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? 内容介绍
本文介绍了人工神经网络技术，该技术可使用由反向传播算法训练的前馈神经网络来确定检测乳腺癌的可能性。在训练期间，反向传播被独立应用于优化，以发展ANN的互连权重。本文探索了一种使用25种特征（例如12例患者病史，13项物理发现，4项乳腺X线摄影发现）的ANN，最后通过活检的结果来确定存在乳腺癌的可能性。
? 部分代码
% *************************************************************************************************************
% Source Code of JAYA Optimization based Feed-Forward
% Neural Network
% Cite: Wang S, Rao RV, Chen P, Zhang Y, Liu A, Wei L. Abnormal breast detection in
% mammogram images by feed-forward neural network trained by Jaya algorithm.
% *************************************************************************************************************
% Enjoy JAYA-ANN!
clc;
close all
% Generating random correlated data
mu = 50;
sigma = 5;
M = mu + sigma * randn(300, 2);
R = [1, 0.75; 0.75, 1];
L = chol(R);
M = M*L;
x = M(:,1); % Example Inputs, Replace by your data inputs for your own experiments
y = M(:,2); % Example labels, Replace by your data labels for your own experiments
%% JAYA algorithms
%% Problem Definition
pop = 30; % Population size
% Min-max normalization of data
m = max(x); mn = min(x); mm = m-mn;
X = ((x-mn)/mm); Y = ((x-mn)/mm);
% 90%:10% splitting of data for training and testing
sz = (ceil(size(X,1))*0.9);
inputs = (X(1:sz))';
targets = (Y(1:sz))';
XTest = (X(sz+1:end))';
YTest = Y(sz+1:end)';
% number of neurons
n = 4;
tic;
% create a neural network
net = feedforwardnet(n);
% configure the neural network for this dataset
net = configure(net, inputs, targets);
% Denormalizaion and Prediction by FNN
FNN_Pred = ((net(XTest))' * mm) + mn;
sz = n^2 + n + n + 1; % Number of design variables i.e., no. of weights in FNN
maxGen = 30; % Maximum number of iterations
mini = repmat(-1,1,sz); % Lower Bound of Variables
maxi = ones(1,sz); % Upper Bound of Variables
objective = @(x) NMSE(x, net, inputs, targets); % Cost Function
disp(['Optimum value = ',num2str(val,10)])
figure;
plot(fopt,'LineWidth', 2);
xlabel('Itteration');
ylabel('Best Cost');
legend('JAYA');
disp(' ' );
% Setting optimized weights and bias in network
net = setwb(net, Best');
% Denormalizaion and Prediction by JAYA_FNN
JAYA_FNN_Pred = ((net(XTest))' * mm) + mn;
YTest = (YTest * mm) + mn;
JAYA_FNN_Execution_Time_Seconds = toc
% Plotting prediction results
figure;
plot(YTest,'LineWidth',2, 'Marker','diamond', 'MarkerSize',8);
hold on;
plot(FNN_Pred, 'LineWidth',2, 'Marker','x', 'MarkerSize',8);
plot(JAYA_FNN_Pred, 'LineWidth',2, 'Marker','pentagram', 'MarkerSize',8);
title('JAYA Optimization based Feed-Forward Neural Network');
xlabel('Time Interval');
ylabel('Values');
legend('Actual Values', 'FNN Predictions', 'JAYA-FNN Predictions');
hold off;
% Performance Evaluaion of FNN and JAYA-FNN
fprintf('Performance Evaluaion of FNN and JAYA-FNN using Normalized Root Mean Square Error \n');
NRMSE_FNN = (abs( sqrt( mean(mean((FNN_Pred - YTest).^2) )) )) / (max(YTest)-min(YTest))
NRMSE_JAYA_FNN = (abs( sqrt( mean(mean((JAYA_FNN_Pred - YTest).^2) ) ) )) / (max(YTest)-min(YTest))
% Objective Function for minimizing normalized mean square error of FNN by
% updation of nework's weights and biases
function [f] = NMSE(wb, net, input, target)
% wb is the weights and biases row vector obtained from the genetic algorithm.
% It must be transposed when transferring the weights and biases to the network net.
net = setwb(net, wb');
% The net output matrix is given by net(input). The corresponding error matrix is given by
error = target - net(input);
% The mean squared error normalized by the mean target variance is
f = (mean(error.^2)/mean(var(target',1)));
% It is independent of the scale of the target components and related to the Rsquare statistic via
% Rsquare = 1 - NMSEcalc ( see Wikipedia)
end
? 运行结果
? 参考文献
[1] Babu G A , Bhukya S N , Kumar R S . Feed forward network with back propagation algorithm for detection of breast cancer[C]// International Conference on Computer Science & Education. IEEE, 2013.
[2]朱正林, 刘权, 张欢. 基于优化广义回归神经网络的碟式太阳能温度预测研究[J]. 南京工程学院学报：自然科学版, 2020, 18(1):5.
