CN107169527A - Classification method of medical image based on collaboration deep learning - Google Patents

Classification method of medical image based on collaboration deep learning Download PDF

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CN107169527A
CN107169527A CN201710417724.XA CN201710417724A CN107169527A CN 107169527 A CN107169527 A CN 107169527A CN 201710417724 A CN201710417724 A CN 201710417724A CN 107169527 A CN107169527 A CN 107169527A
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CN107169527B (en
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夏勇
张建鹏
谢雨彤
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Northwestern Polytechnical University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
    • G06F18/214—Generating training patterns; Bootstrap methods, e.g. bagging or boosting
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/24—Classification techniques
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • G06N3/082—Learning methods modifying the architecture, e.g. adding, deleting or silencing nodes or connections
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • G06N3/084—Backpropagation, e.g. using gradient descent
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
    • G06V2201/00—Indexing scheme relating to image or video recognition or understanding
    • G06V2201/03—Recognition of patterns in medical or anatomical images

Abstract

The invention discloses a kind of classification method of medical image based on collaboration deep learning, the technical problem for solving existing classification method of medical image classification accuracy difference.Technical scheme is, using Cooperative Study method between two depth convolutional neural networks, to be trained by paired mode of learning, each model receives image to youngster as input, a pair of image is transported in corresponding depth convolutional neural networks respectively.These depth convolutional networks are initialized and trained using the method for fine setting pre-training model, a Cooperative Study system is designed, two depth networks is carried out mutual assistance study.The cooperative system is used for exercising supervision to the similarities and differences attribute of youngster to image, whether belong to a classification, and the collaboration error in real time producing two depth convolutional networks carries out backpropagation, the weights of corrective networks, so as to the ability that further Strengthens network learning characteristic is characterized, more efficiently it can differentiate exactly to easily obscuring sample and making.

Description

Classification method of medical image based on collaboration deep learning
Technical field
The present invention relates to a kind of classification method of medical image, more particularly to a kind of medical science figure based on collaboration deep learning As sorting technique.
Background technology
Classification method of medical image has extremely important make in terms of medical retrieval, literature review and medical research With being always the hot research problem in computer-aided diagnosis and medical research field.In the tens of of past numerous studies person In year research, the Image Classfication Technology under the traditional mode of complete set is formd.Its key element be manual feature extraction and Two parts of design of grader.In spite of a set of very perfect theoretical system, traditional image classification method is difficult to realize The seamless union of optimal characteristics and optimum classifier, this causes its performance to be greatly affected.In recent years, depth learning technology Appearance bring feature self study under new breakthrough, end-to-end pattern to image classification problem there is very powerful image table Levy ability.Convolutional neural networks model in deep learning has been successfully applied in Medical Images Classification problem, and phase Huge breakthrough is achieved for traditional images sorting technique.But unlike that possessing the natural scene image classification of mass data Problem, the domain expert that medical image generally requires specialty is labeled, and its cost is very expensive, therefore, has in medical domain The data of mark are very rare.In addition, similitude gives classification between otherness and class in significant class in Medical Images Classification problem Problem brings great puzzlement, it would be desirable to which according to the mode of imaging, the tissue site of non-imaged carries out classification judgement, shadow The anatomical structure and difference of position is easy to so that model is seriously obscured in assorting process as in.
Document " Kumar A, Kim J, Lyndon D, et al.An Ensemble of Fine-Tuned Convolutional Neural Networks for Medical Image Classification[J].IEEE Journal of Biomedical&Health Informatics,2016,PP(99):1-1. " discloses a kind of based on multiple The classification method of medical image of pre-training system integrating.This method is instructed using large-scale image target classification database ImageNet Practice multiple convolutional neural networks, these pre-training networks are finely adjusted according to the medical image data of small sample so that these The parameter adaptation Medical Images Classification task of network.Substantial amounts of experiment has been proven that deep neural network has very strong feature Transfer ability, this solves the problems, such as the small-sample learning in medical image classification to a certain extent.Then by these pre-training The decision probability of network is integrated averagely to obtain last class probability, and this integrated thought is capable of point of further lift scheme Class performance.Document methods described averagely obtains last classification results by the prediction probability for exporting multiple pre-training models, These pre-training networks are mutually independent when training and prediction, for those it is difficult to point to sample for, simply Integrated approach can not improve last classification results.Therefore, the method in the document can not solve medical science shadow well As the problem of similar between difference and class in class in classification.
