CN114818845A - Noise-stable high-resolution range profile feature selection method - Google Patents
Noise-stable high-resolution range profile feature selection method Download PDFInfo
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Abstract
The invention relates to a high-resolution range profile characteristic selection method with stable noise, which comprises the following steps: acquiring a high-resolution range profile sample set of targets, and performing feature extraction on the high-resolution range profile of each target to obtain an original feature set; respectively calculating a Relieff evaluation value, an mrMR evaluation value and a noise robustness parameter of each feature in the original feature set; performing multi-evaluation value fusion processing on the Relieff evaluation value, the mRMR evaluation value and the noise robustness parameter of each feature to obtain a fusion evaluation value of each feature; and according to the fusion evaluation value, performing feature search on the original feature set by using a sequence floating forward search method to obtain an optimal feature subset under a preset dimensionality, and performing subsequent target identification operation by using the optimal feature subset. The method of the invention considers noise factors, utilizes the sequence floating forward search algorithm to search the feature subsets, and the selected feature subsets have small dimensionality, low redundancy and good noise robustness, thereby greatly improving the target identification probability.
Description
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a high-resolution range profile feature selection method with stable noise.
Background
When a radar system detects a ground target, a scene comprises the interference between a target to be attacked and a false target (such as a civil vehicle, a simple house and the like), the scattering characteristic of the false target is similar to that of the target to be attacked, and a target identification technology is required to be adopted for distinguishing and removing the false target. Target identification is a multi-classification problem, and a new sample category is divided by learning the characteristics of known data, forming a description of the known data and then calculating the similarity of a new sample and the known data. In the process of target identification, feature extraction needs to be performed on High Resolution Range Profiles (HRRP) of various targets, the influence of different features on identification performance is different, if feature selection is not performed, the combination of original High-dimensional features not only causes the generalization performance of a model to be poor and the calculation speed to be slow, but also causes subsequent identification performance to be reduced due to higher redundancy among features. Therefore, it is necessary to develop more efficient feature selection algorithms.
Currently, a filtering type feature selection algorithm, an encapsulated type feature selection algorithm and a hybrid type feature selection method are researched more. The filtering type feature selection algorithm is used for calculating the contribution degree of each feature to classification according to data internal relations, the algorithm is independent of subsequent classification algorithms, the calculation amount is low, the speed is high, Wang Xue and the like propose that single features are sorted according to feature importance on the basis of 'K-anonymous feature selection for improving feature importance based on extreme gradient', and features which are ranked at the top are selected from feature sorting to form an optimal feature subset. The packaged feature selection algorithm utilizes the training accuracy of a subsequent learning algorithm to evaluate the quality of the feature subset, has small deviation, but easily has the problems of overfitting, large calculated amount and the like. The hybrid feature selection method comprehensively utilizes a filtering method and an encapsulation method, firstly eliminates most irrelevant or noise sensitive features by using the filtering method, thereby reducing the scale of feature search, and then selects an optimal feature subset by using the encapsulation feature selection method. The hybrid feature selection method has compromise in two aspects of performance and computational complexity, the computational complexity is lower than that of the packaging method, the performance is superior to that of the filtering method, and the over-fitting phenomenon is not easy to occur.
The actual working scene of the radar seeker is very complex, the signal-to-noise ratio of the collected echo data is low, and when the characteristics are selected, the characteristics which are stable to noise should be selected, so that the identification system of the radar seeker has high noise stability. In addition, most targets needing to be identified in practical application are non-cooperative targets, and the storage capacity of the radar seeker is limited, so that the search for an optimal feature subset with small feature dimension, less redundant information among features and high noise robustness is a very important research matter.
Disclosure of Invention
In order to solve the above problems in the prior art, the present invention provides a method for selecting a high-resolution range profile with stable noise, and the technical problems to be solved by the present invention are realized by the following technical solutions:
the invention provides a high-resolution range profile feature selection method with stable noise, which comprises the following steps:
step 1: acquiring a high-resolution range profile sample set of targets, and performing feature extraction on the high-resolution range profile of each target to obtain an original feature set;
step 2: respectively calculating a Relieff evaluation value, an mrMR evaluation value and a noise robustness parameter of each feature in the original feature set;
and step 3: performing multi-evaluation value fusion processing on the Relieff evaluation value, the mRMR evaluation value and the noise robustness parameter of each feature to obtain a fusion evaluation value of each feature;
and 4, step 4: and according to the fusion evaluation value, performing feature search on the original feature set by using a sequence floating forward search method to obtain an optimal feature subset under a preset dimensionality, and performing subsequent target identification operation by using the optimal feature subset.
In one embodiment of the present invention, the step 1 comprises:
acquiring a dual-polarized target high-resolution range profile sample set acquired by a radar, and preprocessing the high-resolution range profile of each target to overcome the sensitivity of the high-resolution range profile;
and performing feature extraction on the preprocessed high-resolution range profile to obtain frequency domain features and time domain features of the high-resolution range profile, and combining to obtain the original feature set.
In one embodiment of the present invention, the step 2 comprises:
calculating a Relieff evaluation value of each feature according to a Relieff evaluation criterion;
calculating an mRMR evaluation value of each feature according to an mRMR evaluation criterion;
and adding noise into the high-resolution range profile sample set of the target, extracting corresponding characteristics of the high-resolution range profile sample set after noise pollution to obtain a noise characteristic set, and calculating a noise robustness parameter of each characteristic according to the noise characteristic set and the original characteristic set.
