CN111553338A - Hyperspectral feature selection method based on simulated annealing algorithm - Google Patents

Hyperspectral feature selection method based on simulated annealing algorithm Download PDF

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CN111553338A
CN111553338A CN202010342167.1A CN202010342167A CN111553338A CN 111553338 A CN111553338 A CN 111553338A CN 202010342167 A CN202010342167 A CN 202010342167A CN 111553338 A CN111553338 A CN 111553338A
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尹忠海
李明杰
刘银年
孙德新
梁建
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QIDONG PHOTOELECTRIC AND REMOTE SENSING CENTER SHANGHAI INSTITUTE OF TECHNICAL PHYSICS OF CHINESE ACADEMY OF SCIENCES
Nantong Academy of Intelligent Sensing
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Abstract

The invention discloses a hyperspectral feature selection method based on a simulated annealing algorithm, which comprises the following steps: step one, formulating a coding mode according to spectral characteristics; selecting a target function according to the spectral characteristics; initializing parameters of a simulated annealing algorithm, and starting to search an optimal result; step four, continuously comparing the values of historical results of past generations and the current result, and continuing to perform the algorithm on a more optimal value; and step five, repeating the step four until the optimal result does not change within the preset stable algebra or reaches the preset algebra. The invention has the advantages that: the difference solution is received with a certain probability and is used for jumping out of the local optimal solution, the global optimal solution is achieved, the hyperspectral feature selection is completed, and a large amount of manpower, material resources and financial resources can be saved.

