CN113505833A - Radar automatic target identification method based on multi-view variable convolutional neural network - Google Patents

Radar automatic target identification method based on multi-view variable convolutional neural network Download PDF

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CN113505833A
CN113505833A CN202110783185.8A CN202110783185A CN113505833A CN 113505833 A CN113505833 A CN 113505833A CN 202110783185 A CN202110783185 A CN 202110783185A CN 113505833 A CN113505833 A CN 113505833A
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裴季方
黄钰林
汪志勇
王陈炜
霍伟博
杨建宇
张寅�
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University of Electronic Science and Technology of China
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    • G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
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Abstract

The invention discloses a radar automatic target identification method based on a multi-view variable convolution neural network, which comprises the following steps: A. acquiring an original radar image; B. preprocessing an original radar image; C. generating multi-view data; D. constructing a deep neural network based on multi-view variable convolution; E. training a deep neural network: initializing network weight and bias, inputting the multi-view radar image combination obtained by processing in the step C into the multi-view variable convolution neural network constructed in the step D for forward propagation, and calculating a cost function; updating parameters of the multi-view variable convolution neural network by using a backward propagation algorithm based on gradient descent; and (5) carrying out forward and backward propagation in an iteration mode until the cost function is converged. The method has the advantages of relieving the problem of insufficient radar image sample size, avoiding the condition of insufficient feature extraction, having strong generalization capability, and fully and effectively utilizing the unique form and scattering information of the radar target to realize accurate identification and classification of the target.

Description

Radar automatic target identification method based on multi-view variable convolutional neural network
Technical Field
The invention belongs to the technical field of radar target identification, and particularly relates to a radar automatic target identification method based on a multi-view variable convolutional neural network.
Background
The radar sensor can realize all-time and all-weather earth observation without the limitation of illumination, weather conditions and the like, has wide application prospect in the fields of aeronautical survey, satellite marine observation, battlefield sensing reconnaissance, agriculture and forestry environment monitoring, geological and landform exploration and the like, and has extremely high civil and military values. The radar Automatic Target Recognition (ATR) is an image interpretation technology based on theories such as modern signal processing and pattern Recognition, and can be roughly divided into three processes of detection, identification and classification, and aims to acquire Target categories possibly contained in an area of interest, thereby providing powerful support for battlefield information analysis.
Currently, in the process of radar ATR, targets are effectively identified mainly by a template-based method and a model-based method. However, the traditional method has the problems of low efficiency, poor real-time performance, high algorithm complexity and the like, and meanwhile, the optimal target characteristics are difficult to extract under the influence of manual experience, so that the identification performance of the system is reduced to some extent. With the development of deep learning in recent years, many achievements are made in the fields of image processing, data mining, and the like. By virtue of excellent automatic learning capability and feature extraction capability, the deep learning-based radar ATR becomes a new popular research direction.
In the aspect of combining deep learning with the field of Radar target recognition, the document "moving D A E. deep convolutional neural networks for ATR from SAR image [ C ]// Algorithms for Synthetic Aperture radio image XXII. International Society for Optics and Photonics,2015,9475: 94750F" applies a deep convolutional neural network to the problem of Radar ten-class identification and obtains good recognition effect, but the training sample amount required by the network is too large, and the fitting is easily generated under the condition of less input sample amount, so that the generalization capability of the network is poor. The document "Chen S, Wang H, Xu F, et al. target classification using the deep dependent networks for SAR images [ J ]. IEEE Transactions on Geoscience and remove Sensing,2016,54(8): 4806) replaces the full link layer with the convolutional layer for classification, which reduces the parameter amount of the network and the time consumption of calculation. However, the scattering characteristics and morphological features of the radar image target are not fully mined and utilized by the network, and the overall recognition performance is not greatly improved.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide the radar automatic target identification method based on the multi-view variable convolutional neural network, which can overcome the defects that the special form and scattering information of a radar target can be fully and effectively utilized and realize accurate target identification and classification.