The content of the invention
In order to overcome the shortcomings of that existing classification method of medical image classification accuracy is poor, the present invention provides a kind of based on collaboration The classification method of medical image of deep learning.This method is led to using Cooperative Study method between two depth convolutional neural networks Cross paired mode of learning to be trained, each model receives image to youngster as input, a pair of image is transported to pair respectively In the depth convolutional neural networks answered.Because the data volume in Medical Images Classification problem is all smaller, therefore use the pre- instruction of fine setting The method for practicing model is initialized and trained to these depth convolutional networks.In order to strengthen network characterization learning ability, design One Cooperative Study system dexterously makes two depth networks carry out mutual assistance study.The cooperative system is used for image to the different of youngster Exercise supervision, i.e., whether belong to a classification with attribute, and the collaboration in real time producing two depth convolutional networks is missed Difference carries out backpropagation, the weights of corrective networks, so that the ability that further Strengthens network learning characteristic is characterized, can more added with Effect ground differentiates exactly to easily obscuring sample and making.
The technical solution adopted for the present invention to solve the technical problems is：A kind of medical image based on collaboration deep learning Sorting technique, is characterized in comprising the following steps：
Step 1: initializing two convolutional neural networks respectively using the parameter of pre-training residual error depth convolutional neural networks Parameter θA,θB, and Cooperative Study system parameter θVS, initialization learning rate η (t) and hyper parameter λ.
Step 2: being trained using image to the pattern pair model of youngster.An image is often inputted to youngster, two depths Pre-training neutral net is spent respectively in the full articulamentum generation depth characteristic of penultimate, is designated as xA T、xB T, by the two depth Feature be coupled obtaining an assemblage characteristic, is designated as (xA T, xB T), three supervisory signals of model are respectively yA,yBAnd yVS。
Step 3: calculating the penalty values l that two pre-training convolutional networks and Cooperative Study system are produced respectivelyA(θA),lB (θB) and lVS(θVS)。
Wherein, M is the number of training set sample, and K is class categories number, and K ' values take 2.
Step 4: calculating Grad：
Hereλ is the weight factor of synergistic signal, final updating model parameter：
θA=θA-η(t)·ΔA, θB=θB-η(t)·ΔB。
The beneficial effects of the invention are as follows：This method is led to using Cooperative Study method between two depth convolutional neural networks Cross paired mode of learning to be trained, each model receives image to youngster as input, a pair of image is transported to pair respectively In the depth convolutional neural networks answered.Because the data volume in Medical Images Classification problem is all smaller, therefore use the pre- instruction of fine setting The method for practicing model is initialized and trained to these depth convolutional networks.In order to strengthen network characterization learning ability, design One Cooperative Study system dexterously makes two depth networks carry out mutual assistance study.The cooperative system is used for image to the different of youngster Exercise supervision, i.e., whether belong to a classification with attribute, and the collaboration in real time producing two depth convolutional networks is missed Difference carries out backpropagation, the weights of corrective networks, so that the ability that further Strengthens network learning characteristic is characterized, can more added with Effect ground differentiates exactly to easily obscuring sample and making.
As a result of Cooperative Study mechanism, the feature learning ability of depth convolutional neural networks is strengthened, and overcomes Sorting algorithm effect based on deep learning caused by Similar Problems between difference and class significantly in class present in medical image The strategy mutually learn between the not good difficult point of fruit, pre-training network, improved jointly is so that model has to the sample of easy misclassification Good resolving ability, substantially increases the accuracy rate of Medical Images Classification.
