CN101334893A - Fused image quality integrated evaluating method based on fuzzy neural network - Google Patents

Fused image quality integrated evaluating method based on fuzzy neural network Download PDF

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CN101334893A
CN101334893A CNA2008100540305A CN200810054030A CN101334893A CN 101334893 A CN101334893 A CN 101334893A CN A2008100540305 A CNA2008100540305 A CN A2008100540305A CN 200810054030 A CN200810054030 A CN 200810054030A CN 101334893 A CN101334893 A CN 101334893A
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CN101334893B (en
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宋乐
林玉池
赵美蓉
齐永岳
黄银国
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Tianjin University
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Abstract

The invention pertains to the field of the image fusion technology in image process, which relates to a quality comprehensive evaluation method of fusion images based on fuzzy neural network and comprises the following steps: a sample set of fusion images is established, and each group of samples comprises a subjective evaluation grade sample of fusion images and two or more than two objective evaluating indicator samples obtained by evaluating the fusion image objectively; a quality evaluation module of fusion images based on fuzzy neural network is established; the obtained samples are trained, and the subjective evaluation grade sample of fusion images is adopted as expected output, and the correlation parameters for evaluating indicator weighing and fuzzy membership function are generated through network learning; the objective evaluating indicator of fusion images to be evaluated is calculated, and the evaluation grade result is generated by taking advantage of the established fusion image quality evaluation module. The method of the invention has comparatively good flexibility, and in the way of network training, novel fusion image quality evaluating indicator is learnt, so as to expand network evaluation ability and realize completely automatic evaluation.

Description

Fused image quality integrated evaluating method based on fuzzy neural network
Technical field
The present invention relates to the image fusion technology field in the Flame Image Process, relate to a kind of fused image quality evaluation method.
Background technology
As emerging branches of learning and subjects, image fusion technology has obtained using extremely widely in all many-sides such as military affairs, medical science, remote sensing with its outstanding detection superiority, and Image Fusion has also entered the comparatively ripe stage.Yet, compare with the degree of ripeness of blending algorithm itself, the evaluation of fused image quality is remained in significant limitation.
At present, the evaluation to fused images comprises subjective assessment and objective evaluation.The former relies on observer's subjective sensation, but the conclusion of estimating can be different and different with the requirement of observer's interest and application and occasion; The latter often judges according to some computable index, do not need artificial participation, but the index kind is numerous, as entropy, cross entropy, mutual information, average gradient, spatial frequency etc., every kind of index can only reflect image co-registration characteristic in a certain respect, is difficult to accomplish comprehensive evaluation.Therefore, seek a kind of human eye subjective assessment conclusion that both comprised, the fused image quality integrated evaluating standard that can embody the objective evaluation quantitative characteristic again is very necessary.
Summary of the invention
The objective of the invention is to overcome the above-mentioned deficiency of prior art, set up a kind of fused image quality integrated evaluating method.Specifically, exactly the subjective conclusion of multiple image co-registration objective evaluation index and human eye is combined, the quality of image co-registration gained image is made comprehensive evaluation comprehensively and accurately.
The present invention is achieved through the following technical solutions:
A kind of fused image quality integrated evaluating method based on fuzzy neural network comprises the following steps:
The first step: set up fused images and estimate sample set, every group of sample comprises the subjective assessment grade sample of a width of cloth fused images and two or more the objective evaluation index sample that this width of cloth fused images is carried out that objective evaluation obtained;
Second step: set up fused image quality evaluation model based on fuzzy neural network, this model is divided into input layer successively, the condition layer, rules layer and output layer, with to the objective evaluation index of fused images input layer as network, relation between each objective evaluation index and the image syncretizing effect is carried out Fuzzy processing by fuzzy membership function, with the output of degree of membership as the condition layer, with the evaluation index weight as the be connected weights of condition layer with rules layer, with the output of evaluation vector as rules layer, in output layer, from evaluation vector, ask for the pairing grade of degree of membership maximal value, obtain the overall quality opinion rating of fused images;
The 3rd step: training sample, the subjective assessment grade sample of estimating sample set with fused images generates the correlation parameter of evaluation index weight, fuzzy membership function as desired output by e-learning;
The 4th step: calculate the objective evaluation index of fused images to be evaluated, utilize the fused image quality evaluation model of having set up, generate the opinion rating result.
