模式识别实验:用MATLAB设计贝叶斯决策算法,并通过鸢尾花数据集iris.csv文件中的每一类的前40条记录作为训练数据,剩余的10条记录作为测试数据,最后验证该算法的有效性
时间: 2023-07-16 09:14:21 浏览: 45
好的,这是一个很好的模式识别实验题目。让我们一步步来实现吧。
首先,我们需要下载并加载iris.csv文件。可以使用以下代码实现:
```matlab
data = readmatrix('iris.csv');
```
然后,我们需要将数据分为训练集和测试集。根据题目要求,我们需要将每个类别的前40条记录作为训练数据,剩余的10条记录作为测试数据。可以使用以下代码实现:
```matlab
train_data = [];
test_data = [];
for i = 1:3
class_data = data((i-1)*50+1:i*50,:);
train_data = [train_data; class_data(1:40,:)];
test_data = [test_data; class_data(41:50,:)];
end
train_labels = train_data(:,end);
train_data = train_data(:,1:end-1);
test_labels = test_data(:,end);
test_data = test_data(:,1:end-1);
```
接下来,我们需要编写一个贝叶斯决策算法。具体来说,我们需要计算每个类别的先验概率、每个类别在每个特征上的条件概率,并使用贝叶斯公式计算后验概率。可以使用以下代码实现:
```matlab
% 计算先验概率
priors = zeros(1,3);
for i = 1:3
priors(i) = sum(train_labels == i) / length(train_labels);
end
% 计算每个类别在每个特征上的条件概率
means = zeros(3,size(train_data,2));
stds = zeros(3,size(train_data,2));
for i = 1:3
class_data = train_data(train_labels == i,:);
means(i,:) = mean(class_data);
stds(i,:) = std(class_data);
end
% 计算后验概率
posteriors = zeros(size(test_data,1),3);
for i = 1:size(test_data,1)
for j = 1:3
likelihood = prod(normpdf(test_data(i,:),means(j,:),stds(j,:)));
posteriors(i,j) = priors(j) * likelihood;
end
posteriors(i,:) = posteriors(i,:) / sum(posteriors(i,:));
end
```
最后,我们需要评估算法的性能。可以使用混淆矩阵、分类准确率和平均分类准确率等指标来评估。可以使用以下代码实现:
```matlab
% 构建混淆矩阵
confusion_mat = zeros(3,3);
for i = 1:size(test_data,1)
true_label = test_labels(i);
pred_label = find(posteriors(i,:) == max(posteriors(i,:)),1);
confusion_mat(true_label,pred_label) = confusion_mat(true_label,pred_label) + 1;
end
% 计算分类准确率和平均分类准确率
accuracy = trace(confusion_mat) / sum(confusion_mat(:));
class_acc = diag(confusion_mat) ./ sum(confusion_mat,2);
mean_acc = mean(class_acc);
```
综上所述,完整的MATLAB代码如下:
```matlab
data = readmatrix('iris.csv');
train_data = [];
test_data = [];
for i = 1:3
class_data = data((i-1)*50+1:i*50,:);
train_data = [train_data; class_data(1:40,:)];
test_data = [test_data; class_data(41:50,:)];
end
train_labels = train_data(:,end);
train_data = train_data(:,1:end-1);
test_labels = test_data(:,end);
test_data = test_data(:,1:end-1);
% 计算先验概率
priors = zeros(1,3);
for i = 1:3
priors(i) = sum(train_labels == i) / length(train_labels);
end
% 计算每个类别在每个特征上的条件概率
means = zeros(3,size(train_data,2));
stds = zeros(3,size(train_data,2));
for i = 1:3
class_data = train_data(train_labels == i,:);
means(i,:) = mean(class_data);
stds(i,:) = std(class_data);
end
% 计算后验概率
posteriors = zeros(size(test_data,1),3);
for i = 1:size(test_data,1)
for j = 1:3
likelihood = prod(normpdf(test_data(i,:),means(j,:),stds(j,:)));
posteriors(i,j) = priors(j) * likelihood;
end
posteriors(i,:) = posteriors(i,:) / sum(posteriors(i,:));
end
% 构建混淆矩阵
confusion_mat = zeros(3,3);
for i = 1:size(test_data,1)
true_label = test_labels(i);
pred_label = find(posteriors(i,:) == max(posteriors(i,:)),1);
confusion_mat(true_label,pred_label) = confusion_mat(true_label,pred_label) + 1;
end
% 计算分类准确率和平均分类准确率
accuracy = trace(confusion_mat) / sum(confusion_mat(:));
class_acc = diag(confusion_mat) ./ sum(confusion_mat,2);
mean_acc = mean(class_acc);
```
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