The present invention is elaborated with reference to embodiment.
Embodiment
Classification method of medical image of the present invention based on collaboration deep learning is comprised the following steps that：
1. image is inputted to youngster.
Using input mode of the image to youngster, two images of being sampled at random from training image are separately input to two phases It is trained in the convolutional neural networks answered.There are three supervisory signals per a couple image, be two respective classes of image respectively Whether distinguishing label and this pair of image belong to same category, the training of the common monitor model of these three signals.
2. double-depth convolutional neural networks are trained.
Double-depth convolutional neural networks module is basic part in this algorithm, and it includes two complete, tools There are the convolutional neural networks A and B of standalone feature.For in principle, the convolutional neural networks of arbitrary structures can be by based on depth The further feature of degree learning model, which is extracted, to be applied in the algoritic module.But, it is contemplated that the finiteness of medical image and Residual error network just regard residual error network as two to the powerful characteristic present ability of image using the technology of fine setting pre-training network The initial model of convolutional network.The pre-training network includes 50 learning layers, and these learning layers parameter be all from ImageNet large-scale image data collection goes to school what acquistion was arrived.Convolutional neural networks A and B can learning parameter be respectively labeled as θA、θB, θ hereAAnd θBDo not share parameter.In order that the residual error network parameter of pre-training can adapt to be fitted Medical Images Classification Data, it is necessary to remove all full articulamentums in raw residual network for a K classification problem, with 1024 god The full articulamentum of full articulamentum and K neuron through member is replaced.The parameter of these new adding layers by be uniformly distributed U (- 0.05,0.05) initialize, and the loss function of each depth network is set to intersect entropy function
Here M is the sample size of whole training set, optimizes the ginseng of convolutional neural networks with stochastic gradient descent algorithm Number θ.Two depth convolutional neural networks are respectively from the image of input to receiving list entries, each own corresponding true mark in youngster Sign to supervise the process of the respective classification learning of two networks.
3. Cooperative Study system.
In order that learning from each other between two neutral nets, improving feature representation ability, one association of unique design jointly Same learning system.The system is used to supervise whether the image above inputted comes from same classification to youngster, and its supervisory signals is Similarities and differences attribute of the image to youngster.Select image to youngster from training data at random, its attribute value table is shown as
Here xAAnd xBIt is that the image obtained from convolutional Neural neutral net A, B learning is characterized to the depth characteristic of youngster, It is exactly the input of cooperative system.yAAnd yBIt is true tag of the input picture to youngster.' VS=1 ' represents a positive image to youngster, ' VS=0 ' represents a negative image to youngster.Using gradient descent algorithm learning network parameter, schemed from a collection of view data As a selection.In order to avoid the imbalance problem of positive and negative class data, the ratio of positive negative sample is artificially controlled to maintain 45%- 55%.xAAnd xBIt is joined together in binder course, then connects a full articulamentum with 2 neurons.In order to realize The normal work of three supervisory signals is, it is necessary to which additionally one softmax layers of addition, prison is removed using following cross entropy loss function Survey synergistic signal.
Here θVSIt is the network parameter of Cooperative Study system.
4. training process.
1. two convolutional neural networks and the network parameter θ of systematic learning system are initializedA,θB,θVS, learning rate η is set , and hyper parameter λ (t).
2. an image is inputted to youngster, and the depth characteristic that two depth convolutional neural networks produce two input pictures is characterized xAAnd xB。
3. it is coupled characteristic present of the image from two convolutional neural networks to youngster, is designated as (xA T, xB T), three supervision Signal is respectively yA、yBAnd yVS。
4. the loss produced by two depth convolutional neural networks and Cooperative Study system is calculated according to formula (1) and (3) Value lA(θA),lB(θB) and lVS(θVS)。
5. Grad is calculated：
Hereλ is the weight factor of synergistic signal.
6. model parameter is updated：θA=θA-η(t)·ΔA, θB=θB-η(t)·ΔB。
5. test process.
