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SoftmaxRegression.py
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SoftmaxRegression.py
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import math #数学基本运算
import matplotlib.pyplot as plt #图形显示
import random #随机数
import numpy as np #矩阵运算库
import pandas as pd #提供高性能易用数据类型和分析工具
import seaborn as sns #绘制数据分布，数据观察函数
from scipy.io import arff #方便导入arff文件数据
import sys #用于表示最大值和最小值
'''
该算法为softmaxRegression算法（多项逻辑回归算法）
数据来源：iris.arff 鸢尾属植物的各项数据
数据内容包括：sepal length (花萼长度)、sepal width(花萼宽度)、
petal length(花瓣长度)、petal width(花瓣宽度)、class（种类）共三类
数据特征前四项为鸢尾属植物的特征，最后一项为植物标签，即所属类别
'''
def readingDatas():
'''
获取鸢尾属植物数据源
:return:
'''
array = arff.loadarff("./Dataset/iris.arff")
df = pd.DataFrame(array[0])
df.insert(0, 'constant', 1) # 添加constant列 值恒为1
df = df.replace(b'Iris-setosa', 0)
df = df.replace(b'Iris-versicolor', 1)
df = df.replace(b'Iris-virginica', 2)
data_array = np.array(df)
dataSet = data_array.tolist()
# print(dataSet)
# print(len(dataSet))
return dataSet
def randomData(dataSet,rate):
'''
随机划分数据集为训练集和测试集
:param dataSet:
:param rate:
:return:
'''
dataSetDemo = dataSet[:] #将数据存入另一个列表防止列表修改
num = len(dataSetDemo)
trainNum = int(rate*num)
np.random.shuffle(dataSetDemo) #将列表随机乱序
trainData = dataSetDemo[0:trainNum] #随机选取80%的数据成为分类数据
testData = dataSetDemo[trainNum:num] #剩下的为测试数据
return trainData,testData
def picture(dataSet):
'''
绘制数据集中特征与标签之间的关系
:param dataSet:
:return:
'''
array = np.array(dataSet)
plt.figure(1)
ax1 = plt.subplot(2, 2, 1)
ax2 = plt.subplot(2, 2, 2)
ax3 = plt.subplot(2, 2, 3)
ax4 = plt.subplot(2, 2, 4)
plt.sca(ax1)
plt.xlabel('sepal length', fontsize=15, color='r')
plt.ylabel('class', fontsize=15, color='r')
plt.scatter(array[:,1], array[:,-1],alpha=0.6) # 绘制散点图，透明度为0.6（这样颜色浅一点，比较好看）
plt.sca(ax2)
plt.xlabel('sepal width', fontsize=15, color='r')
plt.ylabel('class', fontsize=15, color='r')
plt.scatter(array[:,2], array[:,-1],alpha=0.6) # 绘制散点图，透明度为0.6（这样颜色浅一点，比较好看）
plt.sca(ax3)
plt.xlabel('petal length', fontsize=15, color='r')
plt.ylabel('class', fontsize=15, color='r')
plt.scatter(array[:,3], array[:, -1], alpha=0.6) # 绘制散点图，透明度为0.6（这样颜色浅一点，比较好看）
plt.sca(ax4)
plt.xlabel('petal width', fontsize=15, color='r')
plt.ylabel('class', fontsize=15, color='r')
plt.scatter(array[:,4], array[:, -1], alpha=0.6) # 绘制散点图，透明度为0.6（这样颜色浅一点，比较好看）
plt.show()
def decisionBoundary(data,coefficient):
'''
决策边界即拟合的直线函数 z = θ_0x_0 + θ_1x_1 + ... + θ_nx_n 所对应的向量(三维列表)
:param data: 输入的数据
:param coefficient: 线性回归系数
:return: result 目标值
'''
result = []
data = data[:-1]
vec1 = np.array(data)
for coe in coefficient:
vec2 = np.array(coe)
result.append(np.dot(vec1, vec2))
return result
def hypothesisFunction(data,coefficient):
'''
假设函数,计算数据的分类,j假设函数结果为一个分类向量，其中数值最大的为训练结果分类
:param data:
:param coefficient:
:return:
'''
result = []
boundary = decisionBoundary(data, coefficient)
sum = 0
for index in range(len(coefficient)):
demo = math.exp(boundary[index])
result.append(demo)
sum += demo
for index in range(len(result)):
result[index] = result[index] / sum
return result
def costFunction(trainData,coefficient):
cost = 0
for data in trainData:
if data[-1] == 0:
cost += math.log(hypothesisFunction(data,coefficient)[0])
elif data[-1] == 1:
cost += math.log(hypothesisFunction(data,coefficient)[1])
elif data[-1] == 2:
cost += math.log(hypothesisFunction(data,coefficient)[2])
cost = (-1) * cost / len(trainData)
return cost
def gradientDescent(trainData,rate,coefficient):
'''
梯度下降算法
:param trainData:
:param rate:
:param coefficient:
:return:
'''
print('gradientDescent')
coefficientDemo = coefficient[:]
for index1,coe in enumerate(coefficient):#迭代三个分类对应的参数向量
for index2,num in enumerate(coe):
sum = 0
for data in trainData:
result = hypothesisFunction(data, coefficient)
if data[-1] == index1:
sum += (1 - result[index1]) * data[index2]
else:
sum += (0 - result[index1]) * data[index2]
sum = sum * rate / len(trainData)
coefficientDemo[index1][index2] = num + sum
coefficient = coefficientDemo[:]
return coefficient
def classify(trainData,rate):
'''
分类器
:param trainData:
:param rate:
:return:
'''
coefficient = [[1,1,1,1,1],[1,1,1,1,1],[1,1,1,1,1]]
oldCost = 0.0
i = 1
newCost = costFunction(trainData, coefficient)
while abs(oldCost - newCost) > 0.00001:
coefficient = gradientDescent(trainData, rate, coefficient)
oldCost = newCost
newCost = costFunction(trainData, coefficient)
print('第', i, '次迭代：')
print('参数为：', coefficient)
print('代价函数为：', newCost)
print('训练集准确率为：', testSoftmaxRegression(trainData, coefficient))
i = i + 1
return coefficient
def testSoftmaxRegression(testData,coefficient):
rata = 0
for data in testData:
result = hypothesisFunction(data, coefficient)
if data[-1] == result.index(max(result)): rata += 1
rata = rata / len(testData)
return rata
def testDemo():
dataSet = readingDatas()
trainData,testData = randomData(dataSet, 0.8)
picture(dataSet)
coefficient = classify(trainData, 1)
rata = testSoftmaxRegression(testData,coefficient)
print('Softmax算法准确率为：',rata)
if __name__ == "__main__":
testDemo()