Description

Hyperspectral feature selection method based on simulated annealing algorithm
Technical Field
The invention relates to the field of hyperspectral remote sensing, in particular to a hyperspectral feature selection method based on a simulated annealing algorithm.
Background
Hyperspectral remote sensing, also known as imaging spectroscopy, is derived from multispectral remote sensing techniques and can image using tens to hundreds of continuous and narrow spectral bands. With the continuous improvement of the hyperspectral remote sensing technology, the application field is continuously expanded, and the method mainly relates to the fields of atmospheric exploration, environmental monitoring, earth resources, geological science, ecological science, hydrology science and military.
The reflectivity information of each spectral band contained in the hyperspectral image technical image can be obtained after the data of each pixel point in the hyperspectral image technical image is preprocessed. Therefore, the type of the ground object represented by each pixel point in the hyperspectral image can be identified by extracting the spectral reflectivity information, and the exploration of two-dimensional space perception is expanded into perception of three-dimensional space information and spectral information. The method has the characteristics of high spectral resolution, integrated spectra, multiple spectral bands, continuous imaging in a certain spectral range and low spatial resolution. Due to the characteristics of the data in the ultra-high dimensionality of the spectral dimension, the method brings new challenges to the traditional remote sensing image processing:
the high-dimensional data structure introduces a 'Huges' phenomenon (in the high-dimensional data analysis process, under the condition that the number of training samples is limited, the classification precision can rise first and then fall along with the increase of data dimensions) into the hyperspectral image processing process. The high-dimensional data structure makes the data of the hyperspectral image very large; the spatial resolution of the hyperspectral image is not high.
Aiming at the challenges, how to select features according to the characteristics of a hyperspectral image data structure becomes a key in the current hyperspectral remote sensing field. In hyperspectral images, the spectral bands are considered to be important features of themselves. For the hyperspectral technology, a feature selection algorithm drops key and significant bands in original hyperspectral data, and a subset with most features of the original data is used for reducing dimensionality. Namely, it isSetting N dimension characteristic vector space X as X1,x2,...,xN}. Based on a certain criterion, M high-quality features are selected from an original vector space X to form an M-dimensional vector Y, and the vector Y can be described as Y ═ { Y ═ Y1,y2,...,yM(M < N), each component Y is a subset of X, since the vector Y is only a subset of XiIt is necessary that there is a one-to-one correspondence with some of the features in the original vector space.
In the prior art, a method is proposed in which a candidate feature subset is generated from an original data set, then the candidate subset is evaluated by using a certain evaluation criterion, and the evaluation result is compared with a stop condition. And if the stopping condition is met, stopping the feature selection process, and returning and outputting the current candidate feature subset. And finally, verifying the validity of the selected result. Generally, the method comprises four parts, namely subset generation, subset evaluation, stopping criterion and subset verification. The method is easy to fall into a local optimal solution and cause high uncertainty.
In the prior art, a feature selection method based on supervision is also provided, and the feature selection method under supervision learning can be divided into a filtering type method and an encapsulation type method. By adopting the packaging method, due to the interdependence between the characteristic selection process and the classification model, the problems of overfitting and poor generalization performance are easily caused. There are two problems with the filtering method, 1, the very high probability between the selected bands of each filtering method is strongly correlated; 2. The classification of some bands shows a significant and indispensable influence when combined with other bands.
There are also unsupervised feature selection methods in the prior art, in which methods of band ordering, band clustering and band subspace decomposition are usually selected to minimize the mutual nature between the selected bands while minimizing the information richness of the selected band combinations. Features selected using the band ordering method may have a large redundancy resulting in little meaningful information being provided complementary to existing information. Adopting the band clustering algorithm 2) will inevitably result in a deviation of the selected band from the true center point, often because the cluster is selected to approximate the center point. And this method also has a problem that the spectral continuity of HSI is not considered. No matter which method is adopted, the method needs to consume large manpower and is powerless, the efficiency is low, and the method is easy to fall into the local optimal solution.
Disclosure of Invention
The invention aims to solve the technical problems of how to improve the efficiency of hyperspectral feature selection and avoid falling into a local optimal solution, and provides a hyperspectral feature selection method based on a simulated annealing algorithm.
In order to achieve the purpose, the invention provides the following technical scheme: a hyperspectral feature selection method based on a simulated annealing algorithm comprises the following steps:
step one, formulating a coding mode according to spectral characteristics;
selecting a target function according to the spectral characteristics;
initializing parameters of a simulated annealing algorithm, and starting to search an optimal result;
step four, continuously comparing the values of historical results of past generations and the current result, and continuing to perform the algorithm on a more optimal value;
and step five, repeating the step four until the optimal result does not change within the preset stable algebra or reaches the preset algebra.
Furthermore, the stable algebra in the step five is a natural number which is greater than or equal to 5.
Further, the selection of the hyperspectral characteristic is realized through the following steps,
1) setting the initial temperature T0Determining an initial solution state for simulating the initial temperature of the annealing algorithm, and determining the band selection according to a preset criterion, wherein the iteration algebra L of each T value;
2) setting k to 1, a., L, respectively, and repeating steps 3) to 6);
3) generating a new solution S';
4) calculating an increment Δ T ═ C (S') -C (S), where C (S) is a fitness function;
5) if T is less than 0, S' is accepted as new current solution, otherwise probability is used
Figure RE-GDA0002517680770000031
Receiving S' as a new current solution, outputting the current solution as an optimal solution if a termination condition is met, and terminating the program, wherein the termination condition is usually that a plurality of continuous new solutions are not received and terminated by the algorithm;
6) set T to decrease gradually, and T- > 0, then go to 2).
Further, in the preset criterion, the important information contained in the band is measured through a standard deviation criterion, and a formula of the preset criterion is defined as:
Figure RE-GDA0002517680770000041
where PN is the total number of pixels for a band, μ is the average pixel value for that band, and X represents a selected subset of bands.
Further, the redundancy information is measured by a mutual information criterion in the preset criterion, and the formula is defined as:
Figure RE-GDA0002517680770000042
wherein, p (x)i) According to
Figure RE-GDA0002517680770000043
Calculation of h (x)i) Is the band xiN is the total number of pixels of the band. p (x)i,xj) Is the band xiAnd xjBy a joint probability distribution function of
Figure RE-GDA0002517680770000044
h(xi,xj) Is the band xiAnd xjThe joint gray-level histogram of (1).
Further, the objective function form of the preset criterion is:
Figure RE-GDA0002517680770000045
wherein X represents a band subset; len (x) denotes the number of bands of the selected subset of bands.
Compared with the prior art, the invention has the beneficial effects that:
according to the hyperspectral characteristic selection method based on the simulation algorithm, compared with other intelligent algorithms, random factors are introduced in the search process, the difference solution is received at a certain probability and used for jumping out of the local optimal solution, the global optimal solution is achieved, hyperspectral characteristic selection is completed, and a large amount of manpower, material resources and financial resources can be saved.
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FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a diagram of the band composition and new solution generation for selecting any band length in the initial solution space.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in the flowchart of fig. 1, the present embodiment discloses a hyperspectral feature selection method based on a simulated annealing algorithm, which includes the following steps:
step one, formulating a coding mode according to spectral characteristics;