The purpose of the invention is realized by the following technical scheme: a radar automatic target identification method based on a multi-view variable convolutional neural network comprises the following steps:
A. acquiring an original radar image: acquiring target images with the same resolution and radar target azimuth angles corresponding to the images;
B. preprocessing the original radar image: rotating the original radar image to the same direction according to the azimuth angle of the radar target obtained in the step A;
C. multi-view data generation: sequencing the preprocessed radar images according to the sizes of the viewing angles, and generating a multi-viewing-angle combined sample according to the number of the viewing angles and the sizes of observation angles;
D. constructing a deep neural network based on multi-view variable convolution: the whole network comprises three input channels, each channel receives a radar image of a visual angle, and the whole network is divided into five hidden layers: the first two layers are alternating variable convolution layers and maximum pooling layers and are used for extracting morphological characteristics and scattering characteristics of the target under different viewing angles; the third layer is a convolution layer and a maximum pooling layer; the fourth layer is a convolution layer, and the merged characteristic graphs under different visual angles are further subjected to characteristic extraction and data compression; the fifth layer is a convolutional layer Softmax which is used as a classifier to obtain a classification label of the image sample;
E. training a deep neural network: initializing network weight and bias, inputting the multi-view radar image combination obtained by processing in the step C into the multi-view variable convolution neural network constructed in the step D for forward propagation, and calculating a cost function; updating parameters of the multi-view variable convolution neural network by using a backward propagation algorithm based on gradient descent; and (5) carrying out forward and backward propagation in an iteration mode until the cost function is converged.
Further, in step B, when the original radar image is rotated, the mapping transformation between image pixels satisfies:
Figure BDA0003157778740000021
Figure BDA0003157778740000022
wherein the content of the first and second substances,
Figure BDA0003157778740000023
the angle of the counterclockwise rotation of the image is represented, x and y represent the abscissa and ordinate of the original image, respectively, and x 'and y' represent the abscissa and ordinate of the rotated image, respectively.
Further, in the step C, sorting the preprocessed radar images according to the size of the view angle specifically includes: to be provided with
Figure BDA0003157778740000024
Set of radar images representing class i targets, where each image xjCorresponding to different viewing angles
Figure BDA0003157778740000025
The radar images of the same kind of targets are arranged in an ascending order according to the visual angle, and different radar images in the multi-visual angle combined sample are arranged in an ascending order according to the visual angle;
setting the number k of viewing angles and the size theta of an observation angle according to actual imaging conditions and performance indexes, and generating a multi-viewing-angle combined sample according to the number of viewing angles and the size theta of the observation angle; the method specifically comprises the following steps: and combining radar images acquired under any k visual angles in the same target class to jointly form a sample { x }i1,xi2,…,xik}; and the change of the radar image visual angle in the same combined sample is limited not to exceed the size of the observation angle theta, namely
Figure BDA0003157778740000031
Further, the step E includes the following sub-steps:
E1. initializing network weights wlThe distribution is shown in formula (3):
Figure BDA0003157778740000032
Figure BDA0003157778740000033
where l denotes the current number of convolutional layers, hl、wlRespectively representing the height and width of the convolution kernel in the convolution layer, dlRepresenting the number of current convolutional layer convolutional cores;
Figure BDA0003157778740000034
representing an expectation of 0 and a variance of
Figure BDA0003157778740000035
Normal distribution of (2); then, bias term blInitializing to a constant;
E2. forward propagation is performed with ft lShowing the t-th characteristic map of the first layer, if the first layer is a convolution layer
Figure BDA0003157778740000036
Wherein l is more than or equal to 2,
Figure BDA0003157778740000037
representing a convolution kernel connecting the s-th input feature map and the t-th output feature map,
Figure BDA0003157778740000038
representing a bias item corresponding to the tth output feature map of the ith layer; σ (·) represents a nonlinear activation function, and the symbol denotes a convolution operation;
if the l-th layer is a variable convolution layer, firstly acquiring a rearranged image of the l-1-th layer characteristic map:
Figure BDA0003157778740000039
Figure BDA00031577787400000310
wherein the content of the first and second substances,
Figure BDA00031577787400000311
representing the rearranged image of the characteristic map of the layer l-1, wherein m and n represent the mth row and the nth column on the characteristic map; (o)m,on) E is O, and O is an index bias set;
Figure BDA00031577787400000312
a convolution kernel and an offset term for variable convolution, c represents the number of input channels, sign
Figure BDA00031577787400000313
Convolution operation denoted as fill-in Same;
then, the acquired image is convolved once:
Figure BDA00031577787400000314
