[机器学习]07-基于多层感知机的鸢尾花数据集分类

• 多类感知机算法：为每个类别学习一个独立的判别函数。通过梯度下降优化权重，使得对每个样本，其真实类别的判别值大于其他类别。

• 决策规则：对测试样本选择判别函数值最大的类别作为预测结果。

程序代码：

import random
import matplotlib
import numpy as np
from matplotlib import pyplot as plt
from sklearn.preprocessing import StandardScaler

data_dict = {}
train_data = {}
test_data = {}

matplotlib.rcParams.update({'font.size': 7})

with open('Iris数据txt版.txt', 'r') as file:
    for line in file:
        line = line.strip()
        data = line.split('\t')
        if len(data) >= 3:
            try:
                category = data[0]
                attribute1 = eval(data[1])
                attribute2 = eval(data[3])
                if category in ['1', '2', '3']:
                    if category not in data_dict:
                        data_dict[category] = {'Length': [], 'Width': []}

                    data_dict[category]['Length'].append(attribute1)
                    data_dict[category]['Width'].append(attribute2)
            except ValueError:
                print(f"Invalid data in line: {line}")
                continue
for category, attributes in data_dict.items():
    print(f'种类: {category}')
    print(len(attributes["Length"]))
    print(len(attributes["Width"]))
    print(f'属性1: {attributes["Length"]}')
    print(f'属性2: {attributes["Width"]}')

for category, attributes in data_dict.items():
    lengths = attributes['Length']
    widths = attributes['Width']
    train_indices = random.sample(range(len(lengths)), 45)
    test_indices = [i for i in range(len(lengths)) if i not in train_indices]

    train_data[category] = {
        'Length': [lengths[i] for i in train_indices],
        'Width': [widths[i] for i in train_indices]
    }

    test_data[category] = {
        'Length': [lengths[i] for i in test_indices],
        'Width': [widths[i] for i in test_indices]
    }

print(len(train_data['1']['Length']))
print(train_data['1'])
print(len(test_data['1']['Length']))
print(test_data['1'])
print(len(train_data['2']['Length']))
print(train_data['2'])
print(len(test_data['2']['Length']))
print(test_data['2'])
print(len(train_data['3']['Length']))
print(train_data['3'])
print(len(test_data['3']['Length']))
print(test_data['3'])

plt.scatter(train_data['1']['Length'], train_data['1']['Width'], color='silver', label='Category 1')
plt.scatter(train_data['2']['Length'], train_data['2']['Width'], color='paleturquoise', label='Category 2')
plt.scatter(train_data['3']['Length'], train_data['3']['Width'], color='gold', label='Category 3')
plt.xlabel('Length')
plt.ylabel('Width')
plt.legend()
plt.title('Basic Dataset Distribution')
plt.show()

train_data_merge = []
label_data_merge = []
for category in ['1','2','3']:
    for i in range(45):
        attribute1 = train_data[category]['Length'][i]
        attribute2 = train_data[category]['Width'][i]
        merged_point = [attribute1, attribute2, 1]
        train_data_merge.append(merged_point)
        label_data_merge.append(int(category)-1)

#train_data_merge = StandardScaler().fit_transform(train_data_merge)

print(train_data_merge)
print(len(train_data_merge))
print(label_data_merge)
print(len(label_data_merge))
lines = np.zeros([3,3])
epochs = 5000
#initial_learning_rate = 0.5
learning_rate_right = 0.5
learning_rate_wrong = 0.5
for i in range(epochs):
    for j in range(135):
        for k in range(3):
            if k != label_data_merge[j]:
                #print(train_data_merge[category1][j])
                pright = np.dot(train_data_merge[j], lines[label_data_merge[j]])
                pwrong = np.dot(train_data_merge[j], lines[k])

                if pwrong >= pright:
                    gradient_right = np.array(train_data_merge[j])
                    gradient_wrong = np.array(train_data_merge[j])
                    #p_diff = abs(pwrong - pright)
                    #a13_square_sum = sum(x ** 2 for x in gradient_right)
                    #learning_rate_right = initial_learning_rate * p_diff / a13_square_sum
                    #a13_square_sum = sum(x ** 2 for x in gradient_wrong)
                    #learning_rate_wrong = initial_learning_rate * p_diff / a13_square_sum
                    #print(gradient_right,gradient_wrong)
                    lines[label_data_merge[j]] += learning_rate_right * gradient_right
                    lines[k] -= learning_rate_wrong * gradient_wrong
                    #print(lines[label_data_merge[j]])
                    #print(lines[k])

