CN109145838A - Clear cell carcinoma of kidney diagnostic method based on random Gaussian field neural network aiding - Google Patents

Clear cell carcinoma of kidney diagnostic method based on random Gaussian field neural network aiding Download PDF

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CN109145838A
CN109145838A CN201810992268.6A CN201810992268A CN109145838A CN 109145838 A CN109145838 A CN 109145838A CN 201810992268 A CN201810992268 A CN 201810992268A CN 109145838 A CN109145838 A CN 109145838A
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CN109145838B (en
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白禹
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Changzhou Second Peoples Hospital
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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06VIMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
    • G06V20/00Scenes; Scene-specific elements
    • G06V20/60Type of objects
    • G06V20/69Microscopic objects, e.g. biological cells or cellular parts
    • G06V20/695Preprocessing, e.g. image segmentation
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06VIMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
    • G06V10/00Arrangements for image or video recognition or understanding
    • G06V10/20Image preprocessing
    • G06V10/25Determination of region of interest [ROI] or a volume of interest [VOI]
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06VIMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
    • G06V20/00Scenes; Scene-specific elements
    • G06V20/60Type of objects
    • G06V20/69Microscopic objects, e.g. biological cells or cellular parts
    • G06V20/698Matching; Classification

Abstract

The invention discloses a kind of clear cell carcinoma of kidney diagnostic methods based on random Gaussian field neural network aiding, in the training stage, construct the self study complex network structures model of data-driven, pathology block the outputting and inputting as network that original medical image and corresponding band are marked, the study for having supervision is carried out to network;In the judgement stage, unknown input original medical image is given, calculates site morbidity probabilistic geometry mean value to be tested, and provide confidence interval, so that doctor be assisted to determine canceration grade and physiology lesion position.After the present invention is by constructing a kind of random Gaussian field neural network model of data-driven and carrying out the study for having supervision to network model, unknown medical image can effectively be screened, auxiliary doctor positions diseased region, to help doctor preferably to judge the transparent cancer cell diseased region of kidney and lesion grade, alleviate doctor's pressure, accuracy rate is made a definite diagnosis in raising.

Description

Clear cell carcinoma of kidney diagnostic method based on random Gaussian field neural network aiding
Technical field
The present invention relates to medical field of auxiliary, saturating more particularly to a kind of kidney based on random Gaussian field neural network aiding Clear cell carcinoma diagnostic method.
Background technique
Carcinoma of renal parenchyma is derived from the gland cancer of renal cells, and 85% is clear cell carcinoma, some is Granulocyte carcinoma and cell mixing cancer.Often there are bleeding, necrosis, capsule change and calcification in cancer.It is born in kidney essence, infiltrates, presses after growing up Compel, destroy renal plevis kidney calices, develop to outside kidney peplos, form hemangioma bolt or is transferred to lymph node and other organs.Pathologically, Kidney is divided into 4 types: clear cell type kidney, granular cell type kidney, mixed cell type kidney, neoblast type kidney.Its In, the overwhelming majority is clear cell carcinoma of kidney, accounts for the 70%~80% of kidney, cancer cell often arranges slabbing, streak, acinus Shape or tubulose, like renal tubule.Though clear cell carcinoma is that grade malignancy is minimum in kidney, in clinical practice often It is mixed, is classified under microscope in fact extremely difficult with granular cell carcinoma and three type of Fusoid cells cancer.Therefore it is badly in need of one kind to melt The method for closing current artificial intelligence forward position algorithm carries out Classification and Identification to medicine contrastographic picture, and doctor is assisted to diagnose.
In artificial intelligence field of signal processing, artificial neural network is since it is with Nonlinear Modeling and self-adapting data Ability, to be widely used in data classification and parameter mapping aspect.Adaptive base letter inside artificial neural network dependence Link attribute between number, thus the strong correlation between study and characterize data, the classification and recurrence characteristic of response data.It is another Aspect, the probability stochastic model based on Bayesian frame, such as random Gaussian field, provide the processing with neural network differentiated Data means: random Gaussian field energy randomization prediction result not only provides point estimate, moreover it is possible to analyze forecast confidence area Between, this is helpful for realistic problem.The present invention utilizes the two advantage, constructs a kind of completely new system frame Frame, and doctor is assisted using this New Mathematical Model to carry out the diagnosis of medical imaging.