if the first layer is a pooling layer, then
Figure BDA00031577787400000315
Wherein r is1、r2Representing the size of the pooling window, sd representing the pooling step size;
after the sample reaches an output layer, the output is processed by a Softmax classifier, and the posterior probability of the current sample belonging to the ith class is obtained:
Figure BDA0003157778740000041
wherein the content of the first and second substances,
Figure BDA0003157778740000042
respectively representing the ith and the C th input of the layer, wherein C represents the total category number;
E3. calculating a cost function value: the cross entropy loss function is adopted as the cost function of the network, and the calculation formula is
Figure BDA0003157778740000043
Wherein, p (x)i) Representing the true probability that the target class is the ith class, w, b represent the set of weight and bias terms in the network, p (i | k)l(ii) a w, b) represents the posterior probability that the target class is the ith class given w and b;
E4. updating network parameters by adopting a backward propagation algorithm based on self-adaptive gradient, wherein the specific calculation formula is as follows:
Figure BDA0003157778740000044
wherein m istAnd vtFirst order momentum term and second order momentum term, mt-1、vt-1Respectively a first-order momentum term and a second-order momentum term of the previous moment; beta is a1、β2The power value is the value;
Figure BDA0003157778740000045
respectively are respective correction values; w is atWeight, g, representing the t-th iteration modelt＝ΔJ(wt) Representing the gradient magnitude of the t times of iteration cost function relative to w; η represents the learning rate; δ is a very small number used to avoid denominator of 0; the update strategy of the bias term b is the same as w.
The invention has the beneficial effects that: the method overcomes the influence of different azimuth angles of the radar target, relieves the problem of insufficient radar image sample amount, avoids the condition of insufficient feature extraction, has strong generalization capability, and can fully and effectively utilize the unique form and scattering information of the radar target to realize accurate identification and classification of the target.
Drawings
FIG. 1 is a flow chart of the radar automatic target identification method based on the multi-view variable convolutional neural network of the present invention;
fig. 2 is a geometric structure diagram of the multi-view radar ATR of the present embodiment;
FIG. 3 is a diagram illustrating a specific network structure according to the present embodiment;
FIG. 4 is a schematic diagram of the variable convolution feature extraction according to the present embodiment;
FIG. 5 is a schematic diagram illustrating a flow of variable convolution calculation according to the present embodiment;
fig. 6 is a radar target recognition result of the present embodiment;
fig. 7 shows the radar target recognition results of the present embodiment under different sample sizes.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
As shown in fig. 1, the method for automatically identifying a target of a radar based on a multi-view variable convolutional neural network of the present invention includes the following steps:
A. acquiring an original radar image: acquiring target images with the same resolution and radar target azimuth angles corresponding to the images, wherein the azimuth angles are distributed in the range of 0-360 degrees;
B. preprocessing the original radar image: rotating the original radar image to the same direction according to the azimuth angle of the radar target obtained in the step A; when the original radar image rotates, the mapping transformation among image pixel points meets the following requirements:
Figure BDA0003157778740000051
Figure BDA0003157778740000052
wherein the content of the first and second substances,
Figure BDA0003157778740000053
the angle of the counterclockwise rotation of the image is represented, x and y represent the abscissa and ordinate of the original image, respectively, and x 'and y' represent the abscissa and ordinate of the rotated image, respectively.
C. Multi-view data generation: sequencing the preprocessed radar images according to the sizes of the viewing angles, and generating a multi-viewing-angle combined sample according to the number of the viewing angles and the sizes of observation angles;
the sorting of the preprocessed radar images according to the size of the view angle specifically comprises the following steps: to be provided with
Figure BDA0003157778740000054
Set of radar images representing class i targets, where each image xjCorresponding to different viewing angles
Figure BDA0003157778740000055
The radar images of the same kind of targets are arranged in an ascending order according to the visual angle, and different radar images in the multi-visual angle combined sample are arranged according to the visual angleArranging the sizes in ascending order;
setting the number k of viewing angles and the size theta of an observation angle according to actual imaging conditions and performance indexes, wherein the number of viewing angles is set to be 3 and the size theta of the observation angle is set to be 45 degrees in the embodiment; generating a multi-view combined sample according to the number of the view angles and the size of the observation angle; the method specifically comprises the following steps: and combining radar images acquired under any k visual angles in the same target class to jointly form a sample { x }i1,xi2,…,xik}; and the change of the radar image visual angle in the same combined sample is limited not to exceed the size of the observation angle theta, namely
Figure BDA0003157778740000056
The geometry of the multi-view ATR is shown in fig. 2.