print(lines)
min_x = min(min(train_data['1']['Length']), min(train_data['2']['Length']), min(train_data['3']['Length']))
max_x = max(max(train_data['1']['Length']), max(train_data['2']['Length']), max(train_data['3']['Length']))
x_range = np.linspace(min_x,max_x,int(100*(max_x-min_x)))
k1 = -lines[0][0]/lines[0][1]
k2 = -lines[1][0]/lines[1][1]
k3 = -lines[2][0]/lines[2][1]
b1 = -lines[0][2]/lines[0][1]
b2 = -lines[1][2]/lines[1][1]
b3 = -lines[2][2]/lines[2][1]

y_range1 = k1*x_range + b1
y_range2 = k2*x_range + b2
y_range3 = k3*x_range + b3

correct_predictions = 0
test_data_merge = []
test_label = []
for category in ['1','2','3']:
    for i in range(5):
        attribute1 = test_data[category]['Length'][i]
        attribute2 = test_data[category]['Width'][i]
        merged_point = [attribute1, attribute2]
        test_data_merge.append(merged_point)
        test_label.append(int(category)-1)

# 计算判别函数的值，并分类
for category in ['1', '2', '3']:
    for i in range(5):
        attribute1 = test_data[category]['Length'][i]
        attribute2 = test_data[category]['Width'][i]

        discriminant_values = []
        for line in lines:
            discriminant_value = line[0] * attribute1 + line[1] * attribute2 + line[2]
            discriminant_values.append(discriminant_value)
        predicted_category = np.argmax(discriminant_values) + 1
        if predicted_category == int(category):
            correct_predictions += 1

accuracy = correct_predictions / (5 * 3)
print(f"准确率: {accuracy:.2f}%")

plt.plot(x_range, y_range1, color='r', label='Category 1 Line')
plt.plot(x_range, y_range2, color='g', label='Category 2 Line')
plt.plot(x_range, y_range3, color='b', label='Category 3 Line')

plt.scatter(train_data['1']['Length'], train_data['1']['Width'], color='silver', label='Category 1')
plt.scatter(train_data['2']['Length'], train_data['2']['Width'], color='paleturquoise', label='Category 2')
plt.scatter(train_data['3']['Length'], train_data['3']['Width'], color='gold', label='Category 3')

for i in range(len(test_data_merge)):
    attribute1 = test_data_merge[i][0]
    attribute2 = test_data_merge[i][1]
    true_label = test_label[i]

    # 计算判别函数的值
    discriminant_values = []
    for line in lines:
        discriminant_value = line[0] * attribute1 + line[1] * attribute2 + line[2]
        discriminant_values.append(discriminant_value)

    # 预测的类别
    predicted_category = np.argmax(discriminant_values) + 1

    # 根据预测是否正确选择标记形状和颜色
    marker = 'D' if predicted_category == true_label + 1 else 'X'
    color = ['gray', 'teal', 'darkgoldenrod'][true_label]

    plt.scatter(attribute1, attribute2, color=color, label=f'Test Category {true_label + 1}', marker=marker)

plt.xlabel('Length')
plt.ylabel('Width')
plt.legend()
plt.title('Multi-class Classifier')
plt.show()

运行结果：

种类: 1

50

50

属性1: [5.1, 4.9, 4.7, 4.6, 5.0, 5.4, 4.6, 5.0, 4.4, 4.9, 5.4, 4.8, 4.8, 4.3, 5.8, 5.7, 5.4, 5.1, 5.7, 5.1, 5.4, 5.1, 4.6, 5.1, 4.8, 5.0, 5.0, 5.2, 5.2, 4.7, 4.8, 5.4, 5.2, 5.5, 4.9, 5.0, 5.5, 4.9, 4.4, 5.1, 5.0, 4.5, 4.4, 5.0, 5.1, 4.8, 5.1, 4.6, 5.3, 5.0]