For needing to carry out the patient of clear cell carcinoma of kidney resection operation after diagnosing, in the prior art, it is generally required that will The entire kidney of its lesion is cut off, although theory is directly simple, the cost paid for the patient is also huge.And In the laparoscopic renal tumor resection case of current mainstream, need doctor it is subjective to canceration physiological tissue Reginal-block scanning figure As carrying out two-dimentional identification, to make artificial judgment.This process usually needs to rely on a large amount of clinical experiences and knowledge of doctor Accumulation can just accomplish effective pre-estimation.Therefore i.e. time-consuming and laborious, the uncertain ideal of effect.For this purpose, the present invention attempts to lead to It crosses and designs a kind of artificial intelligence auxiliary mechanism, for improving doctor to the accurate positioning of diseased region and the assessment of lesion grade, So as to targetedly cut off, rather than entire kidney excision.
Summary of the invention
In view of the deficiencies of the prior art, it is transparent thin to provide a kind of kidney based on random Gaussian field neural network aiding by the present invention Born of the same parents' cancer diagnostic method by constructing a kind of artificial intelligence random Gaussian field neural network model of data-driven, and provides a large amount of Original medical image and identification result are output and input as system, are implemented intelligent supervised learning, are completed it in learning training Afterwards, unknown medical image can effectively be screened, auxiliary doctor positions diseased region, to help doctor better Judge the transparent cancer cell diseased region of kidney and lesion grade, alleviates doctor's pressure, while improving and making a definite diagnosis accuracy rate.
To achieve the above object, the technical solution adopted by the present invention are as follows:
A kind of clear cell carcinoma of kidney diagnostic method based on random Gaussian field neural network aiding, in the training stage, construction The self study complex network structures model of data-driven, the pathology block that original medical image and corresponding band are marked is as net Network is output and input, and the study for having supervision is carried out to network;In the judgement stage, unknown input original medical image is given, Site morbidity probabilistic geometry mean value to be tested is calculated, and provides confidence interval, so that doctor be assisted to determine canceration grade and life Manage lesion position.
Preferably, specifically includes the following steps:
Image preprocessing: original medical image is converted to the gray level image of gray value expression by S01;
The building and training of neural network model: S02 passes through random Gaussian field for the gray value of gray level image as input Intermediate parameters are mapped as, and link to output layer by connecting non-directed graph mode entirely, output layer is set as the knowledge by manually marking Not as a result, to form the random Gaussian field neural network model with Nonlinear Classification function, the neural network model structure After the completion of building, using a large amount of original medical images and the corresponding identification result with pathology block mark as the neural network Model is output and input, and the study for having supervision is carried out to the neural network model;
S03 is identified using the neural network model: by the medical image at position to be tested through image preprocessing Afterwards, the neural network model is inputted, prediction judges classification mode, and each classification results have certain probability, and obtain simultaneously The confidence interval of predictive estimation is obtained, doctor assists examining by lateral comparison classification results probability size and confidence interval It is disconnected.
Further, the original medical image is the medical scanning image of medicine clear cell carcinoma of kidney.
Preferably, S01 further include steps of using algorithm for image enhancement to original image carry out it is following a kind of or A variety of operations: rotation, unified image size, highlights and contrast at alignment.