D. Constructing a deep neural network based on multi-view variable convolution: and C, building a deep neural network on the basis of the step C. Fig. 3 shows a network structure of the present embodiment, in which the (variable) convolutional layer representation method is "(convolutional kernel size) (variable) convolution, (eigen-map number)/(modified linear unit)", for example, 5 × 5 variable convolution, 8/ReLU; the pooling layer is expressed in terms of "(pooling window size) max pooling". The whole network comprises three input channels, each channel receives a radar image of a visual angle, and the whole network is divided into five hidden layers: the first two layers are alternating variable convolution layers and maximum pooling layers and are used for extracting morphological characteristics and scattering characteristics of the target under different viewing angles; the third layer is a convolution layer and a maximum pooling layer; the fourth layer is a convolution layer, and the merged characteristic graphs under different visual angles are further subjected to characteristic extraction and data compression; the fifth layer is a convolutional layer Softmax which is used as a classifier to obtain a classification label of the image sample; meanwhile, a random inactivation technology is adopted in the network, so that the generalization capability of the network is improved.
The variable convolution is based on the idea of adding extra offset to the spatial sampling positions in the module, so that the convolution kernel is offset at the sampling points of the input feature map, is focused on the interested region or target, and is changed in form by the shape of the convolution kernel. As shown in fig. 4, which is a schematic diagram of feature extraction by variable convolution in this embodiment, a convolution kernel adaptively adjusts the position of each sampling point according to the characteristics of a radar target in an input feature map, so as to extract an optimal feature of the target. In practice, this is achieved by rearranging the pixels in the input feature map. As shown in fig. 5, the rearranged pixels on the feature map may be generated by adding the original index value and the convolved index offset, and then obtaining the index value corresponding to the pixel value in the original image, as shown in formula (15):
xnew(m,n)＝x(m+om,n+on) (15)
wherein x (m, n) and xnew(m, n) respectively representing pixel points with m horizontal coordinates and n vertical coordinates on the original image and the rearranged image; omAnd onRespectively representing the offset of pixel points on the original image on the horizontal axis and the vertical axis, and obtaining specific numerical values of the input characteristic map by performing convolution on the input characteristic map, wherein the size of the convolution is unchanged once, and the number of output channels is twice of the number of input channels; and taking the value of the index out of the range as 0 or the maximum value of the range according to the condition, and acquiring the pixel value by a bilinear interpolation method under the condition that the index value is not an integer. Through the operations, the rearranged feature map is finally obtained, and the feature map is subjected to one-time common convolution to obtain an output feature map.
E. Training a deep neural network: initializing network weight and bias, inputting the multi-view radar image combination obtained by processing in the step C into the multi-view variable convolution neural network constructed in the step D for forward propagation, and calculating a cost function; updating parameters of the multi-view variable convolution neural network by using a backward propagation algorithm based on gradient descent; and (5) carrying out forward and backward propagation in an iteration mode until the cost function is converged.
Step E comprises the following substeps:
E1. initializing network weights wlThe distribution is shown as formula (16):
Figure BDA0003157778740000061
Figure BDA0003157778740000062
where l denotes the current number of convolutional layers, hl、wlRespectively representing the height and width of the convolution kernel in the convolution layer, dlRepresenting the number of current convolutional layer convolutional cores;
Figure BDA0003157778740000063
representing an expectation of 0 and a variance of
Figure BDA0003157778740000064
Normal distribution of (2); then, bias term blInitializing to a constant;
E2. after the network initialization is completed, forward propagation is performed to ft lShowing the t-th characteristic map of the first layer, if the first layer is a convolution layer
Figure BDA0003157778740000071
Wherein l is more than or equal to 2,
Figure BDA0003157778740000072
representing a convolution kernel connecting the s-th input feature map and the t-th output feature map,
Figure BDA0003157778740000073
representing a bias item corresponding to the tth output feature map of the ith layer; σ (·) represents a nonlinear activation function, and the symbol denotes a convolution operation;
if the l-th layer is a variable convolution layer, firstly acquiring a rearranged image of the l-1-th layer characteristic map:
Figure BDA0003157778740000074
Figure BDA0003157778740000075
wherein the content of the first and second substances,
Figure BDA0003157778740000076
representing the rearranged image of the characteristic map of the layer l-1, wherein m and n represent the mth row and the nth column on the characteristic map; (o)m,on) E is O, and O is an index bias set;