属性2: [1.4, 1.4, 1.3, 1.5, 1.4, 1.7, 1.4, 1.5, 1.4, 1.5, 1.5, 1.6, 1.4, 1.1, 1.2, 1.5, 1.3, 1.4, 1.7, 1.5, 1.7, 1.5, 1.0, 1.7, 1.9, 1.6, 1.6, 1.5, 1.4, 1.6, 1.6, 1.5, 1.5, 1.4, 1.5, 1.2, 1.3, 1.4, 1.3, 1.5, 1.3, 1.3, 1.3, 1.6, 1.9, 1.4, 1.6, 1.4, 1.5, 1.4]

种类: 2

50

50

属性1: [7.0, 6.4, 6.9, 5.5, 6.5, 5.7, 6.3, 4.9, 6.6, 5.2, 5.0, 5.9, 6.0, 6.1, 5.6, 6.7, 5.6, 5.8, 6.2, 5.6, 5.9, 6.1, 6.3, 6.1, 6.4, 6.6, 6.8, 6.7, 6.0, 5.7, 5.5, 5.5, 5.8, 6.0, 5.4, 6.0, 6.7, 6.3, 5.6, 5.5, 5.5, 6.1, 5.8, 5.0, 5.6, 5.7, 5.7, 6.2, 5.1, 5.7]

属性2: [4.7, 4.5, 4.9, 4.0, 4.6, 4.5, 4.7, 3.3, 4.6, 3.9, 3.5, 4.2, 4.0, 4.7, 3.6, 4.4, 4.5, 4.1, 4.5, 3.9, 4.8, 4.0, 4.9, 4.7, 4.3, 4.4, 4.8, 5.0, 4.5, 3.5, 3.8, 3.7, 3.9, 5.1, 4.5, 4.5, 4.7, 4.4, 4.1, 4.0, 4.4, 4.6, 4.0, 3.3, 4.2, 4.2, 4.2, 4.3, 3.0, 4.1]

种类: 3

50

50

属性1: [6.3, 5.8, 7.1, 6.3, 6.5, 7.6, 4.9, 7.3, 6.7, 7.2, 6.5, 6.4, 6.8, 5.7, 5.8, 6.4, 6.5, 7.7, 7.7, 6.0, 6.9, 5.6, 7.7, 6.3, 6.7, 7.2, 6.2, 6.1, 6.4, 7.2, 7.4, 7.9, 6.4, 6.3, 6.1, 7.7, 6.3, 6.4, 6.0, 6.9, 6.7, 6.9, 5.8, 6.8, 6.7, 6.7, 6.3, 6.5, 6.2, 5.9]

属性2: [6.0, 5.1, 5.9, 5.6, 5.8, 6.6, 4.5, 6.3, 5.8, 6.1, 5.1, 5.3, 5.5, 5.0, 5.1, 5.3, 5.5, 6.7, 6.9, 5.0, 5.7, 4.9, 6.7, 4.9, 5.7, 6.0, 4.8, 4.9, 5.6, 5.8, 6.1, 6.4, 5.6, 5.1, 5.6, 6.1, 5.6, 5.5, 4.8, 5.4, 5.6, 5.1, 5.1, 5.9, 5.7, 5.2, 5, 5.2, 5.4, 5.1]

45

{'Length': [4.4, 4.8, 5.1, 5.4, 5.2, 4.3, 5.1, 5.2, 5.0, 5.1, 5.1, 4.6, 5.7, 5.0, 4.5, 4.6, 4.8, 5.8, 4.4, 4.9, 5.4, 5.0, 5.2, 5.7, 5.5, 5.1, 4.4, 5.3, 5.0, 5.4, 5.0, 4.8, 4.7, 5.4, 5.5, 5.0, 4.6, 5.1, 4.9, 5.1, 4.9, 5.0, 4.6, 4.9, 5.1], 'Width': [1.3, 1.4, 1.7, 1.5, 1.5, 1.1, 1.4, 1.4, 1.4, 1.6, 1.5, 1.5, 1.7, 1.6, 1.3, 1.0, 1.6, 1.2, 1.4, 1.4, 1.3, 1.3, 1.5, 1.5, 1.3, 1.5, 1.3, 1.5, 1.5, 1.7, 1.4, 1.6, 1.3, 1.7, 1.4, 1.6, 1.4, 1.4, 1.4, 1.9, 1.5, 1.2, 1.4, 1.5, 1.5]}