selecting a target function according to the spectral characteristics;
initializing parameters of a simulated annealing algorithm, and starting to search an optimal result;
step four, continuously comparing the values of historical results of past generations and the current result, and continuing to perform the algorithm on a more optimal value;
and step five, repeating the step four until the optimal result does not change within the preset stable algebra or reaches the preset algebra.
And if possible, the stable algebra in the step five is a natural number which is more than or equal to 5.
Wherein, during the feature selection, the specific steps are as follows to realize the selection of the hyperspectral feature,
1) setting the initial temperature T0Determining an initial solution state for simulating the initial temperature of the annealing algorithm, and determining the band selection according to a preset criterion, wherein the iteration algebra L of each T value;
2) setting k to 1, a., L, respectively, and repeating steps 3) to 6);
3) generating a new solution S';
4) calculating an increment Δ T ═ C (S') -C (S), where C (S) is a fitness function;
5) if T is less than 0, S' is accepted as new current solution, otherwise probability is used
Figure RE-GDA0002517680770000051
Receiving S' as a new current solution, outputting the current solution as an optimal solution if a termination condition is met, and terminating the program, wherein the termination condition is usually that a plurality of continuous new solutions are not received and terminated by the algorithm;
6) set T to decrease gradually, and T- > 0, then go to 2).
More specifically, an initial solution omega is randomly produced through an objective function, the objective function is calculated, a new solution is generated through disturbance, the objective function of the new solution is calculated, the difference between the new solution and the initial solution is calculated, the difference is judged, if the difference is larger than 0, the new solution is accepted according to the Metropolis criterion, if the difference is smaller than or equal to 0, the new solution is accepted and assigned to the initial solution, if the difference is smaller than or equal to 0, whether the iteration frequency is reached is judged, the iteration frequency can be initially set according to requirements, if the iteration frequency is not reached, the disturbance is returned to generate the new solution, and the objective function is calculated. If the iteration times are reached, judging whether a preset termination condition is met or not, namely whether feature selection is realized or not, if the condition set by the feature selection is met, finishing the operation, returning to the optimal solution, if the condition set by the feature selection is not met, reducing the temperature recharging iteration times through a preset program, returning to the disturbance to generate a new solution, and calculating a target function to circulate.
Firstly, the objective function setting process in step 1) is as follows:
the objective function of band selection needs to take into account both the aspect of keeping important information and the aspect of taking out redundant information. The effective information of the wave band can represent clear image content with distinction, and the richness of the image content information can be measured by the high contrast of the image. There are many criteria to measure the contrast of an image, such as standard deviation and information entropy. We use the standard deviation as a criterion to measure important information contained in the band.
The formula is defined as shown:
Figure RE-GDA0002517680770000061
where PN is the total number of pixels in a band and μ is the average pixel value for that band. X represents a selected subset of bands. The larger the standard deviation of the band, the more valid information the band contains. The sum of the standard deviations of the selected band subsets is maximized in the designed objective function.
For the measurement of redundant information, criteria in information theory, such as mutual information and relative entropy, can be used for reference. We use mutual information as a criterion, defined as follows:
Figure RE-GDA0002517680770000071
wherein p (x)i) According to
Figure RE-GDA0002517680770000072
Calculation of h (x)i) Is the band xiN is the total number of pixels of the band. p (x)i,xj) Is the band xiAnd xjBy a joint probability distribution function of
Figure RE-GDA0002517680770000073
h(xi,xj) Is the band xiAnd xjThe joint gray-level histogram of (1). The larger the value of the mutual information is, the larger the redundancy of the correlation of the two wave bands is, the mutual information needs to be minimized, and the designed objective function form is as follows:
Figure RE-GDA0002517680770000074
wherein X represents a subset of bands; len (x) denotes the number of bands of the selected subset of bands. When the formula is maximized, valid information is retained and redundant information is removed.
The band selection process based on the simulated annealing algorithm is as follows:
the Simulated Annealing (SA) is derived from the solid Annealing principle, and is a random optimization algorithm based on a Monte-Carlo iterative solution strategy. According to the solid annealing principle, the solid is heated to be sufficiently high and then is gradually cooled, when the solid is heated, the particles in the solid are changed into a disordered state along with the temperature rise, the internal energy is increased, when the solid is slowly cooled, the particles gradually tend to be ordered, the particles reach an equilibrium state at each temperature and finally reach a ground state at normal temperature, and the internal energy is reduced to be minimum. According to the Metropolis criterion, the probability that a particle will tend to equilibrate at temperature T is
Figure RE-GDA0002517680770000075
Wherein E is the internal energy at the temperature T, delta E is the change quantity of the internal energy, and k is a Boltzmann constant. Simulating the combined optimization problem by using solid annealing, simulating the internal energy E into a target function value f, and evolving the temperature T into a control parameter T to obtain a simulated annealing algorithm for solving the combined optimization problem: starting from the initial solution i and the initial value t of the control parameter, repeating the iteration of 'generating a new solution → calculating the target function difference → accepting or abandoning' on the current solution, gradually attenuating the value t, wherein the current solution when the algorithm is terminated is the obtained approximate optimal solution, which is a heuristic random search process based on a Monte Carlo iterative solution. The annealing process is controlled by a Cooling Schedule (Cooling Schedule) including an initial value t of a control parameter and its attenuation factor Δ t, the number of iterations L at each value of t, and a stop condition S.
The parameters to be initialized for the algorithm simulation in this embodiment are
Initial temperature: t is0 Initial temperature: t isf
A cooling function: t isk+1＝Tk-ΔT Number of iterations L at each temperature
The simulated annealing algorithm flow is as follows:
the simulated annealing algorithm can be decomposed into three parts of a solution space, an objective function and an initial solution.
The initial solution space may select a band component of any band length, as shown in fig. 2. The method for generating the new solution is also shown in fig. 2, and the difference between any two solutions in the previous solution is crossed, and then any spectral band is selected to be varied, i.e. replaced by any band not appearing in the solution. And after the solution space definition and the objective function are completed, describing a simulated annealing algorithm to select the hyperspectral features.
1) Initialization: initial temperature T0Initial solution state (random band selection), iteration algebra L of each T value;
2) and (3) performing steps 3 to 6 on k, namely 1.
3) A new solution S' is generated.
4) The increment Δ T ═ C (S') -C (S) is calculated, where C (S) is a fitness function.
5) If T is less than 0, S' is accepted as new current solution, otherwise probability is used
Figure RE-GDA0002517680770000081
Accepting S' as a new current solution
6) And if the termination condition is met, outputting the current solution as the optimal solution, and terminating the program. The termination condition is typically taken to be that no successive number of new solutions have been accepted by the termination algorithm.
7) T is gradually reduced, and T- > 0, and then the step 2 is carried out.
After the process is completed, the selection of the hyperspectral characteristic can be realized. According to the hyperspectral characteristic selection method based on the simulation algorithm, compared with other intelligent algorithms, random factors are introduced in the search process, the difference solution is received at a certain probability and used for jumping out of the local optimal solution, the global optimal solution is achieved, hyperspectral characteristic selection is completed, and a large amount of manpower, material resources and financial resources can be saved.
The embodiments of the present invention have been described in detail with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. It will be apparent to those skilled in the art that various changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, and the scope of protection is still within the scope of the invention.