In one embodiment of the present invention, calculating the ReliefF evaluation value of each feature according to the ReliefF evaluation criterion includes:
recording the original feature set as X, wherein X is an M × N matrix, each sample comprises M features, and N samples are provided in total;
taking a sample R from X, selecting K adjacent points from the samples of the same class as the sample R in X as H, and selecting K adjacent points from the samples of different classes from the sample R as M;
the weight matrix W is calculated as follows:
in the above formula, q represents the number of iterations, H j Denotes the jth nearest neighbor sample, M, of the same class as sample R j (C) Presentation class
J (th) nearest neighbor sample, p (C) is the probability of occurrence of class C, class (R) is the class of sample R, p (class (R)) is the probability of occurrence of class of sample R, diff (x) i ,R,H j ) Denotes samples R and H j At feature x i The difference in (c) is as follows:
in the selected feature S m-1 On the basis of the above, incremental search is performed, and the importance of the features in the remaining feature space is calculated according to the following formula:
ΔW(x i )＝W([S m-1 ,x i ])-W(S m-1 )；
in the formula, Δ W (x) i ) Represents the feature x i The Relieff evaluation value of (1).
In one embodiment of the present invention, calculating an rmr evaluation value for each feature according to an rmr evaluation criterion includes:
and calculating mutual information of the single characteristics and the categories according to the definition of the mutual information as follows:
in the formula, x i And C respectively represent the ith feature in the original feature set X and the class to which the feature belongs, p (X) i ) Represents a feature x i P (C) represents the marginal probability distribution of class C, p (x) i And C) represents the feature x i And a joint probability distribution for class C;
the correlation between the original feature set X and the category is defined as:
in the formula, M represents the number of features contained in an original feature set X;
mutual information between features is calculated according to the following formula:
the minimum correlation between features is defined as:
mRMR combines two measures, defining the following criteria:
maxΦ(D,Q)＝D-Q；
in the selected feature S m-1 On the basis of the above, incremental search is performed, and the importance of the features in the remaining feature space is calculated according to the following formula:
in the formula,. DELTA.I (x) j ) Represents a feature x j M denotes the number of selected feature subsets, C denotes the feature x i The category (2).
In an embodiment of the present invention, adding noise into the high-resolution range profile sample set of the target, performing corresponding feature extraction on the high-resolution range profile sample set after noise pollution to obtain a noise feature set, and calculating a noise robustness parameter of each feature according to the noise feature set and the original feature set, including:
adding noise to the high resolution range profile of each target;
extracting time domain and frequency domain characteristics from the high-resolution range profile polluted by the noise to obtain a noise characteristic set which is recorded as R (x) i N) in which x i I is 1,2, …, M, n is the index of the signal-to-noise ratio, n is 1, 2.
Calculating the deviation between the features under different signal-to-noise ratios and the corresponding non-noisy features:
R c (x i ,n)＝|R(x i ,n)-R X (x i )|；
calculating a noise robustness parameter of the feature according to the deviation:
in the formula, P snr (x i ) Represents a feature x i The noise robustness parameter of (1).
In one embodiment of the present invention, the step 3 comprises:
normalizing the Relieff evaluation value and the mRMR evaluation value of each feature by adopting a Z-score standardization method to obtain a separability increment value of the feature as follows:
in the formula,. DELTA.H (x) i ) Represents a feature x i Can be increased by a value of DeltaW (x) i ) Represents the feature x i Relieff evaluation value of (a), Δ I (x) i ) Represents a feature x i The mRMR evaluation values of (1), mean and std, respectively represent the calculation process of the mean and standard deviation;
according to the separability increment value and the noise robustness parameter of the feature, calculating to obtain a fusion evaluation value of the feature according to the following formula:
J(x i )＝ΔH(x i )-βP snr (x i )；
in the formula, J (x) i ) Represents the feature x i Fusion evaluation value of (1), P snr (x i ) Represents a feature x i β represents the proportion of the noise robustness factor in the feature selection process.
In one embodiment of the present invention, the step 4 comprises:
sorting the fusion evaluation values of the features, selecting two features with the highest fusion evaluation values as initial feature subsets, and performing feature search by using a sequence forward search method to obtain an optimal feature subset under a preset dimension,
when the k-th search is finished, the feature subset obtained by the search is set as A k Then, the k +1 th search proceeds to:
forward selecting new characteristics: selecting a feature x from a candidate feature set i Joining feature subset A k Forming a new feature subset A k+1 ＝A k +x i Wherein x is i Is such that A k+1 Fusion evaluation value J (A) of k+1 ) Adding the largest features;
and backward removing old features: in A k+1 In which a feature x is selected j Minimizing the fusion evaluation value of the feature subset after the feature is eliminated, and for x j And x i The judgment is carried out, and the judgment is carried out,
if x j And x i If the feature is the same, the feature x is not rejected j And making k equal to k +1, and continuing to search for the next step;
if x j And x i Not of the same character, then x j From A k+1 Removing to generate new feature subset A k ′＝A k+1 -x j Continue from feature subset A k ' of selecting a feature x t The fusion evaluation value J (A) of the feature subset from which the feature has been removed is minimized k ′-x t ) And the characteristic subset A obtained when the search of the step k-1 is completed k-1 Fusion evaluation value J (A) of k-1 ) The judgment is carried out, and the judgment is carried out,
if J (A) k ′-x t )≤J(A k-1 ) Then feature x is not rejected t And order A k ＝A k ' continuously carrying out forward selection of new characteristic operation;
if J (A) k ′-x t )＞J(A k-1 ) Then x is t From A k ' Miss culling, generating a new subset A k-1 ′＝A k -x t And let k equal to k-1, continue to remove old bits backwardsPerforming a marking operation;
and when k is greater than the preset dimensionality, stopping forward selection of a new feature operation.
