机器学习模型-感知机(perceptron)

最新推荐文章于 2025-07-01 11:10:49 发布

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本文详细介绍感知机的基本原理，包括原始形式和对偶形式，并通过乳腺癌数据集进行代码实现，对比了自定义感知机和sklearn库的性能。

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Machine Learning - Perceptron

一.基本原理

二.代码实现

import numpy as np
import pandas as pd
from sklearn import datasets
from sklearn.linear_model import Perceptron

import warnings
warnings.filterwarnings('ignore')

def loadDataset():
    dataset = datasets.load_breast_cancer()
    x = dataset.data
    y = dataset.target
    feats = dataset.feature_names
    labels = dataset.target_names
    return x,y,feats,labels

x,y,feats,labels = loadDataset()

def normalizationData(x,y):
    nx = x.copy()
    dim = x.shape[1]
    for i in range(dim):
        nx[:,i] = (x[:,i]-x[:,i].min())/(x[:,i].max()-x[:,i].min())
    ny = y.copy()
    ny[ny==0] = -1
    return nx,ny

nx,ny = normalizationData(x,y)

def divideDataset(nx,y,rate):
    samples = y.shape[0]
    trainnum = round(samples*rate)
    index = np.random.permutation(range(samples))
    x_train,x_test = nx[index[0:trainnum],:],x[index[trainnum:],:]
    y_train,y_test = y[index[0:trainnum]],y[index[trainnum:]]
    return x_train,x_test,y_train,y_test

x_train,x_test,y_train,y_test = divideDataset(nx,ny,rate=0.8)

def trainModel(x_train,y_train,maxgen,lr):
    dim = x_train.shape[1]
    w = np.zeros(dim)
    b = 0
    for L in range(maxgen):
        S = (np.dot(x_train,w)+b)*y_train
        Mx = np.where(S<=0)[0]
        if len(Mx):
            index = np.random.choice(Mx)
            w = w + lr*y_train[index]*(x_train[index,:]).T
            b = b + lr*y_train[index]
        else:
            break
    return w,b

w,b = trainModel(x_train,y_train,maxgen=200,lr=0.01)

def predictModel(x,y,w,b):
    predict = np.sign(np.dot(x,w)+b)
    acc = len(y[predict==y])/len(y)
    return predict,round(acc,4)

print('======结果比对======\n')
predict_train,train_acc = predictModel(x_train,y_train,w,b)
predict_test,test_acc = predictModel(x_test,y_test,w,b)
print('self-written (origin)==> Train acc = ',train_acc,' Test acc = ',test_acc)

三.对偶形式

def gramMat(x):
    num = x.shape[0]
    gram = []
    for i in range(num):
        for j in range(num):
            gram.append(np.dot(x[i,:],x[j,:].T))
    gram = np.array(gram).reshape(num,num)
    return gram

def dualTrainModel(x_train,y_train,maxgen,lr):
    alpha = np.zeros(y_train.shape[0])
    b = 0
    gram = gramMat(x_train)
    for L in range(maxgen):
        S = y_train*(np.dot(gram.T,alpha*y_train)+b)
        Mx = np.where(S<=0)[0]
        if len(Mx):
            index = np.random.choice(Mx)
            alpha[index] = alpha[index] + lr
            b = b + lr*y_train[index]
        else:
            break
    return alpha,b

alpha,b = dualTrainModel(x_train,y_train,maxgen=200,lr=0.01)

def dualPredictModel(x,y,alpha,b):
    predict = np.zeros(y.shape[0])
    for i in range(x.shape[0]):
        v = np.sum(alpha*y_train*np.dot(x_train,x[i].T))+b
        predict[i] = v
    predict = np.sign(predict)
    acc = len(y[predict==y])/len(y)
    return predict,round(acc,4)

predict_train,train_acc = predictModel(x_train,y_train,w,b)
predict_test,test_acc = predictModel(x_test,y_test,w,b)
print('self-written(dual) ==> Train acc = ',train_acc,' Test acc = ',test_acc)

model = Perceptron(alpha=0.01)
model.fit(x_train,y_train)
train_acc = model.score(x_train,y_train)
test_acc = model.score(x_test,y_test)
print('sklearn ==> Train acc = ',round(train_acc,4),' Test acc = ',round(test_acc,4))