CN112231933B - Feature selection method for radar electromagnetic interference effect analysis - Google Patents
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Abstract
The invention relates to a feature selection method for radar electromagnetic interference effect analysis. According to the feature selection method, the eigen subspace of the feature space is estimated by manifold learning, the dimension and the structure of the subspace are determined, then the linear mapping from the original feature space to the subspace of the subspace is optimized by using a sparse model, and finally feature evaluation and feature selection oriented to radar electromagnetic interference effect analysis are realized. According to the invention, the intrinsic structure of the feature space is mined by utilizing the feature sample data analyzed by the radar electromagnetic interference effect, so that the optimal mapping from the original feature space to the intrinsic feature subspace is estimated, and finally, effective feature evaluation is realized, so that feature selection can be realized independently, and feature selection can be performed in combination with expert knowledge; meanwhile, the number of the selected features can be determined by the dimension of the intrinsic feature subspace, so that artificial selection is avoided; in addition, the selected features can maintain the original feature space structure as much as possible, and redundant features are removed.
Description
Technical Field
The invention relates to the technical field of information processing, in particular to a feature selection method for radar electromagnetic interference effect analysis.
Background
Radar electromagnetic interference effect analysis is an important way for excavating electromagnetic interference mechanism, and relates to a plurality of aspects such as interference signals, radar systems, application fields and the like. Because of the variety of types and parameters of interference signals, complex processing links of radar systems and numerous radar application fields, effective mathematical tools are required to mine intrinsic knowledge from the radar electromagnetic interference process. The Bayesian inference network is an effective tool for realizing radar electromagnetic interference effect analysis, realizes network training through network learning and parameter learning, and further realizes knowledge inference of radar electromagnetic interference effect analysis according to objective evidence.
Compared with the traditional deep learning network, the Bayesian inference network has two advantages. First, the understandability of the network. The Bayesian inference network node is composed of the features extracted in the radar electromagnetic interference process, and has a definite feature meaning. And the network parameters correspond to the conditional probability among the nodes, and the node association is clear and has statistical significance. Thus, bayesian inference networks have a good intelligibility compared to conventional deep learning networks considered as black boxes. Secondly, network reasoning is not directional constraint. Conventional deep learning networks have directionality such that input can only be given at the input layer and output can be obtained at the output layer, i.e., information is transferred from the input layer to the output layer through the network. The Bayesian inference network can obtain effective estimation of other nodes by evidence given by any part of nodes, namely, the inference is not constrained by direction, and the Bayesian inference network has wider application prospect.
Considering the numerous features involved in radar electromagnetic interference effect analysis, a great deal of pressure is generated on a Bayesian inference network. On one hand, each characteristic corresponds to each node of the network, and the plurality of nodes directly cause the excessive computational complexity of the network training; on the other hand, the numerous features increase network structure and parameters, thereby increasing the inference complexity of the network. Especially when a large number of original samples exist, the effectiveness and the inference accuracy of the Bayesian inference network face great challenges. The feature selection analyzes redundant features in the original features by removing radar electromagnetic interference effects, and provides a new idea for relieving Bayesian inference network pressure.
The feature selection generally selects the feature with higher score through feature evaluation, and the score criterion generally adopts expert knowledge, but radar electromagnetic interference effect is complex, and most features are difficult to evaluate directly. Moreover, the number of the selected features often needs to be manually specified, and objective basis is lacked, so that the feature selection accuracy is reduced, and the follow-up Bayesian inference network is affected. These all lead to the failure of the traditional feature selection method in the analysis of the electromagnetic interference effect of the radar, so a new feature selection method is needed to improve the feature selection accuracy and provide conditions for realizing the analysis of the electromagnetic interference effect of the radar based on a Bayesian inference network.
Disclosure of Invention
The invention aims to provide a feature selection method for radar electromagnetic interference effect analysis, which can better maintain a feature space structure of the radar electromagnetic interference effect analysis, improve feature selection accuracy and lay a foundation for reducing feature dimension and feature data quantity.