In test, for a test image x, depth convolutional neural networks A and B, which sets forth, to predict the outcomeWithThat is the activation value of last full articulamentum.At this moment, additionally Cooperative Study system be dropped in last classification prediction, the prediction label for recently entering image x is

Claims (1)

1. a kind of classification method of medical image based on collaboration deep learning, it is characterised in that comprise the following steps：
Step 1: initializing the ginseng of two convolutional neural networks respectively using the parameter of pre-training residual error depth convolutional neural networks Number θA,θB, and Cooperative Study system parameter θVS, initialization learning rate η (t) and hyper parameter λ；
Step 2: being trained using image to the pattern pair model of youngster；An image is often inputted to youngster, two depth are pre- Neutral net is trained in the full articulamentum generation depth characteristic of penultimate, to be designated as x respectivelyA T、xB T, by the two depth characteristics Progress, which is coupled, obtains an assemblage characteristic, is designated as (xA T, xB T), three supervisory signals of model are respectively yA,yBAnd yVS；
Step 3: calculating the penalty values l that two pre-training convolutional networks and Cooperative Study system are produced respectivelyA(θA),lB(θB) and lVS(θVS)；
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Wherein, M is the number of training set sample, and K is class categories number, and K ' values take 2；
Step 4: calculating Grad：
<mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <msup> <mi>l</mi> <mi>A</mi> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mi>A</mi> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <msup> <mi>&amp;theta;</mi> <mi>A</mi> </msup> <mi>k</mi> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mn>1</mn> <mi>M</mi> </mfrac> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </msubsup> <mo>{</mo> <mrow> <msubsup> <mi>x</mi> <mi>A</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>&amp;lsqb;</mo> <mrow> <mfrac> <msup> <mi>e</mi> <mrow> <msubsup> <msup> <mi>&amp;theta;</mi> <mi>A</mi> </msup> <mi>k</mi> <mi>T</mi> </msubsup> <msubsup> <mi>x</mi> <mi>A</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> </mrow> </msup> <mrow> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </msubsup> <msup> <mi>e</mi> <mrow> <msubsup> <msup> <mi>&amp;theta;</mi> <mi>A</mi> </msup> <mi>j</mi> <mi>T</mi> </msubsup> <msubsup> <mi>x</mi> <mi>A</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> </mrow> </msup> </mrow> </mfrac> <mo>-</mo> <msub> <mi>&amp;delta;</mi> <mrow> <msubsup> <mi>ky</mi> <mi>A</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> </mrow> </msub> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mrow> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <msup> <mi>l</mi> <mi>B</mi> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mi>B</mi> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <msup> <mi>&amp;theta;</mi> <mi>B</mi> </msup> <mi>k</mi> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mn>1</mn> <mi>M</mi> </mfrac> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </msubsup> <mo>{</mo> <mrow> <msubsup> <mi>x</mi> <mi>B</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>&amp;lsqb;</mo> <mrow> <mfrac> <msup> <mi>e</mi> <mrow> <msubsup> <msup> <mi>&amp;theta;</mi> <mi>B</mi> </msup> <mi>k</mi> <mi>T</mi> </msubsup> <msubsup> <mi>x</mi> <mi>B</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> </mrow> </msup> <mrow> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </msubsup> <msup> <mi>e</mi> <mrow> <msubsup> <msup> <mi>&amp;theta;</mi> <mi>B</mi> </msup> <mi>j</mi> <mi>T</mi> </msubsup> <msubsup> <mi>x</mi> <mi>B</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