Compared with the prior art, the invention has the beneficial effects that:
1. the robust noise high-resolution range profile feature selection method effectively combines the Relieff evaluation value and the mRMR evaluation value noise robustness parameters of the features to make more comprehensive and correct evaluation on the separability of the features.
2. The high-resolution range profile feature selection method with stable noise utilizes a sequence floating forward feature search algorithm to search the feature subset, ensures that the result is close to the global optimum, avoids global search, continuously selects new features forward in the search process, and backwards eliminates old features, so that the dimension of the final feature subset is smaller, the small feature dimension means good generalization performance, and the noise stability factor is considered when calculating the feature evaluation value, so that the noise stability of the finally selected feature subset is better.
3. The high-resolution range profile feature selection method with stable noise analyzes each feature more comprehensively, takes noise factors into consideration, utilizes the sequence floating forward search algorithm to search the feature subsets, and the selected feature subsets have the advantages of small dimensionality, low redundancy, good noise stability and great improvement on the target identification probability.
The foregoing description is only an overview of the technical solutions of the present invention, and in order to make the technical means of the present invention more clearly understood, the present invention may be implemented in accordance with the content of the description, and in order to make the above and other objects, features, and advantages of the present invention more clearly understood, the following preferred embodiments are described in detail with reference to the accompanying drawings.
Drawings
FIG. 1 is a schematic diagram of a noise-robust high-resolution range profile feature selection method according to an embodiment of the present invention;
FIG. 2 is a flow chart of a method for selecting a high-resolution range profile with robust noise according to an embodiment of the present invention;
FIG. 3 is a graph comparing the recognition results of the method of the present invention with those of the prior art provided by the embodiment of the present invention;
FIG. 4 is a comparison diagram of the search with or without features based on the proposed method of the present invention;
FIG. 5 is a graph of noise robustness parameters for various features provided by embodiments of the present invention;
fig. 6 is a comparison graph of the impact of robustness to noise on recognition performance provided by embodiments of the present invention.
Detailed Description
To further illustrate the technical means and effects of the present invention for achieving the predetermined objects, a method for selecting a high-resolution range profile with robust noise according to the present invention is described in detail below with reference to the accompanying drawings and the detailed description.
The foregoing and other technical matters, features and effects of the present invention will be apparent from the following detailed description of the embodiments, which is to be read in connection with the accompanying drawings. The technical means and effects of the present invention adopted to achieve the predetermined purpose can be more deeply and specifically understood through the description of the specific embodiments, however, the attached drawings are provided for reference and description only and are not used for limiting the technical scheme of the present invention.
Example one
The HRRP is a vector sum of projection of target scattering point sub-echoes acquired based on radar broadband signals in the radar sight direction, contains characteristic information such as target structure and scattering point distribution, and has the advantages of easiness in acquisition, small calculation amount, loose error estimation, high calculation speed and the like. Therefore, HRRP becomes a research hotspot in the field of radar target identification and classification.
Target recognition based on HRRP is generally divided into a training stage and a recognition stage, and each stage comprises three links of preprocessing, feature extraction and selection, classifier design or test and the like. Wherein, the pretreatment mainly overcomes three sensitivities of HRRP, including: pose sensitivity, translation sensitivity, and amplitude sensitivity. The feature extraction includes both various mathematical and physical features extracted from the HRRP that characterize the nature of the target, and projection of the original high-dimensional feature matrix or the original HRRP transform into some spatial operation with good separability. And screening the extracted features by using a feature selection algorithm, selecting a group of optimal feature subsets with good separability, taking the optimal feature subsets of the training samples as the input of the classifier, optimizing the parameters of the classifier, and performing performance verification on the classifier by using the identification samples to be detected. From the three links, it can be found that the optimal feature subset of the training sample directly affects the performance of the classifier, and therefore, it is particularly important to select the feature subset with good separability, small information redundancy and small dimension.
In target identification based on HRRP radar, identification performance, noise robustness and storage requirement are all keys for measuring the performance of a classifier. Combining the above factors, the present embodiment provides a robust noise-based selection method for high-resolution range profile features.