5

{'Length': [5.4, 4.8, 4.8, 4.7, 5.0], 'Width': [1.5, 1.4, 1.9, 1.6, 1.6]}

45

{'Length': [6.1, 5.4, 5.7, 6.2, 5.2, 6.7, 5.7, 6.5, 6.4, 6.4, 6.7, 6.3, 6.7, 6.3, 5.5, 6.8, 5.7, 5.6, 5.9, 6.2, 5.6, 5.0, 6.3, 5.5, 5.8, 6.0, 5.1, 6.1, 4.9, 6.6, 6.0, 6.1, 5.0, 5.5, 5.8, 5.6, 5.6, 5.5, 7.0, 6.0, 6.0, 6.1, 5.7, 5.6, 6.9], 'Width': [4.7, 4.5, 4.5, 4.5, 3.9, 4.7, 4.2, 4.6, 4.5, 4.3, 4.4, 4.9, 5.0, 4.7, 4.4, 4.8, 3.5, 4.5, 4.2, 4.3, 4.2, 3.3, 4.4, 3.7, 4.0, 4.5, 3.0, 4.6, 3.3, 4.6, 4.0, 4.0, 3.5, 3.8, 4.1, 4.1, 3.9, 4.0, 4.7, 4.5, 5.1, 4.7, 4.2, 3.6, 4.9]}

5

{'Length': [5.9, 6.6, 5.8, 5.5, 5.7], 'Width': [4.8, 4.4, 3.9, 4.0, 4.1]}

45

{'Length': [7.2, 7.9, 7.7, 6.3, 6.1, 5.7, 6.4, 6.0, 6.3, 6.0, 6.3, 7.7, 7.3, 6.5, 5.6, 7.1, 7.7, 5.8, 5.8, 6.5, 6.2, 6.2, 6.4, 6.7, 6.4, 6.7, 5.9, 6.3, 4.9, 7.4, 7.2, 6.9, 6.5, 7.7, 5.8, 6.8, 6.4, 6.3, 7.2, 6.5, 6.7, 6.9, 6.7, 6.9, 6.3], 'Width': [6.0, 6.4, 6.7, 5.1, 4.9, 5.0, 5.6, 4.8, 4.9, 5.0, 5, 6.7, 6.3, 5.8, 4.9, 5.9, 6.9, 5.1, 5.1, 5.5, 5.4, 4.8, 5.3, 5.7, 5.6, 5.8, 5.1, 5.6, 4.5, 6.1, 5.8, 5.7, 5.2, 6.1, 5.1, 5.5, 5.5, 5.6, 6.1, 5.1, 5.7, 5.1, 5.2, 5.4, 6.0]}