Figure BDA0003157778740000077
a convolution kernel and an offset term for variable convolution, c represents the number of input channels, sign
Figure BDA0003157778740000078
Convolution operation denoted as fill-in Same;
then, the acquired image is convolved once:
Figure BDA0003157778740000079
if the first layer is a pooling layer, then
Figure BDA00031577787400000710
Wherein r is1、r2Representing the size of the pooling window, sd representing the pooling step size;
after the sample reaches an output layer, the output is processed by a Softmax classifier, and the posterior probability of the current sample belonging to the ith class is obtained:
Figure BDA00031577787400000711
wherein the content of the first and second substances,
Figure BDA00031577787400000712
respectively representing the ith and the C th input of the layer, wherein C represents the total category number;
E3. calculating a cost function value: the cross entropy loss function is adopted as the cost function of the network, and the calculation formula is
Figure BDA00031577787400000713
Wherein, p (x)i) Representing the true probability that the target class is the ith class, w, b represent the set of weight and bias terms in the network, p (i | k)l(ii) a w, b) represents the posterior probability that the target class is the ith class given w and b;
E4. updating network parameters by adopting a backward propagation algorithm based on self-adaptive gradient, wherein the specific calculation formula is as follows:
Figure BDA0003157778740000081
wherein m istAnd vtFirst order momentum term and second order momentum term, mt-1、vt-1Respectively a first-order momentum term and a second-order momentum term of the previous moment; beta is a1、β2The power value is the value;
Figure BDA0003157778740000082
respectively are respective correction values; w is atWeight, g, representing the t-th iteration modelt＝ΔJ(wt) Representing the gradient magnitude of the t times of iteration cost function relative to w; η represents the learning rate; δ is a very small number used to avoid denominator of 0; the update strategy of the bias term b is the same as w.
Fig. 6 is a radar target recognition result of the embodiment after training is completed, in which the abscissa represents a predicted tag and the ordinate represents a real tag. Fig. 7 shows radar target recognition results under different training sample sizes, where the abscissa represents sample data size and the ordinate represents recognition rate. The result shows that the method can fully utilize the information characteristics of the radar target and can still maintain excellent identification performance under the condition of reducing the quantity of training samples.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.

Claims (4)

1. A radar automatic target identification method based on a multi-view variable convolutional neural network is characterized by comprising the following steps:
A. acquiring an original radar image: acquiring target images with the same resolution and radar target azimuth angles corresponding to the images;
B. preprocessing the original radar image: rotating the original radar image to the same direction according to the azimuth angle of the radar target obtained in the step A;
C. multi-view data generation: sequencing the preprocessed radar images according to the sizes of the viewing angles, and generating a multi-viewing-angle combined sample according to the number of the viewing angles and the sizes of observation angles;
D. constructing a deep neural network based on multi-view variable convolution: the whole network comprises three input channels, each channel receives a radar image of a visual angle, and the whole network is divided into five hidden layers: the first two layers are alternating variable convolution layers and maximum pooling layers and are used for extracting morphological characteristics and scattering characteristics of the target under different viewing angles; the third layer is a convolution layer and a maximum pooling layer; the fourth layer is a convolution layer, and the merged characteristic graphs under different visual angles are further subjected to characteristic extraction and data compression; the fifth layer is a convolutional layer Softmax which is used as a classifier to obtain a classification label of the image sample;
E. training a deep neural network: initializing network weight and bias, inputting the multi-view radar image combination obtained by processing in the step C into the multi-view variable convolution neural network constructed in the step D for forward propagation, and calculating a cost function; updating parameters of the multi-view variable convolution neural network by using a backward propagation algorithm based on gradient descent; and (5) carrying out forward and backward propagation in an iteration mode until the cost function is converged.
2. The method according to claim 1, wherein in step B, when the original radar image is rotated, the mapping transformation between image pixels satisfies:
Figure FDA0003157778730000011
Figure FDA0003157778730000012
wherein the content of the first and second substances,
Figure FDA0003157778730000013
the angle of the counterclockwise rotation of the image is represented, x and y represent the abscissa and ordinate of the original image, respectively, and x 'and y' represent the abscissa and ordinate of the rotated image, respectively.