Referring to fig. 1 and fig. 2 in combination, fig. 1 is a schematic diagram of a robust-noise high-resolution range profile feature selection method according to an embodiment of the present invention; fig. 2 is a flowchart of a method for selecting a high-resolution range profile with robust noise according to an embodiment of the present invention. As shown, the method includes:
step 1: acquiring a high-resolution range profile sample set of targets, and performing feature extraction on the high-resolution range profile of each target to obtain an original feature set;
specifically, step 1 comprises:
step 1.1: acquiring a dual-polarized target high-resolution range profile sample set acquired by a radar, preprocessing the high-resolution range profile of each target, and overcoming the sensitivity of the high-resolution range profile;
in this embodiment, the high-resolution range profile sample set includes N groups of high-resolution range profiles of the dual-polarized radar for the target, and the high-resolution range profile includes a co-polarized high-resolution range profile S LL And cross-polarized high-resolution range profile S RL 。
The sensitivity to overcome the high resolution range profile is mainly to overcome three sensitivities of HRRP, including: pose sensitivity, translation sensitivity, and amplitude sensitivity. Specifically, a barycentric alignment method is used to avoid translational sensitivity, the amplitude is normalized to overcome the amplitude sensitivity, and the minimum interval at which no over-the-range cell walk occurs is selected as a training sample to overcome the attitude sensitivity.
Step 1.2: and performing feature extraction on the preprocessed high-resolution range profile to obtain frequency domain features and time domain features of the high-resolution range profile, and combining to obtain an original feature set.
Specifically, the preprocessed homopolarization high-resolution range profile S LL And cross-polarized high-resolution range profile S RL Fourier transform is carried out on the two paths of data to obtain two paths of frequency domain data S corresponding to the two paths of data L ′ L And S' RL The four paths of data are subjected to feature extraction to obtain 50 features such as entropy features, polarization angle features, amplitude features, moment features, mean values, standard deviations, average rising voltage features, differential fluctuation features and the like, specific features and labels are shown in table 1, and the features form an original feature set X: x ═ X m,n In which M is [1, M ]]，n∈[1,N]M is the number of features contained in each sample, and N is the number of samples in the high-resolution range profile sample set.
TABLE 1 characteristics and designations
In the embodiment, the features are respectively extracted from two angles of a time domain and a frequency domain, four paths of data reflect target characteristics of different levels, so that the characteristics of the target are displayed more thoroughly, the extracted features can reflect the characteristics of the target, and the subsequent target identification rate can be improved.
And 2, step: respectively calculating a Relieff evaluation value, an mrMR evaluation value and a noise robustness parameter of each feature in the original feature set;
specifically, step 2 comprises:
step 2.1: calculating a Relieff evaluation value of each feature according to a Relieff evaluation criterion;
the Relieff algorithm is to obtain the evaluation value of each feature by comparing the inter-class distance and the intra-class distance to iteratively update the weight of the feature according to the condition that each feature is in the range with the Euclidean distance of k. The Relieff algorithm comprehensively considers the inter-class distance and the intra-class distance of local features, and evaluates the classification capability of the features through 'hypothesis spacing': if the distance between classes is greater than the distance in the classes, the weight is increased; if the distance between classes is less than the distance in classes, the weight is decreased. And continuously updating the weight value through the comparison between the inter-class distance and the intra-class distance, and taking the final weight value obtained through calculation as the evaluation value of each characteristic.
Specifically, step 2.1 comprises:
(1) marking the original feature set as X, wherein X is an M × N matrix, that is, each sample contains M features, and N samples are provided in total;
(2) taking a sample R from X, selecting K adjacent points from the samples of the same class as the sample R in X as H, and selecting K adjacent points from the samples of different classes from the sample R as M;
(3) the weight matrix W is calculated as follows:
in the above formula, q represents the number of iterations, H j Denotes the jth nearest neighbor sample, M, of the same class as sample R j (C) Presentation class
J (th) nearest neighbor sample, p (C) is the probability of occurrence of class C, class (R) is the class of sample R, p (class (R)) is the probability of occurrence of class of sample R, diff (x) i ,R,H j ) Denotes samples R and H j At feature x i The difference in (c) is as follows:
(4) in the selected feature S m-1 On the basis of the above-mentioned data, making incremental search, and making the rest of features in the feature spaceThe significance of the signature is calculated as follows:
ΔW(x i )＝W([S m-1 ,x i ])-W(S m-1 ) (3)；
in the formula, Δ W (x) i ) Represents a feature x i The Relieff evaluation value of (1).
In the present embodiment, Δ W (x) i ) The larger the value, the more the feature x is represented i The greater the separability and the less redundancy with the selected feature. Feature x that the Relieff algorithm will maximize Δ W i As the selected feature.
Step 2.2: calculating an mRMR evaluation value of each feature according to an mRMR evaluation criterion;
the mRMR algorithm calculates correlation coefficients between each feature and each category and between features using a mutual information theory, and uses the difference between the two as an evaluation value of each feature. Mutual information represents the content of the information commonly owned between the two variables, can be used for measuring the strength of the mutual dependence between the two variables, is not limited to linear correlation, and can also be used for evaluating the nonlinear relation between the variables. Given two random variables X and Y, their respective marginal probability distributions and joint probability distributions are p (X), p (Y), and p (X, Y), respectively, the mutual information between them is defined as:
if the variables X and Y are completely unrelated or independent, the mutual information is minimum, and the result is 0, namely no overlapped information exists between the two variables; conversely, the higher the degree of interdependence between variables X and Y, the larger the mutual information value, and the more the same information is contained.
Specifically, step 2.2 comprises:
(1) according to the definition of mutual information, calculating the mutual information of the single characteristic and the category according to the following formula:
in the formula, x i And C respectively represent the ith feature in the original feature set X and the class to which the feature belongs, p (X) i ) Represents a feature x i P (C) represents the marginal probability distribution of class C, p (x) i And C) represents the feature x i And a joint probability distribution for class C.