Above-mentioned evaluation method, the objective evaluation index that adopts in the first step preferably includes two classes, and a class is the index of reflection fused images sharpness, and another kind of is the index of reflection fused images quantity of information; Described objective evaluation index can comprise five kinds of entropy, cross entropy, standard deviation, spatial frequency and bias exponents.
Can adopt Gauss's membership function as fuzzy membership function in second step, sample set is carried out cluster with the K-means method, the corresponding rule of each group after the cluster, initialization fuzzy rule.
Preferably adopt following formula training sample in the 3rd step, and the error of calculation, when error during more than or equal to setting threshold, adjust parameter and continue e-learning, until error less than setting threshold, thereby determine the Center Parameter c of Gauss's membership function, the index weights W that the width cs and the second layer to the are three layers: c ij ( n + 1 ) = c ij ( n ) - η ∂ E p ( n ) ∂ c ij ( n ) + αΔc , σ ij ( n + 1 ) = σ ij ( n ) - η ∂ E p ( n ) ∂ σ ij ( n ) + αΔσ , W ij ( n + 1 ) = W ij ( n ) - η ∂ E p ( n ) ∂ W ij ( n ) + αΔW , In the formula: η is a learning rate; α is a factor of momentum; Δ c=c i(n)-c i(n-1); Δ σ=σ i(n)-σ i(n-1); N is a frequency of training; S SE(n) be the n time error sum of squares, S SE = Σ i = 1 k ( y i - y i , ) 2 ; I=1,2 ..., k; y iOutput valve for learning sample; y i' be y behind the network training iReal output value; K is the learning sample number.
Through the substantive test image is experimentized, the result shows the fused image quality integrated evaluating method based on fuzzy neural network foundation that the present invention proposes, with respect to existing evaluation method, can reflect more comprehensively feature of fused images, overcome merely by the subjectivity of human eye judgement generation and the one-sidedness of single factor objective evaluation index, evaluation result is objective rationally, and main, objective evaluation conclusion has consistance preferably.In addition, this method has better flexibility, can learn the evaluating ability of extended network to novel fused image quality evaluation index by the mode of network training.The most important, this method has realized robotization evaluation completely, evaluation procedure need not artificial participation, has laid solid theory for realizing the closed loop adapting to image fusion with feedback characteristic.
Description of drawings
Fig. 1 is the structural drawing of fuzzy neural network model among the present invention.
Embodiment
Below in conjunction with embodiment and description of drawings the present invention is further described.
The present invention at first studies the subjective evaluation method of fused image quality, with the people as the observer, the quality of a large amount of fused images is made subjective qualitative evaluation, set up image subjective assessment sample set by statistical experiment, and be divided into " excellent, good, in, general, poor " totally five grades by evaluation criterion.Then, the method for objectively evaluating of research fused image quality is summarized to the objective evaluation index, sort out, the relative merits of comparative analysis the whole bag of tricks are chosen representative evaluation index, the index that comprises reflection fused images sharpness, and the index of reflection fused images quantity of information etc.Above-mentioned fused images through subjective assessment is carried out objective evaluation calculate, write down the actual result of every kind of evaluating.
On the basis of above research, set up fused image quality evaluation model based on fuzzy neural network.This model is imported multiple typical image co-registration objective evaluation index as network, carry out Fuzzy processing by fuzzy membership function, export as target with the subjective assessment sample set, automatically generate correlation parameters such as evaluation index weight by e-learning, and choose suitable factor of momentum network learning procedure is optimized.This model has made full use of the structural knowledge representation ability of fuzzy logic inference and the self-learning capability of neural network, and is final, makes this network model possess the ability of fused image quality being carried out thoroughly evaluating.
Generally speaking, what the observer was concerned about most mainly is the quantity of information and the sharpness of fused images, but reflects that the evaluation index quantity of this two aspects feature is more.In order to realize the comprehensive evaluation to fused images, spy of the present invention has chosen five kinds of representative evaluatings therein, is respectively entropy, cross entropy, standard deviation, spatial frequency and bias exponent.
