CN-116306817-B - Radial basis function neural network learning method for breast cancer discrete feature data classification

Abstract

The invention provides a radial basis function neural network learning method for breast cancer discrete feature data classification, and belongs to the field of artificial intelligent mode data fitting, identification and classification. The method of the invention determines a plurality of center points simultaneously in each iteration process, which greatly accelerates the training speed of the model and reaches 50-320 times of the effectiveness of the traditional OLS method, the size of the model is obviously reduced because the center points and the width values determined by the method are effective, the model precision is improved only by using few center points, the model precision obtained by the method can be improved by 3 orders of magnitude under the condition that the model parameters are the same, and meanwhile, the method can be used in different types of data and applications without different parameter settings aiming at different applications because the width values of the basis function are automatically calculated, thereby simplifying the use difficulty of the method.

Inventors

• LIU HAILONG
• WANG DEGANG
• SUN LIFEI
• LI SEN
• ZHANG ZHENGLONG
• DU HAN
• QIN KAIRONG
• SUN CHANGKAI
• LIU RONG
• GUAN SHUI

Assignees

• 大连理工大学

Dates

Publication Date

20260512

Application Date

20230317

Claims (1)

1. 1. A radial basis function neural network learning method for breast cancer discrete feature data classification is characterized by comprising the following specific implementation processes: Construction of radial basis function neural networks The RBF network comprises an input layer, a hidden layer and an output layer, wherein the input layer provides input data, the hidden layer comprises a plurality of radial basis function nodes to realize the mapping of an input data space to a feature space, the output layer is a linear model to realize the linear fitting or classification of the feature space data, a Gaussian function phi (x) is adopted as a radial basis function, and a training data set D comprises N input and output data pairs Wherein The data is input for the dimension m 0 , For m 2 -dimensional output data, the output of the j-th radial basis function of the hidden layer is expressed as: (1) Wherein, the Is the center point of the jth gaussian function, Here the second norm, i.e. the distance between the i-th input data and the j-th center point, σ j is the width of the j-th gaussian function, the output layer implements a multi-dimensional output, the k-th output being expressed as: Wherein, the For the linear combination coefficients of the output layer linear model, Each dimension output of the output layer is connected with m 1 radial basis function outputs of the hidden layers, and m 1 m 2 connection coefficients are all obtained; Definition of the definition (2) Then there is (3) Wherein the method comprises the steps of The matrix formed for the hidden layer radial basis function output values has a dimension Nxm 1 , wherein the elements are , The RBF network model learning method has the task of determining all basis functions by the learning method based on the input data set for training Parameter values and output layer connection coefficients of (2) Is a value of (2); The radial basis function neural network learning method estimates basis function center points and Gaussian function width values based on model residual error extreme points and local area ranges thereof, gradually determines all center points and width values in an incremental mode through iterative calculation, and finally provides a training learning scheme of the RBF network; the scheme comprises two steps in each iteration process, wherein one step is to update the radial basis function network parameters, namely the center point and the Gaussian function width, through a nested second layer iteration process, and the other step is to perform corresponding performance evaluation calculation on the updated network; The construction of the radial basis function neural network learning method comprises the following steps: 1. network performance evaluation in the nth iteration, Firstly, determining a center point as by inner layer nested iteration The corresponding Gaussian function width is These two parameters determine the radial basis gaussian function of the hidden layer, and input data The output data of the hidden layer obtained after the radial basis function mapping is that By means of And determining an estimate of the output layer linear model coefficients by least squares Thereby completing the construction of the nth iteration on the parameters of the whole model, wherein the model has the parameters 、 、 After the nth iterative calculation determines all model parameters, the residual error corresponding to the kth dimension output is the following when the model inputs the ith data , wherein, Corresponding input data for network model The total error of the outputs of all dimensions is expressed in vector form as The total error of all data outputs is expressed as Wherein The model performance is evaluated using normalized root mean square error, i.e., the evolution of the model error energy as a percentage of the total energy of the input dataset When training the model, the model performance information can be obtained directly through a single NRMSE value; 2. Network updating criterion, if the normalized root mean square error after the nth iteration is greater than the preset target error threshold value And the number of the radial basis function center points of the model is smaller than a preset threshold m 1,n <m 1 , the model needs to carry out the n+1th iteration, further adds the center points and determines the corresponding Gaussian function width value, then repeats the network performance evaluation calculation process in the n-th iteration process to judge whether further n+2th iteration is needed, and continues until the iteration condition is not met finally, in the n+1th iteration process, firstly, the residual error obtained based on the n-th iteration result is obtained Determining a center point to be added and a corresponding Gaussian function width value by a second layer inner layer nested iteration method; 3. internally nested iterative updating of network parameters, definition Presetting a threshold value In actual operation, the elastic setting of the threshold is realized by changing the proportionality coefficient so as to adapt to the conditions that the residual is gradually reduced and the effective center point is difficult to find, and then the inner layer iteration is firstly carried out according to the residual norm vector And a preset threshold value The input data is divided into two parts: 1) For solving local central points Non-zero residual portion corresponding to input data point ; 2) For providing zero error value points Part corresponding to input data point ; The input data point corresponding to the maximum residual value is recorded as By calculation of And (3) with Distance between Determining the separation Nearest residual norm Zero point , And (3) with Corresponding distance is ; And Namely a center point which needs to be newly added and the corresponding Gaussian basis function width thereof, selecting a second layer of nesting to further circularly add the center point in an iterative processing mode, and specifically, calculating And Distance between Will be Has therein After removal of the input data points of (a) a new data set point is obtained Residual norms corresponding to the residual norms New and new Maximum point As a further added center point, determining new corresponding Gaussian function width values by repeating the above process The process is repeated repeatedly until the whole original is traversed The local residual maximum value point in (2) or only iterating a certain specific number of times according to the provided limiting requirement, namely only adding a certain specific number of center points, thereby completing the addition of a plurality of center points and the determination of the width value of the corresponding Gaussian function in the n+1th iteration process, and performing iterative calculation of the whole method until the calculation result meets the preset condition, namely Or (b) Finally obtaining the model parameter center point C and the Gaussian radial basis function width ; The sigma is required to be further adjusted before the radial basis function neural network is used, and finally lambda sigma is used as the width value of the Gaussian radial basis function, wherein a proper lambda value is selected according to the expected model performance error; The dataset calculates 9 features of breast tumor cell morphology and gives a tumor benign and malignant signature comprising 0 or 1,9 features including mass thickness, cell size uniformity, cell shape uniformity, limbic adhesion, single epithelial cell size, nude nuclei, pale chromatin, normal nucleoli, mitosis, each sample feature taking an integer in the range of 1-10, these discrete data constituting a characteristic distribution of benign or malignant breast cancer.