Wherein, I (x) i (ii) a C) The larger the value is, the more category information contained in the characteristics is shown, and the larger the contribution degree to the classification is; otherwise, I (x) i (ii) a C) Smaller values indicate that the features contain less category information and contribute less to the classification.
(2) The correlation between the original feature set X and the category is defined as:
in the formula, M represents the number of features contained in an original feature set X;
(3) mutual information between features is calculated according to the following formula:
wherein, I (x) i ；x j ) The larger the value, the more the feature x is represented i And feature x j The greater the correlation between them, i.e. the greater the redundancy.
(4) The minimum correlation between features is defined as:
(5) in order to select a feature set with high separability and low redundancy, mRMR combines two measures, and defines the following criteria:
maxΦ(D,Q)＝D-Q (9)；
(6) in the selected feature S m-1 On the basis of the above-mentioned data, making incremental search, and making importance of features in residual feature space according toThe following formula is calculated:
in the formula,. DELTA.I (x) i ) Represents a feature x i M denotes the number of selected feature subsets, C denotes the feature x i The category (2).
Wherein, Δ I (x) i ) The larger the value, the more the feature x is represented i The greater the separability and the less redundancy with the selected features. The mRMR algorithm will maximize the Δ I of the feature x i As the selected feature.
Step 2.3: noise is added into the high-resolution range profile sample set of the target, corresponding characteristic extraction is carried out on the high-resolution range profile sample set after noise pollution, a noise characteristic set is obtained, and a noise robustness parameter of each characteristic is calculated according to the noise characteristic set and the original characteristic set.
Specifically, step 2.3 comprises:
(1) adding noise to the high resolution range image samples of each target;
in this embodiment, the signal-to-noise ratio of the dual-polarized HRRP is made to be [5:5:30] dB.
(2) Respectively extracting the time domain and frequency domain characteristics of the high-resolution range profile after noise pollution to obtain a noise characteristic set which is recorded as R (x) i N) in which x i I is 1,2, …, M, n is the index of the signal-to-noise ratio, n is 1, 2.
(3) Calculating the deviation between the features under different signal-to-noise ratios and the corresponding non-noisy features:
R c (x i ,n)＝|R(x i ,n)-R X (x i )| (11)；
(4) calculating a noise robustness parameter of the feature according to the deviation:
in the formula, P snr (x i ) Represents a feature x i The noise robustness parameter of (1).
From the definition of the noise robustness parameter, the more sensitive a feature is to noise, P snr The larger the value, and conversely the more robust the feature is with respect to noise, P snr The smaller the value.
Since the signal-to-noise ratio of the echo signal collected by the radar seeker may be low, when selecting the feature, the noise robustness factor should be fully considered, and the feature robust to noise should be selected, so that the identification system of the radar seeker has high noise robustness.
And step 3: performing multi-evaluation value fusion processing on the Relieff evaluation value, the mRMR evaluation value and the noise robustness parameter of each feature to obtain a fusion evaluation value of each feature;
since the dimensions of the evaluation values calculated by different evaluation criteria are different and have different value ranges, normalization processing is required before the evaluation values (separability values) of the features calculated by the two criteria of ReliefF and mRMR are fused.
Specifically, step 3 includes:
step 3.1: and normalizing the Relieff evaluation value and the mRMR evaluation value of each feature by adopting a Z-score standardization method to obtain a separability increment value of the feature as follows:
ΔH(x i ) Represents a feature x i Can be increased by a value of DeltaW (x) i ) Represents a feature x i Relieff evaluation value of (a), Δ I (x) i ) Represents a feature x i The rmr evaluation values of (a) and (b), mean and std, represent the calculation processes of the mean and standard deviation, respectively.
Step 3.2: and calculating to obtain a fusion evaluation value of the feature according to the separability increment value and the noise robustness parameter of the feature and the following formula:
J(x i )＝ΔH(x i )-βP snr (x i ) (14)；
in the formula, J (x) i ) Represents a feature x i Fusion evaluation value of (1), P snr (x i ) Represents a feature x i β represents the proportion of the noise robustness factor in the feature selection process.
Since the importance of the feature is determined by the separability and the noise robustness of the feature, in the embodiment, J is used as an important basis for feature search, and then a subset of the feature with high separability and strong noise robustness can be selected.
And 4, step 4: and according to the fusion evaluation value, performing feature search on the original feature set by using a sequence floating forward search method to obtain an optimal feature subset under a preset dimensionality, and performing subsequent target identification operation by using the optimal feature subset.