(1) entropy
Entropy is to weigh the important indicator that image information is enriched degree.For the independent image of a width of cloth, can think that the gray-scale value of its each element is separate sample, then this width of cloth gray distribution of image is P={P 1, P 2..., P i..., P L-1, promptly gray-scale value is the pixel count N of i iWith the ratio of image total pixel number N, P i=N i/ N, L are the total number of greyscale levels of image.Entropy can be defined by following formula:
E = - Σ i = 0 L - 1 P i · log 2 ( P i ) - - - ( 1 )
(2) cross entropy
Cross entropy has reflected the information gap between the distribution of two width of cloth gradation of images, and its formula is:
CE = Σ i = 0 L - 1 p i log 2 p i q i - - - ( 2 )
In the formula: p iAnd q iBe respectively pixel count that original image and fused images gray-scale value equal i with the ratio of the total pixel count of image.
If CE 1And CE 2Be respectively the cross entropy of two width of cloth original images and fused images, then the overall cross entropy of fused images and two width of cloth original images is:
CE t = [ ( CE 1 ) 2 + ( CE 2 ) 2 ] / 2 - - - ( 3 )
(3) standard deviation
Standard deviation is tried to achieve indirectly by average, has reflected the dispersion degree of gradation of image value with respect to the gradation of image average, i.e. the distribution situation of image pixel value.The standard deviation of fused images is defined as:
SD = 1 M × N Σ i = 0 M - 1 Σ j = 0 N - 1 ( I ( i , j ) - I ‾ ) 2 - - - ( 4 )
(4) spatial frequency
Spatial frequency has reflected the overall active degree of piece image spatial domain.
The spatial row frequency of image is:
RF = 1 M × N Σ i = 0 M - 1 Σ j = 1 N - 1 [ F ( i , j ) - F ( i , j - 1 ) ] 2 - - - ( 5 )
Space row frequency is:
CF = 1 M × N Σ i = 1 M - 1 Σ j = 0 N - 1 [ F ( i , j ) - F ( i - 1 , j ) ] 2 - - - ( 6 )
Then the spatial frequency of image is:
SF = RF 2 + CF 2 - - - ( 7 )
The difference of the spatial frequency of ideal image and fused images has just reflected the effect that merges.
(5) bias exponent
Bias exponent is each grey scale pixel value of fused images and the mean value of source images respective pixel gray value differences absolute value with the ratio of source images respective pixel gray scale, is also referred to as relative deviation sometimes, and its expression formula is:
D = 1 M × N Σ i = 1 M Σ j = 1 N | F ( i , j ) - A ( i , j ) | A ( i , j ) - - - ( 8 )
The size of bias exponent is represented the relative different of fused images and source images average gray value, under the ideal situation, and D=0.
By above analysis as can be known, preceding two kinds of parameters stress information content of image, and the back stresses sharpness for two kinds, and bias exponent then more can reflect the variation before and after merging.Above five kinds of parameters are constituted evaluation indice X, be described as X={x 1, x 2, x 3, x 4, x 5.Adopt following fuzzy language to describe to the relation between each single factor index value and the image syncretizing effect among the evaluation indice X:
(1) entropy.The image entropy is big more, and the quantity of information that comprises in the key diagram picture is many more, and syncretizing effect is good more;
(2) cross entropy.The image cross entropy is more little, illustrates that fused images and source images difference are more little, and syncretizing effect is good more;
(3) standard deviation.The standard deviation of image is big more, and the grey level distribution of key diagram picture is overstepping the bounds of propriety looses, and the contrast of image is also just big more, and the visual degree of information is just good more.
(4) spatial frequency.Spatial frequency values is big more, and the texture definition of key diagram picture is high more, and the effect of image is good more.
(5) bias exponent.The bias exponent of image is more little, illustrates that fused images and source images are approaching more, and the image after promptly merging has kept the spectral information of original image preferably when improving spatial resolution.
Need to prove why select of the input of these five kinds of parameters as the FNN model, mainly be for discuss convenient for the purpose of, be not limited only to this five types.The observer can adjust the input pointer collection according to actual needs flexibly, obtains new network parameter through training again, the usability of expansion appraisement system.This dirigibility and extensibility, the big advantage that nerual network technique had just.
According to Fuzzy Set Theory, the element x among the fuzzy set A belongs to the degree degree of membership μ of A AExpression, μ here A∈ [0,1], then fuzzy set A can be expressed as:
A={μ A(x 1)+μ A(x 2)+...+μ A(x i)}={∑μ A(x i)} (9)
In the formula, x iBe among the fuzzy set A element (i=1,2 ... n);
μ A(x i) be x iCorresponding degree of membership value;
∑ compiles for each element.