Claims (6)

1. A hyperspectral feature selection method based on a simulated annealing algorithm is characterized by comprising the following steps:
step one, formulating a coding mode according to spectral characteristics;
selecting a target function according to the spectral characteristics;
initializing parameters of a simulated annealing algorithm, and starting to search an optimal result;
step four, continuously comparing the values of historical results of past generations and the current result, and continuing to perform the algorithm on a more optimal value;
and step five, repeating the step four until the optimal result does not change within the preset stable algebra or reaches the preset algebra.
2. The method for selecting hyperspectral features based on simulated annealing algorithm according to claim 1, wherein the stable algebra in the fifth step is a natural number greater than or equal to 5.
3. The hyperspectral feature selection method based on simulated annealing algorithm according to claim 1 is characterized in that the hyperspectral feature selection is realized by the following steps,
1) setting the initial temperature T0Determining an initial solution state for simulating the initial temperature of the annealing algorithm, and determining the band selection according to a preset criterion, wherein the iteration algebra L of each T value;
2) setting k to 1, a., L, respectively, and repeating steps 3) to 6);
3) generating a new solution S';
4) calculating an increment Δ T ═ C (S') -C (S), where C (S) is a fitness function;
5) if T is less than 0, S' is accepted as new current solution, otherwise probability is used
Figure FDA0002468895230000011
Receiving S' as a new current solution, outputting the current solution as an optimal solution if a termination condition is met, and terminating the program, wherein the termination condition is usually that a plurality of continuous new solutions are not received and terminated by the algorithm;
6) set T to decrease gradually, and T- > 0, then go to 2).
4. The method for selecting hyperspectral features based on simulated annealing algorithm according to claim 3, wherein the preset criterion is used for measuring important information contained in a waveband through a standard deviation criterion, and the formula is defined as:
Figure FDA0002468895230000021
where PN is the total number of pixels for a band, μ is the average pixel value for that band, and X represents a selected subset of bands.
5. The simulated annealing algorithm-based hyperspectral feature selection method according to claim 4, wherein the preset criterion measures redundant information through a mutual information criterion, and the formula is defined as:
Figure FDA0002468895230000022
wherein, p (x)i) According to
Figure FDA0002468895230000023
Calculation of h (x)i) Is the band xiN is the total number of pixels of the band. p (x)i,xj) Is the band xiAnd xjBy a joint probability distribution function of
Figure FDA0002468895230000024
h(xi,xj) Is the band xiAnd xjThe joint gray-level histogram of (1).
6. The simulated annealing algorithm-based hyperspectral feature selection method according to claim 5, wherein the objective function form of the preset criterion is as follows:
Figure FDA0002468895230000025
wherein X represents a band subset; len (x) denotes the number of bands of the selected subset of bands.
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Application publication date: 20200818

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