Specifically, step 4 includes:
sorting the fusion evaluation values of the features, selecting two features with the highest fusion evaluation values as initial feature subsets, and performing feature search by using a sequence forward search method to obtain an optimal feature subset under a preset dimension,
when the k-th search is finished, the feature subset obtained by the search is set as A k Then, the k +1 th search proceeds to:
(1) forward selecting new characteristics: selecting a feature x from a candidate feature set i Joining feature subset A k Forming a new feature subset A k+1 ＝A k +x i Wherein x is i Is such that A k+1 Fusion evaluation value J (A) of (2) k+1 ) Adding the largest features;
(2) and backward removing old features: in A k+1 In which a feature x is selected j Minimizing the fusion evaluation value of the feature subset after the feature is eliminated, and for x j And x i The judgment is carried out, and the judgment is carried out,
if x j And x i If the feature is the same, the feature x is not rejected j And making k equal to k +1, and continuing to search for the next step;
if x j And x i Not of the same character, then x j From A k+1 Removing to generate new feature subset A k ′＝A k+1 -x j Continue from feature subset A k ' of selecting a feature x t The fusion evaluation value J (A) of the feature subset from which the feature is removed is reduced to the minimum k ′-x t ) And the characteristic subset A obtained when the search of the step k-1 is completed k-1 Fusion evaluation value J (A) of k-1 ) The judgment is carried out, and the judgment is carried out,
if J (A) k ′-x t )≤J(A k-1 ) Then feature x is not rejected t And order A k ＝A k ' continuously carrying out forward selection of new characteristic operation;
if J (A) k ′-x t )＞J(A k-1 ) Then x is t From A k ' Miss culling, generating a new subset A k-1 ′＝A k -x t And making k equal to k-1, and continuing to remove the old features;
and when k is greater than the preset dimensionality, stopping forward selection of a new feature operation.
It should be noted that, the optimal feature subset is used for performing subsequent target recognition operation, the optimal feature subset is input into an SVM classifier subsequently, a classifier model is trained, and the classifier is subjected to performance test by using test data to obtain recognition results of various targets.
It should be noted that step 4 may also be repeated to obtain the recognition result of the optimal feature subset in different dimensions, and the set of feature subsets with the best recognition result is used as the optimal feature subset of the whole system.
The method for selecting the high-resolution range profile features with stable noise effectively combines the ReliefF evaluation value and the mRMR evaluation value noise stability parameters of the features to make a more comprehensive and correct evaluation on the separability of the features. The method comprises the steps of utilizing a sequence floating forward feature search algorithm to search a feature subset, ensuring that a result is close to global optimum, avoiding global search, continuously selecting new features forward in the searching process, and removing old features backward, so that the final feature subset has small dimension, the small feature dimension means good generalization performance, and noise robustness factors are considered when feature evaluation values are calculated, and the finally selected feature subset has better noise robustness. The method can analyze each feature more comprehensively, considers noise factors, utilizes a sequence floating forward search algorithm to search the feature subsets, and the selected feature subsets have small dimensionality, low redundancy, good noise robustness and great improvement on the target identification probability.
Example two
The embodiment verifies and explains the effect of the noise-robust high-resolution range profile feature selection method of the first embodiment through a specific test.
The test conditions are as follows:
the radar transmitting signals adopt a linear frequency modulation-stepping frequency system, the signal frequency is located in a W wave band, the number of pulses is 128, the pulse stepping frequency delta f is 10MHz, and the synthetic bandwidth of the radar transmitting signals obtained by the parameters is 1.2 GHz.
Simulation content and result analysis:
the present embodiment uses actual measurement data of six types of targets, such as radar vehicles, trucks, corner reflectors, houses, hangars, and shelter cars, as sample template library data. Preprocessing operations such as gravity center alignment and amplitude normalization are carried out on the measured data, Fourier transform is respectively carried out on the same polarization data and the cross polarization data to obtain two paths of frequency domain data, 50 characteristics such as entropy characteristics, polarization angle characteristics, amplitude characteristics, moment characteristics, mean values, standard deviations, average rising voltage and difference fluctuation characteristics are respectively extracted from the four paths of data, and specific characteristic names and corresponding labels are shown in table 1.
In order to verify the performance advantages of the feature selection method of the invention, two traditional filtering feature selection algorithms are compared. Comparison results referring to table 2 and fig. 3, fig. 3 is a graph comparing the identification results of the method of the present invention provided by the embodiment of the present invention and the existing method. As can be seen from the table 2, the average correct recognition probability of the method is higher than that of the other two feature selection algorithms with single evaluation criteria, the average correct recognition rate is improved by nearly 1.15 percent, the number of the optimal feature subsets is the least, the calculation speed can be better improved and the memory pressure can be reduced in practical engineering application, and the feature dimension is small, so that the method has better generalization performance. As can be seen from fig. 3, when the feature dimensions are the same, the average correct recognition rate of the feature selection method of the present invention is higher than those of the other two feature selection algorithms with a single evaluation criterion, but when the dimensions are increased to a certain number, the average correct recognition results of the three feature selection algorithms are not very different; in addition, the recognition result of the feature selection method of the invention shows a stable trend after the number of feature dimensions is 5, and the other two single evaluation criteria have small-range fluctuation.
TABLE 2 comparison of recognition results
In order to study the influence of feature search on the performance of the recognition system, a comparison experiment of feature search is performed on the premise of being based on a comprehensive evaluation criterion, and the result is shown in fig. 4, where fig. 4 is a comparison diagram of feature search based on the method provided by the embodiment of the present invention. It can be seen from the figure that after feature search is performed, a better recognition result can be obtained under a lower feature dimension, when feature search is not performed, the recognition result is improved along with the increase of the feature dimension, and when the feature dimension is increased to a certain number, the recognition results of the two methods are closer. Therefore, after feature search is carried out, the number of feature dimensions can be further reduced on the premise that the whole recognition algorithm keeps a better recognition result.