Fused image quality essential elements of evaluation fuzzy set is represented with Q.For the result that fused image quality is estimated, excellent, good with fuzzy set P{ here, in, generally, poor represent.The domain of Q represents with X, and the domain of P represents with Y, and the fuzzy relation R of Q and P can represent with fuzzy cartesian product, that is:
R=Q×P (10)
μ R(x, y) fuzzy membership of having described between fused image quality essential elements of evaluation Q and the evaluation result P concerns.Here select Gaussian function ambiguity in definition degree of membership for use, its correlation parameter need not given in advance, can obtain by the mode of neural metwork training, and dirigibility is strong.Gauss's membership function is defined as follows:
Gaussian { x ; c , σ } = exp [ - ( x - c ) 2 σ 2 ] - - - ( 11 )
Gauss's membership function determines that by c and σ c represents the center of membership function, the width of σ decision membership function.Each quality evaluation index is owing to different application, and its shared weight is also inequality, establishes weight vectors and is expressed as: W=(ω 1, ω 2, ω 3, ω 4, ω 5).ω kBe the weight of evaluation index k, and ω 1+ ω 2+ ω 3+ ω 4+ ω 5=1, ω k∈ [0,1].Then obtain evaluation vector e by compound operation, then the pairing grade of degree of membership maximal value is the fused image quality opinion rating among the e.The parameter of membership function and weight vectors can be artificially given by expert group, have very big subjectivity, and accuracy is low; Use the learning ability of neural network, network is trained and definite degree of membership and weight vectors, have more science, objectivity.
Generally, fuzzy neural network has input layer, condition layer, rules layer and output layer.As not adopting equivalent process directly to be designed to every layer all is full connection, network complexity, huge then, cause model training consuming time, be not easy convergence.The FNN structure of the present invention's design as shown in Figure 1.This is a kind of follow-on fuzzy neural network, and as seen from the figure, it has calculates advantages such as simple, that each network layer derivation physical significance is obvious, can finish the operations such as obfuscation, fuzzy operation and output of input.
Ground floor: input layer, X T={ x 1, x 2, x 3, x 4, x 5Be the information input of network, at this x iBe each objective evaluation desired value, i.e. X of fused images T=[entropy, cross entropy, standard deviation, spatial frequency, bias exponent].For every different evaluation index is integrated, need carry out normalized to each evaluation index.Here, adopt the range transformation formula with all kinds of index normalization, as the formula (12):
h i ( x i ) = x i - x i min x i max - x i min - - - ( 12 )
In the formula: h i(x i) ∈ [0,1], represent original value x iNormalized value.x Imax, x IminRepresent for n group fused images x in its corresponding n group evaluating data respectively iMaximal value and minimum value.
The second layer: condition layer, each node are represented a fuzzy language variable, this be excellent, good, in, general and poor, 25 neurons of needs altogether.The output of this layer is degree of membership, and expression input belongs to the degree of this linguistic variable, and the ground floor neuron has been determined the parameter of obfuscation, c and σ parameter in promptly definite Gauss's membership function to the neuronic connection weights of the second layer.
The 3rd layer: rules layer, at this with 5 neurons, represent respectively excellent, good, in, general and poor, input is weighted and computing, obtain evaluation vector e.The neuronic connection weights that the neuron to the of the second layer is three layers are exactly the weights W of estimating.If the second layer outputs to the i that is input as of this layer k(k=1 ..., 5), this layer output Q z(z=1 .., 5), then
O z=i k·W kz (13)
In the formula: W KzExpression k is to the connection weight of z.
The 4th layer: output layer, in evaluation vector e, ask for the pairing grade of degree of membership maximal value, obtain the overall quality opinion rating of fused images.
It more than is exactly the structure of this fuzzy neural network model.This Model parameter all is unknown, will adopt improved back propagation learning algorithm that sample data is calculated below, obtains model parameter, just can be applied to actual image fusion estimation system.
Network training need be determined two class parameters, and a class is the Center Parameter c of Gauss's membership function, width cs; Another kind of is the index weights W of three layers of the second layers to the.Be provided with m group input and output sample (x p, d p), p=1,2 ..., m.