5

{'Length': [7.6, 6.4, 6.1, 6.7, 6.8], 'Width': [6.6, 5.3, 5.6, 5.6, 5.9]}

\[4.4, 1.3, 1\], \[4.8, 1.4, 1\], \[5.1, 1.7, 1\], \[5.4, 1.5, 1\], \[5.2, 1.5, 1\], \[4.3, 1.1, 1\], \[5.1, 1.4, 1\], \[5.2, 1.4, 1\], \[5.0, 1.4, 1\], \[5.1, 1.6, 1\], \[5.1, 1.5, 1\], \[4.6, 1.5, 1\], \[5.7, 1.7, 1\], \[5.0, 1.6, 1\], \[4.5, 1.3, 1\], \[4.6, 1.0, 1\], \[4.8, 1.6, 1\], \[5.8, 1.2, 1\], \[4.4, 1.4, 1\], \[4.9, 1.4, 1\], \[5.4, 1.3, 1\], \[5.0, 1.3, 1\], \[5.2, 1.5, 1\], \[5.7, 1.5, 1\], \[5.5, 1.3, 1\], \[5.1, 1.5, 1\], \[4.4, 1.3, 1\], \[5.3, 1.5, 1\], \[5.0, 1.5, 1\], \[5.4, 1.7, 1\], \[5.0, 1.4, 1\], \[4.8, 1.6, 1\], \[4.7, 1.3, 1\], \[5.4, 1.7, 1\], \[5.5, 1.4, 1\], \[5.0, 1.6, 1\], \[4.6, 1.4, 1\], \[5.1, 1.4, 1\], \[4.9, 1.4, 1\], \[5.1, 1.9, 1\], \[4.9, 1.5, 1\], \[5.0, 1.2, 1\], \[4.6, 1.4, 1\], \[4.9, 1.5, 1\], \[5.1, 1.5, 1\], \[6.1, 4.7, 1\], \[5.4, 4.5, 1\], \[5.7, 4.5, 1\], \[6.2, 4.5, 1\], \[5.2, 3.9, 1\], \[6.7, 4.7, 1\], \[5.7, 4.2, 1\], \[6.5, 4.6, 1\], \[6.4, 4.5, 1\], \[6.4, 4.3, 1\], \[6.7, 4.4, 1\], \[6.3, 4.9, 1\], \[6.7, 5.0, 1\], \[6.3, 4.7, 1\], \[5.5, 4.4, 1\], \[6.8, 4.8, 1\], \[5.7, 3.5, 1\], \[5.6, 4.5, 1\], \[5.9, 4.2, 1\], \[6.2, 4.3, 1\], \[5.6, 4.2, 1\], \[5.0, 3.3, 1\], \[6.3, 4.4, 1\], \[5.5, 3.7, 1\], \[5.8, 4.0, 1\], \[6.0, 4.5, 1\], \[5.1, 3.0, 1\], \[6.1, 4.6, 1\], \[4.9, 3.3, 1\], \[6.6, 4.6, 1\], \[6.0, 4.0, 1\], \[6.1, 4.0, 1\], \[5.0, 3.5, 1\], \[5.5, 3.8, 1\], \[5.8, 4.1, 1\], \[5.6, 4.1, 1\], \[5.6, 3.9, 1\], \[5.5, 4.0, 1\], \[7.0, 4.7, 1\], \[6.0, 4.5, 1\], \[6.0, 5.1, 1\], \[6.1, 4.7, 1\], \[5.7, 4.2, 1\], \[5.6, 3.6, 1\], \[6.9, 4.9, 1\], \[7.2, 6.0, 1\], \[7.9, 6.4, 1\], \[7.7, 6.7, 1\], \[6.3, 5.1, 1\], \[6.1, 4.9, 1\], \[5.7, 5.0, 1\], \[6.4, 5.6, 1\], \[6.0, 4.8, 1\], \[6.3, 4.9, 1\], \[6.0, 5.0, 1\], \[6.3, 5, 1\], \[7.7, 6.7, 1\], \[7.3, 6.3, 1\], \[6.5, 5.8, 1\], \[5.6, 4.9, 1\], \[7.1, 5.9, 1\], \[7.7, 6.9, 1\], \[5.8, 5.1, 1\], \[5.8, 5.1, 1\], \[6.5, 5.5, 1\], \[6.2, 5.4, 1\], \[6.2, 4.8, 1\], \[6.4, 5.3, 1\], \[6.7, 5.7, 1\], \[6.4, 5.6, 1\], \[6.7, 5.8, 1\], \[5.9, 5.1, 1\], \[6.3, 5.6, 1\], \[4.9, 4.5, 1\], \[7.4, 6.1, 1\], \[7.2, 5.8, 1\], \[6.9, 5.7, 1\], \[6.5, 5.2, 1\], \[7.7, 6.1, 1\], \[5.8, 5.1, 1\], \[6.8, 5.5, 1\], \[6.4, 5.5, 1\], \[6.3, 5.6, 1\], \[7.2, 6.1, 1\], \[6.5, 5.1, 1\], \[6.7, 5.7, 1\], \[6.9, 5.1, 1\], \[6.7, 5.2, 1\], \[6.9, 5.4, 1\], \[6.3, 6.0, 1\]

135

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

135

\[ 58.9 -90.95 30.

-0.25 -44.65 216.5

-58.65 135.6 -246.5 \]

准确率: 0.87%

进程已结束,退出代码0