> </mrow> </msup> </mrow> </mfrac> <mo>-</mo> <msub> <mi>&amp;delta;</mi> <mrow> <msubsup> <mi>ky</mi> <mi>B</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> </mrow> </msub> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mrow> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <msup> <mi>l</mi> <mrow> <mi>V</mi> <mi>S</mi> </mrow> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mrow> <mi>V</mi> <mi>S</mi> </mrow> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <msup> <mi>&amp;theta;</mi> <mrow> <mi>V</mi> <mi>S</mi> </mrow> </msup> <msup> <mi>k</mi> <mo>&amp;prime;</mo> </msup> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mn>1</mn> <mi>M</mi> </mfrac> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </msubsup> <mo>{</mo> <mrow> <mo>(</mo> <msup> <msub> <mi>x</mi> <mi>A</mi> </msub> <mi>T</mi> </msup> <mo>,</mo> <msup> <msub> <mi>x</mi> <mi>B</mi> </msub> <mi>T</mi> </msup> <mo>)</mo> </mrow> <mo>&amp;lsqb;</mo> <mrow> <mfrac> <msup> <mi>e</mi> <mrow> <msubsup> <msup> <mi>&amp;theta;</mi> <mrow> <mi>V</mi> <mi>S</mi> </mrow> </msup> <msup> <mi>k</mi> <mo>&amp;prime;</mo> </msup> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <msup> <msub> <mi>x</mi> <mi>A</mi> </msub> <mi>T</mi> </msup> <mo>,</mo> <msup> <msub> <mi>x</mi> <mi>B</mi> </msub> <mi>T</mi> </msup> <mo>)</mo> </mrow> </mrow> </msup> <mrow> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msup> <mi>K</mi> <mo>&amp;prime;</mo> </msup> </msubsup> <msup> <mi>e</mi> <mrow> <msubsup> <msup> <mi>&amp;theta;</mi> <mrow> <mi>V</mi> <mi>S</mi> </mrow> </msup> <mi>j</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <msup> <msub> <mi>x</mi> <mi>A</mi> </msub> <mi>T</mi> </msup> <mo>,</mo> <msup> <msub> <mi>x</mi> <mi>B</mi> </msub> <mi>T</mi> </msup> <mo>)</mo> </mrow> </mrow> </msup> </mrow> </mfrac> <mo>-</mo> <msub> <mi>&amp;delta;</mi> <mrow> <msup> <mi>k</mi> <mo>&amp;prime;</mo> </msup> <msubsup> <mi>y</mi> <mrow> <mi>v</mi> <mi>s</mi> </mrow> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> </mrow> </msub> </mrow> <mo>&amp;rsqb;</mo> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msup> <mi>&amp;Delta;</mi> <mi>A</mi> </msup> <mo>=</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msup> <mi>l</mi> <mi>A</mi> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mi>A</mi> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <msup> <mi>&amp;theta;</mi> <mi>A</mi> </msup> <mi>k</mi> </msub> </mrow> </mfrac> <mo>+</mo> <mi>&amp;lambda;</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <msup> <mi>l</mi> <mrow> <mi>V</mi> <mi>S</mi> </mrow> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mrow> <mi>V</mi> <mi>S</mi> </mrow> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <msup> <mi>&amp;theta;</mi> <mrow> <mi>V</mi> <mi>S</mi> </mrow> </msup> <msup> <mi>k</mi> <mo>&amp;prime;</mo> </msup> </msub> </mrow> </mfrac> <mo>,</mo> <msup> <mi>&amp;Delta;</mi> <mi>B</mi> </msup> <mo>=</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msup> <mi>l</mi> <mi>B</mi> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mi>B</mi> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <msup> <mi>&amp;theta;</mi> <mi>B</mi> </msup> <mi>k</mi> </msub> </mrow> </mfrac> <mo>+</mo> <mi>&amp;lambda;</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <msup> <mi>l</mi> <mrow> <mi>V</mi> <mi>S</mi> </mrow> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mrow> <mi>V</mi> <mi>S</mi> </mrow> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <msup> <mi>&amp;theta;</mi> <mrow> <mi>V</mi> <mi>S</mi> </mrow> </msup> <msup> <mi>k</mi> <mo>&amp;prime;</mo> </msup> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
Hereλ is the weight factor of synergistic signal, final updating model parameter：
θA=θA-η(t)·ΔA, θB=θB-η(t)·ΔB。
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