAnd fjThe j-th columns of Y and F respectively,is fjD is a degree matrix, defined as shown in formula (4):
will D-1/2WD-1/2Is marked as WnThe problem in the formula (3) is composed of c optimization problems, which are independent from each other and similar in solving process, and only one of the optimization problems is analyzed, so that f is equal to fjThe method comprises the following steps:
3) decomposition of the Hessian matrix: the problem in the formula (5) is solved by using a Newton method, and the information of the first order and the second order gradient of the problem is respectively shown in formulas (6) and (7):
thus obtaining the Hessian matrix H ═ alpha I + L of the objective functionnLet Wn=Wnd+WnuWherein W isnd=diag(Wn) From Ln=I-WnThe method comprises the following steps:
A=αI+(1+θ)(I-Wnd) (8),
B=Wnu+θ(I-Wnd) (9),
wherein theta is a parameter for controlling decomposition, and the Hessian matrix can be decomposed into a combination of A and B as shown in formula (10):
H=A-B (10);
4) approximation of newton step size: when solving by the Newton method, the Newton step length of the k step is represented by the formula (10):
let P equal Wn-αI,Q=(I-P)-1Q ≈ I + P by Taylor expansion, the Newton step size of equation (11) is approximated by equation (12):
5) and (3) iterative solution: equation (5) is solved according to equation (13) using the approximate newton step size in equation (12):
in equation (13), k in the upper right corner of the variable is the number of iterations, and f 0=0,f1When 1 is equal toWhen the result is true, terminating the iteration;
6) distributed solution: the matching terms in the formula (5) are respectively expressed asThe first order gradient information at the ith node is shown in equation (14):
wijis WnThe element in the ith row and j column corresponds to the weight value between the node i and the node j on the graph, so that for the node i, the following elements exist:
6-8) will f on all nodesi k+1Are spliced into fk+1Judging the termination conditionWhether or not: if the condition is terminatedIf it is true, fk+1Setting a corresponding column in the one-hot matrix, and starting to solve the next column of the one-hot matrix; if the condition is terminatedIf not, f is usedk+1Performing the next iteration with the initial value;
7) solving a classification result: obtaining a one-hot coding matrix F through the step 6), and finally obtaining a classification result through a formula (15)
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