Preferably, S02 is further included steps of
(a1) setting x indicates that the vector that input image pixels data are constituted, y indicate output classification, construct following random Gaussian Field neural network model:
Y (x)=W (x) [f (x)+σf∈]+σyz (1)
Wherein,
∈=∈ (x) and z=z (x) is two white Gaussian noise process with different covariance parameters respectively, and ∈'s is general Rate is distributed as N (0, Iq), N (0, Iq) indicate that mean value is 0, covariance matrix IqIt is the Gaussian Profile of the unit matrix of Q × Q dimension, The probability distribution of z is N (0, Ip), N (0, Ip) indicate that mean value is 0, covariance matrix IpIt is the Gauss of the unit matrix of P × P dimension Distribution, σfAnd σyIt is energy coefficient to be estimated respectively,
W (x) is the matrix of a P × Q, wherein each element W (x)ijIt is all an independent random Gaussian field, i.e.,Wherein kwIt may be any type of positive semidefinite kernel function,
F (x)=f (f1(x),f2(x),…,fq(x)) be Q dimension vector, wherein any one element is all independent Random Gaussian field, i.e.,
(a2) training dataset is set to be combined intoUnknown model parameters u=(f, W), f and W are respectively indicated Bring data point intoF (x) and W (x) later has following prior probability distribution according to the definition of random Gaussian field:
p(u|σffw)=N (0, CB) (2)
Wherein θfwRespectively indicate the hyper parameter that the kernel function being related in f (x) and W (x) is included, CBIt is a NQ (P + 1) the block diagonal battle array of × NQ (P+1) dimension,
Likelihood score function can be obtained according to (1) formula simultaneously are as follows:
It can be obtained with Bayes' theorem:
Wherein, (4) formula is target formula to be estimated, and the estimation for obtaining (4) formula can obtain the estimation of y (x), is sentenced Other result;
(a3) (4) formula is optimized using variation Bayesian Method, to obtain optimal models structural parameters.Variation Bayes Essence be by a kind of iterative manner come so that probability distribution q () approaching to reality to be estimated Posterior probability distribution p () (i.e. formula 4), i.e., by minimizing distortion function Dist:
Wherein,H [] indicates entropy function, gives firstInverse gamma distribution (IG) is distributed, That is:
Secondly, design APPROXIMATE DISTRIBUTION q (v) is as follows:
WhereinIt is that inverse gamma is distributed, qfi,qwijIt is the Gaussian Profile of N-dimensional,
Optimal value is sought finally, being iterated to (7) formula, i.e., carries out segmented line in gradient direction using conjugate gradient decent Property search, searching make the maximized θ of (7) formulafw
Preferably, S03 is further included steps of
(b1) for a new unknown medical image, calling S01 step first carries out image preprocessing;
(b2) classification judgement is carried out using the trained network model of S02 step, first according to Bayesian formula, accurately Target prediction function should are as follows:
Secondly, the thought using variation Bayesian Method carries out approximation, if in above formula It is obtained even normal probability distribution can be multiplied by two approximation probability distributions, according to the Gaussian Profile conditional probability of standard and side The attribute of edge probability, integrates above formula, obtains the mean value mean (y of estimation judgement*) and variance cov (y*)ij, variance cov (y*)ijAs confidence interval, as follows:
In formula, k indicates to differentiate type, δijIt is kronecker delta function, on the basis of obtaining judgement mean value, It carries out that maximum one kind of across comparison select probability and is used as court verdict, meanwhile, determine that the judgement is tied according to variance function Fruit has great variation possible, to constitute complete judgment criteria.
Preferably, random Gaussian field parameters, neural network model parameter by variation Bayesian Method marginalisation maximum seemingly So estimate to obtain under degree criterion.
Compared with prior art, the beneficial effects of the present invention are 1) nerve of the present invention building based on random Gaussian field Network model, the pathology block that a large amount of original medical image and corresponding band are marked as the input of neural network model with Output, the study for having supervision is carried out to neural network model, then inputs the medical image at unknown new position to be tested Neural network model to building and by there is the learning training of supervision obtains site morbidity probability Estimation judgement to be tested Mean value and confidence interval, auxiliary doctor determine canceration grade and physiology lesion block, improve positioning of the doctor to diseased region And the accuracy of lesion grade assessment;2) method of the invention is used to carry out assisting in diagnosis and treatment to medical image, has merged artificial intelligence Energy algorithm, can help doctor preferably to judge the transparent cancer cell diseased region of kidney and lesion grade, thus alleviate doctor's pressure, It improves simultaneously and makes a definite diagnosis accuracy rate, promote working efficiency;3) neural network model of the invention is the nerve based on random Gaussian field Neural network model not only includes probability characteristics, but also includes the non-frequency characteristic of neural network, can be carried out to unknown image Nonlinear probability classification, and confidence interval analysis is provided as a result, substantially increasing the confidence level of complementary diagnosis.