(1) Center Parameter c's determines.Center Parameter c determines with the K-means clustering algorithm.The flow process of this algorithm can be described as following five steps:
A. import cluster number k and the database that comprises m data object.This moment k=5, m=5;
B. select k object as initial cluster center arbitrarily from m data object;
C. for other object of be left, then, respectively they are distributed to (the cluster centre representative) cluster the most similar to it according to the similarity (distance) of they and these cluster centres;
D. recomputate the average (Center Parameter) of each cluster that changes, according to the average (Center Parameter) of each new cluster object, calculate the distance of each object and these new cluster centre objects, and again corresponding object is divided according to minor increment;
E. circulated for the 4th step till each cluster no longer changes, promptly the variance evaluation function begins till the convergence.K cluster of variance minimum sandards satisfied in output, and the average of each cluster (Center Parameter).
(2) width cs determines.Width is on average determined by difference, promptly takes out the total data that output is z (for example output is " excellent ") from m group sample data, is provided with m group data, then
σ = 1 m Σ | x i - c | , i = 1,2 , . . . , m - - - ( 14 )
(3) the index weights W determines.The index weight is determined by total number percent.Take out the total data that output is z (for example output is " excellent ") from m group sample data, be provided with m group data, it is μ that the degree of membership of second layer output is done input Zik, i=1,2 ..., 5, k=1,2 ..., m, then
zi=∑(μ zik)/∑(μ zjk) j=1,2,...,5 (15)
As I among Fig. 1 11To R 1Connection weight be:
W 11=∑(μ 11k)/∑(μ 1jk) k=1,2,...,m,j=1,2,...,5 (16)
The learning algorithm of this fuzzy neural network is based on the BP algorithm, and promptly the back propagation learning method proposes.Traditional BP convergence of algorithm speed is absorbed in local minimum slowly, easily, has adopted improved BP algorithm to carry out parameter adjustment and optimization here, has overcome above-mentioned shortcoming to a certain extent.
Suppose that the squared error function of describing fuzzy neural network is:
E p = 1 2 ( y - D ) 2 - - - ( 17 )
In the formula, y is actual output; D is a desired output.
In learning process to x Ij, σ IjAnd W IjAdjustment amount can be expressed as follows:
c ij ( n + 1 ) = c ij ( n ) - η ∂ E p ( n ) ∂ c ij ( n ) , σ ij ( n + 1 ) = σ ij ( n ) - η ∂ E p ( n ) ∂ σ ij ( n ) ,
W ij ( n + 1 ) = W ij ( n ) - η ∂ E p ( n ) ∂ W ij ( n ) - - - ( 18 )
In the formula, η is a learning rate.
In learning process, traditional BP algorithm is along with error amount is more and more littler, and the amplitude that causes gradient decline to be adjusted is also more and more littler, thereby the network learning and training time is increased, and speed of convergence is slack-off; In addition, network might sink into local minimum.For fear of above situation, in formula (19), add factor of momentum α, then adjustment amount can be expressed as:
c ij ( n + 1 ) = c ij ( n ) - η ∂ E p ( n ) ∂ c ij ( n ) + αΔc , σ ij ( n + 1 ) = σ ij ( n ) - η ∂ E p ( n ) ∂ σ ij ( n ) + αΔσ ,
W ij ( n + 1 ) = W ij ( n ) - η ∂ E p ( n ) ∂ W ij ( n ) + αΔW - - - ( 19 )
In the formula: Δ c=c i(n)-c i(n-1); Δ σ=σ i(n)-σ i(n-1); Δ W=W i(n)-W i(n-1).
Incorporating of factor of momentum α makes the acceleration weights descend to the direction that reduces, and simultaneously network had stabilization.In addition, in the network training process, single, changeless learning rate is difficult to take into account simultaneously the convergence situation in the different error spans, and particularly near minimal point, single learning rate can make speed of convergence slow down.Therefore, adopted adaptive learning speed, to overcome the defective of single learning rate, its adjustment formula is:
Figure A20081005403000101
In the formula, n is a frequency of training; S SE(n) be the n time error sum of squares, S SE = Σ i = 1 k ( y i - y i , ) 2 ; I=1,2 ..., k; y iOutput valve for learning sample; y iBe y behind the network training iReal output value; K is the learning sample number.