3. The method for radar automatic target recognition based on the multi-view variable convolutional neural network according to claim 1, wherein in the step C, the sorting of the preprocessed radar images according to the view size specifically comprises: to be provided with
Figure FDA0003157778730000015
Set of radar images representing class i targets, where each image xjCorresponding to different viewing angles
Figure FDA0003157778730000014
The radar images of the same kind of targets are arranged in an ascending order according to the visual angle, and different radar images in the multi-visual angle combined sample are arranged in an ascending order according to the visual angle;
setting the number k of viewing angles and the size theta of an observation angle according to actual imaging conditions and performance indexes, and generating a multi-viewing-angle combined sample according to the number of viewing angles and the size theta of the observation angle; the method specifically comprises the following steps: and combining radar images acquired under any k visual angles in the same target class to jointly form a sample { x }i1,xi2,…,xik}; and the change of the radar image visual angle in the same combined sample is limited not to exceed the size of the observation angle theta, namely
Figure FDA0003157778730000021
4. The method for radar automatic target recognition based on the multi-view variable convolutional neural network of claim 1, wherein the step E comprises the following sub-steps:
E1. initializing network weights wlThe distribution is shown in formula (3):
Figure FDA0003157778730000022
Figure FDA0003157778730000023
where l denotes the current number of convolutional layers, hl、wlRespectively representing the height and width of the convolution kernel in the convolution layer, dlRepresenting the number of current convolutional layer convolutional cores;
Figure FDA0003157778730000024
representing an expectation of 0 and a variance of
Figure FDA0003157778730000025
Normal distribution of (2); then, bias term blInitializing to a constant;
E2. forward propagation is performed to
Figure FDA0003157778730000026
Showing the t-th characteristic map of the first layer, if the first layer is a convolution layer
Figure FDA0003157778730000027
Wherein l is more than or equal to 2,
Figure FDA0003157778730000028
representing a convolution kernel connecting the s-th input feature map and the t-th output feature map,
Figure FDA0003157778730000029
representing a bias item corresponding to the tth output feature map of the ith layer; σ (·) represents a nonlinear activation function, and the symbol denotes a convolution operation;
if the l-th layer is a variable convolution layer, firstly acquiring a rearranged image of the l-1-th layer characteristic map:
Figure FDA00031577787300000210
Figure FDA00031577787300000211
wherein the content of the first and second substances,
Figure FDA00031577787300000212
representing the rearranged image of the characteristic map of the layer l-1, wherein m and n represent the mth row and the nth column on the characteristic map; (o)m,on) E is O, and O is an index bias set;
Figure FDA00031577787300000213
a convolution kernel and an offset term for variable convolution, c represents the number of input channels, sign
Figure FDA00031577787300000214
Convolution operation denoted as fill-in Same;
then, the acquired image is convolved once:
Figure FDA0003157778730000031
if the first layer is a pooling layer, then
Figure FDA0003157778730000032
Wherein r is1、r2Representing the size of the pooling window, sd representing the pooling step size;
after the sample reaches an output layer, the output is processed by a Softmax classifier, and the posterior probability of the current sample belonging to the ith class is obtained:
Figure FDA0003157778730000033
wherein the content of the first and second substances,
Figure FDA0003157778730000034
respectively representing the ith and the C th input of the layer, wherein C represents the total category number;
E3. calculating a cost function value: the cross entropy loss function is adopted as the cost function of the network, and the calculation formula is
Figure FDA0003157778730000035
Wherein, p (x)i) Representing the true probability that the target class is the ith class, w, b represent the set of weight and bias terms in the network, p (i | k)l(ii) a w, b) represents the posterior probability that the target class is the ith class given w and b;
E4. updating network parameters by adopting a backward propagation algorithm based on self-adaptive gradient, wherein the specific calculation formula is as follows:
Figure FDA0003157778730000036
wherein m istAnd vtFirst order momentum term and second order momentum term, mt-1、vt-1Respectively a first-order momentum term and a second-order momentum term of the previous moment; beta is a1、β2The power value is the value;
Figure FDA0003157778730000037
respectively are respective correction values; w is atWeight, g, representing the t-th iteration modelt＝ΔJ(wt) Representing the gradient magnitude of the t times of iteration cost function relative to w; η represents the learning rate; δ is a very small number used to avoid denominator of 0; the update strategy of the bias term b is the same as w.
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