Detailed description of the invention
Fig. 1 is the stream according to the clear cell carcinoma of kidney diagnostic method based on random Gaussian field neural network aiding of embodiment Cheng Tu;
Fig. 2 is the schematic diagram of random Gaussian field neural network model of the invention;
Fig. 3 is the schematic diagram according to the clear cell carcinoma of kidney diseased region of the invention of embodiment;
Fig. 4 is the schematic diagram according to the clear cell carcinoma of kidney diseased region of the invention of embodiment.
Specific embodiment
The invention will be further described with reference to the accompanying drawing and by specific embodiment, and following embodiment is descriptive , it is not restrictive, this does not limit the scope of protection of the present invention.
The present invention provides a kind of clear cell carcinoma of kidney diagnostic method based on random Gaussian field neural network aiding, in training Stage constructs the self study complex network structures model of data-driven, the pathology that original medical image and corresponding band are marked Block is output and input as network, and the study for having supervision is carried out to network;In the judgement stage, it is original to give unknown input Medical image calculates site morbidity probabilistic geometry mean value to be tested, and provides confidence interval, so that doctor be assisted to determine canceration Grade and physiology lesion position.As shown in the picture, specifically includes the following steps:
Image preprocessing: original medical image is converted to the gray level image of gray value expression, and utilized traditional by S01 Algorithm for image enhancement rotated, is aligned, unified image size, is highlighted and contrast etc. operates, wherein the original doctor The medical scanning image that image is medicine clear cell carcinoma of kidney is treated, the pathology block with mark includes being labeled with calculus and uronephrosis Pathology block, be labeled with the pathology block of tumour;
The building and training of neural network model: S02 passes through random Gaussian field for the gray value of gray level image as input Intermediate parameters are mapped as, and link to output layer by connecting non-directed graph mode entirely, output layer is set as the knowledge by manually marking Not as a result, to form the random Gaussian field neural network model with Nonlinear Classification function, the neural network model structure After the completion of building, using a large amount of original medical images and the corresponding identification result with pathology block mark as the neural network Model is output and input, and the study for having supervision is carried out to the neural network model;Wherein, random Gaussian field parameters, nerve Network model parameter is estimated to obtain by variation Bayesian Method under marginalisation maximum likelihood degree criterion;
S03 is identified using the neural network model: by the medical image at position to be tested through image preprocessing Afterwards, the neural network model is inputted, prediction judges classification mode, and each classification results have certain probability, and obtain simultaneously The confidence interval of predictive estimation is obtained, then judges that classification results, each classification results have by Neural Network model predictive There is certain probability, and system provides the confidence interval of prediction judging result, doctor can pass through lateral comparison classification results Probability size and possibility coverage area (confidence interval) carry out auxiliary diagnosis, so that it is determined that the canceration grade at position to be tested With physiology lesion block.
Specifically, as shown in Fig. 2, S02 is further included steps of
(a1) setting x indicates that the vector that input image pixels data are constituted, y indicate output classification, construct following random Gaussian Field neural network model:
Y (x)=W (x) [f (x)+σf∈]+σyz (1)
Wherein,
∈=∈ (x) and z=z (x) is two white Gaussian noise process with different covariance parameters respectively, and ∈'s is general Rate is distributed as N (0, Iq), N (0, Iq) indicate that mean value is 0, covariance matrix IqIt is the Gaussian Profile of the unit matrix of Q × Q dimension, The probability distribution of z is N (0, Ip), N (0, Ip) indicate that mean value is 0, covariance matrix IpIt is the Gauss of the unit matrix of P × P dimension Distribution, σfAnd σyIt is energy coefficient to be estimated respectively,
W (x) is the matrix of a P × Q, wherein each element W (x)ijIt is all an independent random Gaussian field, i.e.,Wherein kwIt may be any type of positive semidefinite kernel function,
F (x)=f (f1(x),f2(x),…,fq(x)) be Q dimension vector, wherein any one element is all independent Random Gaussian field, i.e.,
(a2) training dataset is set to be combined intoUnknown model parameters u=(f, W), f and W are respectively indicated Bring data point intoF (x) and W (x) later has following prior probability distribution according to the definition of random Gaussian field:
p(u|σffw)=N (0, CB) (2)
Wherein θfwRespectively indicate the hyper parameter that the kernel function being related in f (x) and W (x) is included, CBIt is a NQ (P + 1) the block diagonal battle array of × NQ (P+1) dimension,