Description

Radial basis function neural network learning method for breast cancer discrete feature data classification Technical Field The invention belongs to the field of artificial intelligence (artificial neural network) mode data fitting, identification and classification, and particularly relates to a novel radial basis function (Radial Basis Function, RBF) neural network (Neural Networks, NN) learning method for breast cancer discrete feature data fitting and classification. Background The breast cancer classification based on the artificial intelligence algorithm can provide a lot of correlation and reference information, and has important auxiliary application significance and clinical value for diagnosis and subsequent treatment. Discrete feature breast cancer data can relatively simplify data construction and acquisition, reduce data storage space and accelerate data processing speed, but has certain requirements on a model of a classification algorithm. The invention provides a radial basis function neural network learning algorithm for realizing classification processing of breast cancer discrete feature data. The radial basis function neural network is a universal approximator, and can approximate any continuous function or mapping relation with certain precision under certain conditions. The RBF neural network has simple structure, strong performance and important application value, is widely applied in various fields, and can be used for system identification and modeling, nonlinear system control, pattern identification and classification and the like. The model realized based on the RBF neural network has better generalization capability and is the basis for further realizing a plurality of practical applications and functions. The RBF network model has a simple structure and comprises three layers of neuron nodes, namely an input layer, a hidden layer and an output layer. The hidden layer node comprises a hidden layer node, an input layer node, an output layer, a hidden layer node and a hidden layer node, wherein the number of the input layer node is the same as the number of the input data dimension to provide input data for the whole network, each neuron node of the hidden layer is connected with the input layer, an activation function of the hidden layer node is a Radial Basis Function (RBF), a connection coefficient of the hidden layer node and the input layer node is a central point of the radial basis function, and the output layer provides output for the whole network and can be multidimensional, wherein each dimension output is a linear combination of the hidden layer node output. The RBF network model needs to determine appropriate network parameter values according to training data (including input mode and output target value data) corresponding to a specific problem, specifically including the number, position (center point), width value of radial basis functions of hidden layer nodes, and linear connection coefficients between the hidden layer and the output layer, and whether these parameter values are appropriate or not can ultimately determine performance of the radial basis function network model for processing the specific problem, such as fitting or classification accuracy. The RBF network parameter training method has unique characteristics and modes. Currently, there are a number of RBF network parameter training methods. SCHWENKER and the like carry out better and systematic summary on the RBF network training method according to the stage number required by the radial basis function network training, and propose concepts of training the RBF network in a one-stage, two-stage and three-stage learning mode. The method comprises the steps of training part or all parameters of RBF network in one learning process, such as output layer linear connection coefficients or hidden layer parameters, and the like, wherein a specific learning algorithm comprises a support vector learning method (Support Vector Learning Method, SVLM) for determining the output layer connection coefficients, an orthogonal least squares method (Orthogonal Least Squares, OLS) or a direct calculation pseudo-inverse method, and the like, and when the output layer parameter values are trained in one stage by using the methods, the parameters of the hidden layer of the network model are directly determined by certain specific methods. The hidden layer parameters comprise positions and widths of radial basis functions which can be obtained through an unsupervised clustering method (such as k-means) or a supervision method (such as Learning Vector Quantization (LVQ) or decision tree) and the width values of the basis functions are required to be determined through further statistical calculation after a central point is obtained, and the three-stage training method is to perform fine tuning optimization on the model parameters obtained through two-stage training through a counter-propagation-like algorithm. In fact, f