In order to achieve the above object, the present invention provides the following solutions:
a feature selection method for radar electromagnetic interference effect analysis comprises the following steps:
acquiring original characteristics facing radar electromagnetic interference effect;
determining an original feature space and an original sample set according to the original features;
determining subspace model parameters according to the original sample set; the subspace model parameters include: subspace dimension and representation weight matrix;
constructing a characteristic subspace estimation model according to the subspace model parameters;
determining a feature subspace according to the feature subspace estimation model;
determining a linear mapping model from original features in the original feature space to sub-features of the feature subspace according to the original feature space and the feature subspace;
determining a linear mapping estimated value according to the linear mapping model;
and carrying out feature evaluation and selection on the original features by adopting the linear mapping estimated value to obtain selected features, thereby completing feature selection oriented to radar electromagnetic interference effect analysis.
Preferably, the determining a subspace model parameter according to the original sample set specifically includes:
obtaining the maximum distance from any original sample in the original sample set to a sample in a k neighborhood set of the original sample set;
determining the subspace dimension according to the maximum distance;
from the original sample set and the original sample setk neighborhood set, adopting preset conditionDetermining the representation weight matrix;
wherein W is a weight matrix, R N×N Is N multiplied by N, N is the total number of original samples, x i For the i-th original sample, w ij For the (i, j) th sample in the k-neighborhood set, x j For the j-th original sample, Λ i And the index set corresponding to the sample in the k neighborhood set.
Preferably, the determining a linear mapping model from the original feature in the original feature space to the sub-features of the feature subspace according to the original feature space and the feature subspace specifically includes:
measuring the proximity degree of the original feature space and the feature subspace by adopting a Euclidean distance to obtain an approximation term of the linear mapping model;
determining a priori terms of the linear mapping model by adopting a sparse constraint condition;
the linear mapping model is determined from the approximation term and the prior term.
Preferably, the characteristic evaluation and selection of the original characteristic by using the linear mapping estimation value are performed to obtain a selected characteristic, which specifically includes:
determining an evaluation value of each original feature according to the linear mapping estimation value, and determining an evaluation value set according to the evaluation value;
after elements in the evaluation value set are arranged in a descending order, extracting the first d ordered elements, and extracting features corresponding to the first d elements; the characteristics are selected characteristics.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
according to the feature selection method for the radar electromagnetic interference effect analysis, the eigen subspace of the feature space is estimated by manifold learning, the dimension and the structure of the subspace are determined, then the linear mapping from the original feature space to the subspace of the subspace is optimized by using a sparse model, and finally feature evaluation and feature selection for the radar electromagnetic interference effect analysis are realized. According to the invention, the intrinsic structure of the feature space is mined by utilizing the feature sample data analyzed by the radar electromagnetic interference effect, so that the optimal mapping from the original feature space to the intrinsic feature subspace is estimated, and finally, effective feature evaluation is realized, so that feature selection can be realized independently, and feature selection can be performed in combination with expert knowledge; meanwhile, the number of the selected features can be determined by the dimension of the intrinsic feature subspace, so that artificial selection is avoided; in addition, the selected features can maintain the original feature space structure as much as possible, and redundant features are removed.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a feature selection method for radar electromagnetic interference effect analysis provided by the invention;
FIG. 2 is a feature selection flow chart of an embodiment of the present invention using the feature selection method disclosed in the present invention;
FIG. 3 is a feature evaluation chart in an embodiment of the invention;
FIG. 4 is a graph of Bayesian network training time (seconds) versus time for an embodiment of the present invention;
fig. 5 is a graph of bayesian network inference accuracy comparison in an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a feature selection method for radar electromagnetic interference effect analysis, which can better maintain a feature space structure of the radar electromagnetic interference effect analysis, improve feature selection accuracy and lay a foundation for reducing feature dimension and feature data quantity.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
Fig. 1 is a flowchart of a feature selection method for analysis of electromagnetic interference effect of radar provided by the present invention, and fig. 2 is a feature selection flowchart of a feature selection method disclosed by the present invention in an embodiment of the present invention, as shown in fig. 1 and fig. 2, a feature selection method for analysis of electromagnetic interference effect of radar includes:
step 100: the original characteristics facing the electromagnetic interference effect of the radar are obtained.