Likelihood score function can be obtained according to (1) formula simultaneously are as follows:
It can be obtained with Bayes' theorem:
Wherein, (4) formula is target formula to be estimated, and the estimation for obtaining (4) formula can obtain the estimation of y (x), is sentenced Other result;
(a3) (4) formula is optimized using variation Bayesian Method, to obtain optimal models structural parameters.Variation Bayes Essence be by a kind of iterative manner come so that probability distribution q () approaching to reality to be estimated Posterior probability distribution p () (i.e. formula 4), i.e., by minimizing distortion function:
Wherein,H [] indicates entropy function, gives firstInverse gamma distribution (IG) is distributed, That is:
Wherein, energy coefficient σ to be estimatedfAnd σyIt can be obtained from (6) formula, secondly, design APPROXIMATE DISTRIBUTION q (v) is as follows:
WhereinIt is that inverse gamma is distributed,It is the Gaussian Profile of N-dimensional,
Optimal value is sought finally, being iterated to (7) formula, i.e., carries out segmented line in gradient direction using conjugate gradient decent Property search, searching make the maximized θ of (7) formulafw
Specifically, S03 is further included steps of
(b1) for a new unknown medical image, calling S01 step first carries out image preprocessing;
(b2) classification judgement is carried out using the trained network model of S02 step, first according to Bayesian formula, accurately Target prediction function should are as follows:
Secondly, the thought using variation Bayesian Method carries out approximation, if in above formula It is obtained even normal probability distribution can be multiplied by two approximation probability distributions, according to the Gaussian Profile conditional probability of standard and side The attribute of edge probability, integrates above formula, obtains the mean value mean (y of estimation judgement*) and variance cov (y*)ij, variance cov (y*)ijAs confidence interval, as follows:
In formula, k indicates to differentiate type, δijIt is kronecker delta function, on the basis of obtaining judgement mean value, It carries out that maximum one kind of across comparison select probability and is used as court verdict, meanwhile, the judgement is determined according to confidence interval As a result have great variation possible, to constitute complete judgment criteria.
Finally, it should be noted that the above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations;Although Present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that: it still may be used To modify to technical solution documented by previous embodiment, or some or all of the technical features are equal Replacement;And these are modified or replaceed, technical solution of the embodiment of the present invention that it does not separate the essence of the corresponding technical solution.

Claims (6)

1. the clear cell carcinoma of kidney diagnostic method based on random Gaussian field neural network aiding, which is characterized in that
In the training stage, the self study complex network structures model of data-driven is constructed, by original medical image and corresponding band Pathology block the outputting and inputting as network of mark, the study for having supervision is carried out to network;In the judgement stage, give unknown Input original medical image, site morbidity probabilistic geometry mean value to be tested is calculated, and provide confidence interval, to assist curing Teacher determines canceration grade and physiology lesion position.
2. the clear cell carcinoma of kidney diagnostic method according to claim 1 based on random Gaussian field neural network aiding, It is characterized in that, specifically includes the following steps:
Image preprocessing: original medical image is converted to the gray level image of gray value expression by S01;
The building and training of neural network model: S02 is mapped using the gray value of gray level image as input by random Gaussian field For intermediate parameters, and output layer is linked to by connecting non-directed graph mode entirely, output layer is set as the identification knot by manually marking Fruit, to form the random Gaussian field neural network model with Nonlinear Classification function, the neural network model has been constructed Cheng Hou, using a large amount of original medical images and the corresponding identification result with pathology block mark as the neural network model Output and input, the study for having supervision is carried out to the neural network model;
S03 is identified using the neural network model: defeated by the medical image at position to be tested after image preprocessing Enter the neural network model, prediction judges classification mode, and each classification results have certain probability, and are predicted simultaneously The confidence interval of estimation, doctor is by lateral comparison classification results probability size and confidence interval come auxiliary diagnosis.
3. the clear cell carcinoma of kidney diagnostic method according to claim 1 based on random Gaussian field neural network aiding, It is characterized in that, S01, which is further included steps of, carries out following one or more behaviour to original image using algorithm for image enhancement Make: rotation, unified image size, highlights and contrast at alignment.
