# 用Python实现机器学习算法——感知器算法

2个月前 阅读 37 点赞 1

Python 被称为是最接近 AI 的语言。最近一位名叫Anna-Lena Popkes（德国波恩大学计算机科学专业的研究生，主要关注机器学习和神经网络。）的小姐姐在GitHub上分享了自己如何使用Python（3.6及以上版本）实现7种机器学习算法的笔记，并附有完整代码。所有这些算法的实现都没有使用其他机器学习库。这份笔记可以帮大家对算法以及其底层结构有个基本的了解，但并不是提供最有效的实现。

• 数据集
• 是d-维向量
• 是一个目标变量，它是一个标量

• 它有一个实值加权向量
• 它有一个实值偏置量 b
• 它使用 Heaviside step 函数作为其激活函数

In [1]:

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_blobs
from sklearn.model_selection import train_test_split
np.random.seed(123)

% matplotlib inline


In [2]:

X, y = make_blobs(n_samples=1000, centers=2)
fig = plt.figure(figsize=(8,6))
plt.scatter(X[:,0], X[:,1], c=y)
plt.title("Dataset")
plt.xlabel("First feature")
plt.ylabel("Second feature")
plt.show()


In [3]:

y_true = y[:, np.newaxis]

X_train, X_test, y_train, y_test = train_test_split(X, y_true)
print(f'Shape X_train: {X_train.shape}')
print(f'Shape y_train: {y_train.shape})')
print(f'Shape X_test: {X_test.shape}')
print(f'Shape y_test: {y_test.shape}')


Shape X_train: (750, 2)

Shape y_train: (750, 1))

Shape X_test: (250, 2)

Shape y_test: (250, 1)

In [6]:

class Perceptron():

def __init__(self):
pass

def train(self, X, y, learning_rate=0.05, n_iters=100):
n_samples, n_features = X.shape

# Step 0: Initialize the parameters
self.weights = np.zeros((n_features,1))
self.bias = 0

for i in range(n_iters):
# Step 1: Compute the activation
a = np.dot(X, self.weights) + self.bias

# Step 2: Compute the output
y_predict = self.step_function(a)

# Step 3: Compute weight updates
delta_w = learning_rate * np.dot(X.T, (y - y_predict))
delta_b = learning_rate * np.sum(y - y_predict)

# Step 4: Update the parameters
self.weights += delta_w
self.bias += delta_b

return self.weights, self.bias

def step_function(self, x):
return np.array([1 if elem >= 0 else 0 for elem in x])[:, np.newaxis]

def predict(self, X):
a = np.dot(X, self.weights) + self.bias
return self.step_function(a)


In [7]:

p = Perceptron()
w_trained, b_trained = p.train(X_train, y_train,learning_rate=0.05, n_iters=500)


In [10]:

y_p_train = p.predict(X_train)
y_p_test = p.predict(X_test)

print(f"training accuracy: {100 - np.mean(np.abs(y_p_train - y_train)) * 100}%")
print(f"test accuracy: {100 - np.mean(np.abs(y_p_test - y_test)) * 100}%")


training accuracy: 100.0%

test accuracy: 100.0%

In [13]:

def plot_hyperplane(X, y, weights, bias):
"""
Plots the dataset and the estimated decision hyperplane
"""
slope = - weights[0]/weights[1]
intercept = - bias/weights[1]
x_hyperplane = np.linspace(-10,10,10)
y_hyperplane = slope * x_hyperplane + intercept
fig = plt.figure(figsize=(8,6))
plt.scatter(X[:,0], X[:,1], c=y)
plt.plot(x_hyperplane, y_hyperplane, '-')
plt.title("Dataset and fitted decision hyperplane")
plt.xlabel("First feature")
plt.ylabel("Second feature")
plt.show()


In [14]:

plot_hyperplane(X, y, w_trained, b_trained)


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