The criterion of adjusting learning rate is to check this study error whether less than learning error last time, if, illustrating that then this iteration is effective, current learning rate relatively is fit to the error variation tendency, can suitably strengthen learning rate; Otherwise illustrate that adjustment is excessive, should reduce learning rate this moment.
According to above-mentioned algorithm, the calculation procedure of system is as follows:
(1) part of choosing sample is as training objects, and remainder is used for the evaluating network system performance;
(2) sample of choosing is carried out cluster with the K-means method, the corresponding rule of each group after the cluster is divided into the R group as cluster, and R bar fuzzy rule is then arranged;
(3) the initialization fuzzy rule is determined c Ij, σ IjAnd W IjAnd learning rate η and factor of momentum α;
(4) training sample and error of calculation E p, when error during, then stop next step less than some limit values, adjust parameter and also repeat above step.
In sum, utilize fuzzy neural network, can replace loaded down with trivial details, a large amount of artificial statistics scorings, and can judge the quality of image syncretizing effect accurately, overcome the limitation that the single factor evaluation index is brought, help the realization of full-automatic adapting to image emerging system, have very important using value.

Claims (5)

1. the fused image quality integrated evaluating method based on fuzzy neural network comprises the following steps:
The first step: set up fused images and estimate sample set, every group of sample comprises the subjective assessment grade sample of a width of cloth fused images and two or more the objective evaluation index sample that this width of cloth fused images is carried out that objective evaluation obtained;
Second step: set up fused image quality evaluation model based on fuzzy neural network, this model is divided into input layer successively, the condition layer, rules layer and output layer, with to the objective evaluation index of fused images input layer as network, relation between each objective evaluation index and the image syncretizing effect is carried out Fuzzy processing by fuzzy membership function, with the output of degree of membership as the condition layer, with the evaluation index weight as the be connected weights of condition layer with rules layer, with the output of evaluation vector as rules layer, in output layer, from evaluation vector, ask for the pairing grade of degree of membership maximal value, obtain the overall quality opinion rating of fused images;
The 3rd step: training sample, the subjective assessment grade sample of estimating sample set with fused images generates the correlation parameter of evaluation index weight, fuzzy membership function as desired output by e-learning;
The 4th step: calculate the objective evaluation index of fused images to be evaluated, utilize the fused image quality evaluation model of having set up, generate the opinion rating result.
2. fused image quality integrated evaluating method according to claim 1 is characterized in that, the objective evaluation index that adopts in the first step comprises two classes, and a class is the index of reflection fused images sharpness, and another kind of is the index of reflection fused images quantity of information.
3. fused image quality integrated evaluating method according to claim 2 is characterized in that, described objective evaluation index comprises five kinds of entropy, cross entropy, standard deviation, spatial frequency and bias exponents.
4. fused image quality integrated evaluating method according to claim 1, it is characterized in that, adopt Gauss's membership function as fuzzy membership function in second step, sample set is carried out cluster with the K-means method, corresponding rule of each group after the cluster, the initialization fuzzy rule.
5. fused image quality integrated evaluating method according to claim 4, it is characterized in that, adopt following formula training sample in the 3rd step, and the error of calculation, when error during more than or equal to setting threshold, adjust parameter and continue e-learning, until error less than setting threshold, thereby determine the Center Parameter c of Gauss's membership function, the index weights W that the width cs and the second layer to the are three layers: c ij ( n + 1 ) = c ij ( n ) - η ∂ E p ( n ) ∂ c ij ( n ) + αΔc , σ ij ( n + 1 ) = σ ij ( n ) - η ∂ E p ( n ) ∂ σ ij ( n ) + αΔσ , W ij ( n + 1 ) = W ij ( n ) - η ∂ E p ( n ) ∂ W ij ( n ) + αΔW , In the formula: η is a learning rate; α is a factor of momentum; Δ c=c i(n)-c i(n-1); Δ σ=σ i(n)-σ i(n-1); Δ W=W i(n)-W i(n-1);
Figure A2008100540300002C4
N is a frequency of training; S SE(n) be the n time error sum of squares, S SE = Σ i = 1 k ( y i - y i , ) 2 ; I=1,2 ..., k; y iOutput valve for learning sample; y i' be y behind the network training iReal output value; K is the learning sample number.
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