In order to verify the noise robustness of the invention, on the premise of being based on the comprehensive evaluation criterion, a comparison experiment is carried out on whether noise robustness factors are considered, and the result is shown in table 3 and fig. 5-6, and it can be known from table 3 that the features screened out by considering the noise robustness factors are less influenced by noise, and the feature dimension is small and the recognition performance is good. Fig. 5 is a graph of noise robustness parameters of each feature provided by the embodiment of the present invention, and a higher parameter value indicates that the noise robustness of the feature is poor, and as can be seen from fig. 5, the features with feature numbers 16, 28, 45, 47 and 50 are more sensitive to noise. Fig. 6 is a comparison graph of the influence of noise robustness on the recognition performance according to the embodiment of the present invention, and it can be seen from fig. 6 that in the features screened out in consideration of the noise robustness, the sensitivity to noise is low, and the recognition result gradually decreases with the decrease of the signal-to-noise ratio, but the decrease speed is slow; under the condition of not considering noise robustness factors, the screened optimal feature subset comprises features with high noise sensitivity, such as the two features with the numbers of 16 and 28, the identification result is sharply reduced along with the reduction of the signal-to-noise ratio, and the capability of correct identification is almost lost when the signal-to-noise ratio is 5 dB.
TABLE 3 influence of noise robustness on recognition rate
| Whether or not to consider noise robustness | Optimal feature subset | Average correct recognition rate |
| Whether or not | 13、16、39、29、43、44、28、7 | 95.21％ |
| Is that | 13、39、29、44、43 | 96.97％ |
The method for selecting the high-resolution range profile features with stable noise analyzes the features from a plurality of different angles, the Relieff criterion measures the contribution degree of a certain feature to classification by using the distance between the features, the mRMR respectively calculates the correlation between the features and the classification by using a mutual information theory, and the noise stability of the feature is measured by calculating the deviation between the feature value polluted by the noise and the original feature value. And taking the feature evaluation value as a basis, performing feature search by using a sequence floating forward search algorithm, and fully considering the combination effect among the features to optimize the feature subset obtained by searching. And finally, selecting the group of feature subsets with the best recognition result as the optimal feature subset of the whole system by using the packaging type feature selection idea and using the recognition result of the SVM classifier as an evaluation standard.
Compared with a feature selection algorithm with a single evaluation criterion, the feature selection method has better identification performance under the condition of lower feature dimension, the identification performance is more stable along with the rise of the feature dimension, when the optimal feature subset is selected, a sequence forward floating search algorithm is adopted, the result can reach the global optimum on the basis of avoiding global search, in addition, a noise robustness factor is considered when the feature evaluation value is calculated, and therefore, the feature selection method also has a certain identification function under the condition of lower signal-to-noise ratio.
The feature selection method can quickly remove redundant features, achieves effective identification, has small feature dimension and better robustness, is a better method for carrying out feature separability analysis on high-resolution range profiles, and has certain engineering application significance.
It should be noted that, in this document, the terms "comprises", "comprising" or any other variation are intended to cover a non-exclusive inclusion, so that an article or apparatus comprising a series of elements includes not only those elements but also other elements not explicitly listed. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of additional like elements in the article or device comprising the element.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, numerous simple deductions or substitutions may be made without departing from the spirit of the invention, which shall be deemed to belong to the scope of the invention.
Claims (8)
1. A method for selecting a noise-robust high-resolution range profile feature, comprising the steps of:
step 1: acquiring a high-resolution range profile sample set of targets, and performing feature extraction on the high-resolution range profile of each target to obtain an original feature set;
step 2: respectively calculating a Relieff evaluation value, an mrMR evaluation value and a noise robustness parameter of each feature in the original feature set;
and step 3: performing multi-evaluation value fusion processing on the Relieff evaluation value, the mRMR evaluation value and the noise robustness parameter of each feature to obtain a fusion evaluation value of each feature;
and 4, step 4: and according to the fusion evaluation value, performing feature search on the original feature set by using a sequence floating forward search method to obtain an optimal feature subset under a preset dimensionality, and performing subsequent target identification operation by using the optimal feature subset.
2. The method according to claim 1, wherein the step 1 comprises:
acquiring a dual-polarized target high-resolution range profile sample set acquired by a radar, and preprocessing the high-resolution range profile of each target to overcome the sensitivity of the high-resolution range profile;
and performing feature extraction on the preprocessed high-resolution range profile to obtain frequency domain features and time domain features of the high-resolution range profile, and combining to obtain the original feature set.
3. The method according to claim 1, wherein the step 2 comprises:
calculating a Relieff evaluation value of each feature according to a Relieff evaluation criterion;
calculating an mRMR evaluation value of each feature according to an mRMR evaluation criterion;
and adding noise into the high-resolution range profile sample set of the target, extracting corresponding characteristics of the high-resolution range profile sample set after noise pollution to obtain a noise characteristic set, and calculating a noise robustness parameter of each characteristic according to the noise characteristic set and the original characteristic set.
4. The method of claim 3, wherein calculating the Relieff score for each feature according to the Relieff score criterion comprises:
recording the original feature set as X, wherein X is an M × N matrix, each sample comprises M features, and N samples are provided in total;
taking a sample R from X, selecting K adjacent points from the samples of the same class as the sample R in X as H, and selecting K adjacent points from the samples of different classes from the sample R as M;
the weight matrix W is calculated as follows:
in the above formula, q represents the number of iterations, H j Denotes the jth nearest neighbor sample, M, of the same class as sample R j (C) Presentation class
J (th) nearest neighbor sample, p (C) is the probability of occurrence of class C, class (R) is the class of sample R, p (class (R)) is the probability of occurrence of class of sample R, diff (x) i ,R,H j ) Denotes samples R and H j At feature x i The difference in (c) is as follows:
in the selected feature S m-1 On the basis of the above, incremental search is performed, and the importance of the features in the remaining feature space is calculated according to the following formula:
ΔW(x i )＝W([S m-1 ,x i ])-W(S m-1 )；
in the formula, Δ W (x) i ) Represents a feature x i The Relieff evaluation value of (1).