4. the clear cell carcinoma of kidney diagnostic method according to claim 1 based on random Gaussian field neural network aiding, It is characterized in that, S02 is further included steps of
(a1) setting x indicates that the vector that input image pixels data are constituted, y indicate output classification, constructs following random Gaussian field mind Through network model:
Y (x)=W (x) [f (x)+σf∈]+σyz (1)
Wherein,
∈=∈ (x) and z=z (x) is two white Gaussian noise process with different covariance parameters, the probability point of ∈ respectively Cloth is N (0, Iq), N (0, Iq) indicate that mean value is 0, covariance matrix IqIt is the Gaussian Profile of the unit matrix of Q × Q dimension, z's Probability distribution is N (0, Ip), N (0, Ip) indicate that mean value is 0, covariance matrix IpIt is the Gauss point of the unit matrix of P × P dimension Cloth, σfAnd σyIt is energy coefficient to be estimated respectively,
W (x) is the matrix of a P × Q, wherein each element W (x)ijIt is all an independent random Gaussian field, i.e.,Wherein kwIt may be any type of positive semidefinite kernel function,
F (x)=f (f1(x),f2(x),…,fq(x)) be a Q dimension vector, wherein any one element be all it is independent with Machine Gaussian field, i.e.,
(a2) training dataset is set to be combined intoUnknown model parameters u=(f, W), f and W are respectively indicated and are brought into Data pointF (x) and W (x) later has following prior probability distribution according to the definition of random Gaussian field:
p(u|σffw)=N (0, CB) (2)
Wherein θfwRespectively indicate the hyper parameter that the kernel function being related in f (x) and W (x) is included, CBIt is a NQ (P+1) The block diagonal battle array of × NQ (P+1) dimension,
Likelihood score function can be obtained according to (1) formula simultaneously are as follows:
It can be obtained with Bayes' theorem:
Wherein, (4) formula is target formula to be estimated, and the estimation for obtaining (4) formula can obtain the estimation of y (x), obtains differentiating knot Fruit;
(a3) (4) formula is optimized using variation Bayesian Method, so that optimal models structural parameters are obtained, the sheet of variation Bayes Matter is by a kind of iterative manner come so that the Posterior probability distribution p () of probability distribution q () approaching to reality to be estimated is (i.e. public Formula 4), i.e., by minimizing distortion function Dist:
Wherein,H [] indicates entropy function, gives firstDistribute inverse gamma distribution (IG), it may be assumed that
Secondly, design APPROXIMATE DISTRIBUTION q (v) is as follows:
WhereinIt is that inverse gamma is distributed,It is the Gaussian Profile of N-dimensional,
Optimal value is sought finally, being iterated to (7) formula, i.e., carries out piecewise linearity in gradient direction using conjugate gradient decent and searches Rope, searching make the maximized θ of (7) formulafw
5. the clear cell carcinoma of kidney diagnostic method according to claim 1 based on random Gaussian field neural network aiding, It is characterized in that, S03 is further included steps of
(b1) for a new unknown medical image, calling S01 step first carries out image preprocessing;
(b2) classification judgement is carried out using the trained network model of S02 step, first according to Bayesian formula, accurate target Anticipation function should are as follows:
Secondly, the thought using variation Bayesian Method carries out approximation, if in above formula It is obtained even normal probability distribution can be multiplied by two approximation probability distributions, according to the Gaussian Profile conditional probability of standard and side The attribute of edge probability, integrates above formula, obtains the mean value mean (y of estimation judgement*) and variance cov (y*)ij, variance cov (y*)ijAs confidence interval, as follows:
In formula, k indicates to differentiate type, δijIt is kronecker delta function, on the basis of obtaining judgement mean value, carries out That maximum one kind of across comparison select probability is used as court verdict, meanwhile, it is more to determine that the result has according to variance function Big variation is possible, to constitute complete judgment criteria.
6. the clear cell carcinoma of kidney diagnostic method according to claim 4 or 5 based on random Gaussian field neural network aiding, It is characterized in that, random Gaussian field parameters, neural network model parameter are by variation Bayesian Method in marginalisation maximum likelihood degree Estimation obtains under criterion.
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