Step 101: the original feature space and the original sample set are determined from the original features. In the invention, the original characteristic of radar electromagnetic interference effect analysis is { f 1 ,f 2 ,…,f D Where D is the number of original features and the set of collected original feature samples is p= { x 1 ,x 2 ,…,x N X, where x n ∈R D And N is the total number of samples. Representing the original feature samples as a matrix form x= [ X ] 1 ,x 2 ,…,x N ] T ∈R N×D . The raw features, raw feature samples and parameters involved in the following steps are shown in table 1:
TABLE 1 original features, original samples and parameters in the algorithm
| D | N | k | d | η |
| 16 | 1000 | 15 | 12 | 0.5 |
In order to improve the calculation efficiency and the inference accuracy, after the step 101 of the present invention, normalization processing is further required:
assume thatFor the column vector of the original sample X, the feature dimension first needs to be removed in order to analyze the feature space structure:
wherein I 2 Is vector quantityNorms. To simplify the notation, X in the following represents the raw sample data after normalization processing.
Step 102: subspace model parameters are determined from the original sample set. The subspace model parameters include: subspace dimensions and representation weight matrices.
The step 102 specifically includes:
the maximum distance of any one original sample in the original sample set to the samples in the k neighborhood set of the original sample set is obtained.
Subspace dimensions are determined based on the maximum distance.
Adopting preset conditions according to the original sample set and a k neighborhood set of the original sample setA representation weight matrix is determined.
Wherein W is a weight matrix, R N×N Is N multiplied by N, N is the total number of original samples, x i For the i-th original sample, w ij For the (i, j) th sample in the k-neighborhood set, x j For the j-th original sample, Λ i And the index set corresponding to the sample in the k neighborhood set.
Step 103: and constructing a characteristic subspace estimation model according to the subspace model parameters.
In step 103, based on step 102, subspace dimensions are first estimated, and feature subspaces are then estimated using local linear mapping. For any sample x n E, P, let k neighborhood set be Γ n Distance x n The most recent k samples.
The subspace dimension estimation process comprises the following steps:
let r n,k ＝max{|x n -x||x∈Γ n The maximum distance of any sample from its k-neighborhood set is represented, then the subspace dimension is:
wherein, the liquid crystal display device comprises a liquid crystal display device,the average distance corresponding to the k neighborhood set. If d is not an integer, taking the smallest integer not smaller than d as the final estimation of the subspace dimension.
The original characteristic space k neighborhood set represents the weight estimation process as follows:
let the original characteristic space k neighborhood set representation weight matrix be W E R N×N And the (i, j) th element is w ij Then rightThe weight matrix can be found by the following optimization problem:
wherein is lambda i Representing sample x i K neighborhood set Γ of e P i Index sets corresponding to the samples in (a).
Based on the estimation process, the construction process of the characteristic subspace estimation model is as follows:
in order to maintain the space structure, the original characteristic space k neighborhood set is used for representing the weight estimation characteristic subspace, and the original characteristic space sample x is set n The coordinates of e P in the feature subspace are y n ∈R d Then the subspace can be modeled as:
wherein I is d ∈R d×d Is an identity matrix.
This model shows that the original feature space and the feature subspace share a k-neighborhood set representation weight, so that both have similar spatial structures.
Step 104: and determining the feature subspace according to the feature subspace estimation model. The method specifically comprises the following steps:
and designing a solving algorithm of the feature subspace estimation model by utilizing a Lagrangian multiplier method.
Let y= [ Y ] 1 ,y 2 ,…,y N ] T ∈R N×d The above model is written in matrix form as:
wherein Tr (·) is a matrix trace function, and r= (I) N -W) T (I N -W)，I N ∈R N×N Is an identity matrix. From the lagrangian multiplier method, the solution of the model should satisfy:
RY＝λY。
where λ is the lagrange multiplier, corresponding to the eigenvalue of matrix R.