5. The method of claim 3, wherein computing the mRMR evaluation value for each feature according to an mRMR evaluation criterion comprises:
and calculating mutual information of the single characteristics and the categories according to the definition of the mutual information as follows:
in the formula, x i And C respectively represent the ith feature in the original feature set X and the class to which the feature belongs, p (X) i ) Represents a feature x i P (C) represents the marginal probability distribution of class C, p (x) i And C) represents the feature x i And a joint probability distribution for class C;
the correlation between the original feature set X and the category is defined as:
in the formula, M represents the number of features contained in an original feature set X;
mutual information between features is calculated according to the following formula:
the minimum correlation between features is defined as:
mRMR combines two measures, defining the following criteria:
maxΦ(D,Q)＝D-Q；
in the selected feature S m-1 On the basis of the above, incremental search is performed, and the importance of the features in the remaining feature space is calculated according to the following formula:
in the formula,. DELTA.I (x) j ) Represents a feature x j M denotes the number of selected feature subsets, C denotes the feature x i The category (2).
6. The method for selecting noise-robust high-resolution range profile features according to claim 3, wherein the method for selecting noise-robust high-resolution range profile features comprises the steps of adding noise into a high-resolution range profile sample set of the target, performing corresponding feature extraction on the high-resolution range profile sample set after noise pollution to obtain a noise feature set, and calculating a noise robustness parameter of each feature according to the noise feature set and the original feature set, and comprises the following steps:
adding noise to the high resolution range profile of each target;
extracting time domain and frequency domain characteristics from the high-resolution range profile polluted by the noise to obtain a noise characteristic set which is recorded as R (x) i N) in which x i For the ith feature, I is 1,2, …, M, n is the index of the signal-to-noise ratio, n is 1, 2.
Calculating the deviation between the features under different signal-to-noise ratios and the corresponding non-noisy features:
R c (x i ,n)＝|R(x i ,n)-R X (x i )|；
calculating a noise robustness parameter of the feature according to the deviation:
in the formula, P snr (x i ) Represents a feature x i The noise robustness parameter of (1).
7. The method according to claim 1, wherein the step 3 comprises:
normalizing the Relieff evaluation value and the mRMR evaluation value of each feature by adopting a Z-score standardization method to obtain a separability increment value of the feature as follows:
in the formula,. DELTA.H (x) i ) Represents a feature x i Can be increased by a value of DeltaW (x) i ) Represents a feature x i Relieff evaluation value of (a), Δ I (x) i ) Represents a feature x i The mRMR evaluation values of (1), mean and std, respectively represent the calculation process of the mean and standard deviation;
according to the separability increment value and the noise robustness parameter of the feature, calculating to obtain a fusion evaluation value of the feature according to the following formula:
J(x i )＝ΔH(x i )-βP snr (x i )；
in the formula, J (x) i ) Represents a feature x i Fusion evaluation value of (1), P snr (x i ) Represents a feature x i β represents the proportion of the noise robustness factor in the feature selection process.
8. The method of claim 1, wherein the step 4 comprises:
sorting the fusion evaluation values of the features, selecting two features with the highest fusion evaluation values as initial feature subsets, and performing feature search by using a sequence forward search method to obtain an optimal feature subset under a preset dimension,
when the k-th search is finished, the feature subset obtained by the search is set as A k Then, the k +1 th search proceeds to:
forward selecting new characteristics: selecting a feature x from a candidate feature set i Joining feature subset A k Forming a new feature subset A k+1 ＝A k +x i Wherein x is i Is such that A k+1 Fusion evaluation value J (A) of k+1 ) Adding the largest features;
and backward removing old features: in A k+1 In which a feature x is selected j Minimizing the fusion evaluation value of the feature subset after the feature is eliminated, and for x j And x i The judgment is carried out, and the judgment is carried out,
if x j And x i If the feature is the same, the feature x is not rejected j And making k equal to k +1, and continuing to search for the next step;
if x j And x i Not of the same character, then x j From A k+1 Removing to generate new feature subset A k ′＝A k+1 -x j Continue from feature subset A k ' of selecting a feature x t The fusion evaluation value J (A) of the feature subset from which the feature is removed is reduced to the minimum k ′-x t ) And the characteristic subset A obtained when the search of the step k-1 is completed k-1 Fusion evaluation value J (A) of k-1 ) The judgment is carried out, and the judgment is carried out,
if J (A) k ′-x t )≤J(A k-1 ) Then feature x is not rejected t And order A k ＝A k ' continuously carrying out forward selection of new characteristic operation;
if J (A) k ′-x t )＞J(A k-1 ) Then x is t From A k ' Miss culling, generating a new subset A k-1 ′＝A k -x t And making k equal to k-1, and continuing to remove the old features;
and when k is greater than the preset dimensionality, stopping forward selection of a new feature operation.
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