Let d+1 minimum eigenvalues (from small to large) of matrix R correspond to eigenvectors { u }, in turn 1 ,u 2 ,…,u d+1 Solution of model is y= [ u ] 2 ,u 3 ,…,u d+1 ]. The solution is the feature subspace in step 104.
Step 105: a linear mapping model from the original features in the original feature space to the sub-features of the feature subspace is determined from the original feature space and the feature subspace.
The step 105 specifically includes:
and measuring the proximity degree of the original feature space and the feature subspace by adopting the Euclidean distance to obtain an approximation term of the linear mapping model.
And determining the prior term of the linear mapping model by adopting a sparse constraint condition.
A linear mapping model is determined from the approximation term and the prior term.
The specific calculation process for implementing the step 105 is as follows:
let X e R be the original sample from the original feature space N×D To the corresponding original sample Y E R in the feature subspace N×d Is mapped into S epsilon R D×d The linear mapping S estimation process is:
estimation model approximation term construction
In order to make XS and Y approximate as much as possible, namely the feature subspace after feature selection and the original feature eigen subspace are consistent as much as possible, euclidean distance is adopted to measure the approaching degree of the two spaces, namely:
estimating model prior term construction
The feature selection, namely removing the feature with small contribution degree, so that the contribution degree of the original feature has sparse characteristics, the linear mapping S has sparse prior, and the sparse prior can be measured by the following formula:
wherein s is ij For the S-th (i) of the process, j) the number of elements of the set, I.I 2,1 Is a matrixNorms.
Estimation modeling and solving
Based on the model approximation term and the prior term, a sparse optimization model for solving the linear mapping S can be constructed as follows:
wherein eta>0 is the regularization parameter. The solution S= [ S ] of the model can be obtained through a sparse reconstruction algorithm 1 ,s 2 ,…,s D ] T Wherein s is i Is the i-th row vector of the matrix S.
Step 106: a linear mapping estimate is determined based on the linear mapping model.
Step 107: and performing feature evaluation and selection on the original features by adopting the linear mapping estimated value to obtain selected features, thereby completing feature selection oriented to radar electromagnetic interference effect analysis.
The step 107 specifically includes:
and determining an evaluation value of each original feature according to the linear mapping estimation value, and determining an evaluation value set according to the evaluation value.
And after the elements in the evaluation value set are arranged in a descending order, extracting the first d ordered elements, and extracting features corresponding to the first d elements. The characteristics are the selected characteristics.
Based on the above calculation, the calculation process of step 107 specifically includes:
based on the linear mapping S, feature evaluation and selection can be achieved. Taking into account the meaning of the linear mapping, i.e. each row vector of the matrix SA kind of electronic deviceThe norm measures the contribution of the feature to the feature subspace structure retention, and therefore to feature f i ∈{f 1 ,f 2 ,…,f D Evaluation value set E i Can be expressed as:
E i ＝||s i || 2 ,i＝1,2,…,D。
therefore, the evaluation value set { E } 1 ,E 2 ,…,E D As shown in FIG. 3, the smallest 4 features are the 2 nd, 5 th, 8 th and 12 th features, respectively, so that the final selected feature is obtained by removing the 4 featuresThe method is used for subsequent radar electromagnetic interference effect analysis.
According to the invention, after feature selection, the radar electromagnetic interference effect analysis feature data is directly subjected to Bayesian network training and reasoning, and under the same condition, the Bayesian network training and reasoning based on all features is used as a comparison method, wherein 70% of data are used for training, and the rest 30% of data are used for test reasoning. The training time and the inference accuracy of the two methods are shown in fig. 4 and fig. 5, respectively. It can be found that through feature selection, the Bayesian network training efficiency and the reasoning precision are improved, and the radar electromagnetic interference effect analysis efficiency is greatly improved.
In summary, in order to improve the training efficiency and the reasoning precision of the radar electromagnetic interference effect analysis based on the Bayesian reasoning network, firstly, feature dimensions are removed through feature sample data normalization processing, secondly, a manifold learning algorithm is utilized to estimate a feature subspace, then a sparse optimization model and an algorithm are utilized to solve the linear mapping from the original feature space to the feature subspace, further, feature evaluation and selection are realized based on the linear mapping, and finally, a feature selection method oriented to the radar electromagnetic interference effect analysis is provided.
The invention belongs to the field of information processing, and particularly relates to a feature selection method for radar electromagnetic interference effect analysis, which is mainly applied to the information fields of feature optimization, pattern recognition, data preprocessing and the like. Compared with the traditional feature selection method, the method has the following advantages in feature selection for radar electromagnetic interference effect analysis:
(1) The feature selection can be realized independently, and the feature selection can be performed in combination with expert knowledge.
(2) The number of features selected may be determined by the dimensions of the eigen feature subspace, avoiding human selection.
(3) The selected features can maintain the original feature space structure as much as possible, and redundant features are removed.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present invention and the core ideas thereof; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.
Claims (2)
1. The characteristic selection method for radar electromagnetic interference effect analysis is characterized by comprising the following steps:
acquiring original characteristics facing radar electromagnetic interference effect;
determining an original feature space and an original sample set according to the original features;
determining subspace model parameters according to the original sample set; the subspace model parameters include: subspace dimension and representation weight matrix;
the determining subspace model parameters according to the original sample set specifically comprises the following steps:
obtaining the maximum distance from any original sample in the original sample set to a sample in a k neighborhood set of the original sample set;
determining the subspace dimension according to the maximum distance;
the subspace dimension is:
wherein, the liquid crystal display device comprises a liquid crystal display device,the average distance corresponding to the k neighborhood set; if d is not an integer, taking the minimum integer not less than d as the final estimation of subspace dimension; r is (r) n,k ＝max{|x n -x|x∈Γ n -the maximum distance of any one original sample in the original sample set to a sample in the k-neighborhood set of the original sample set; x is x n An nth original sample of the original sample set; Γ -shaped structure n Is a distance x n The nearest k neighborhood sets the set of samples; x is a set Γ n Any of the original samples;
adopting preset conditions according to the original sample set and a k neighborhood set of the original sample setDetermining the representation weight matrix;
wherein W is a weight matrix, R N×N Is N multiplied by N, N is the total number of original samples, x i For the i-th original sample, w ij For the (i, j) th sample in the k-neighborhood set, x j For the j-th original sample, Λ i The index set corresponding to the sample in the k neighborhood set;
constructing a characteristic subspace estimation model according to the subspace model parameters;
determining a feature subspace according to the feature subspace estimation model;
determining a linear mapping model from original features in the original feature space to sub-features of the feature subspace according to the original feature space and the feature subspace, wherein the linear mapping model specifically comprises the following steps:
and measuring the proximity degree of the original feature space and the feature subspace by adopting the Euclidean distance, wherein the approximation term of the linear mapping model is obtained by:
determining the prior term of the linear mapping model as adopting sparse constraint conditions
Determining the linear mapping model according to the approximation term and the prior term is as follows:
wherein X is an original sample in the original feature space, Y is an original sample in the feature subspace, S is a linear mapping matrix, S ij In the (i) th of the S, j) the number of elements of the set, I.I 2,1 D is the number of rows of S, D is the number of columns of S; η (eta)>0 is a regularization parameter;
determining a linear mapping estimation value according to the linear mapping model;
and carrying out feature evaluation and selection on the original features by adopting the linear mapping estimated value to obtain selected features, thereby completing feature selection oriented to radar electromagnetic interference effect analysis.
2. The radar electromagnetic interference effect analysis-oriented feature selection method according to claim 1, wherein the feature evaluation and selection of the original feature by using the linear mapping estimation value are specifically included:
determining an evaluation value of each original feature according to the linear mapping estimation value, and determining an evaluation value set according to the evaluation value;
after elements in the evaluation value set are arranged in a descending order, extracting the first d ordered elements, and extracting features corresponding to the first d elements; the characteristics are selected characteristics.
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