Iris数据集的Fisher线性分类及可视化

一、线性分类及准确率

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt 
path=r'F:/人工智能与机器学习/iris.csv'
df = pd.read_csv(path, header=0)
Iris1=df.values[0:50,0:4]
Iris2=df.values[50:100,0:4]
Iris3=df.values[100:150,0:4]
m1=np.mean(Iris1,axis=0)
m2=np.mean(Iris2,axis=0)
m3=np.mean(Iris3,axis=0)
s1=np.zeros((4,4))
s2=np.zeros((4,4))
s3=np.zeros((4,4))
for i in range(0,30,1):
    a=Iris1[i,:]-m1
    a=np.array([a])
    b=a.T
    s1=s1+np.dot(b,a)    
for i in range(0,30,1):
    c=Iris2[i,:]-m2
    c=np.array([c])
    d=c.T
    s2=s2+np.dot(d,c) 
    #s2=s2+np.dot((Iris2[i,:]-m2).T,(Iris2[i,:]-m2))
for i in range(0,30,1):
    a=Iris3[i,:]-m3
    a=np.array([a])
    b=a.T
    s3=s3+np.dot(b,a) 
sw12=s1+s2
sw13=s1+s3
sw23=s2+s3
#投影方向
a=np.array([m1-m2])
sw12=np.array(sw12,dtype='float')
sw13=np.array(sw13,dtype='float')
sw23=np.array(sw23,dtype='float')
#判别函数以及T
#需要先将m1-m2转化成矩阵才能进行求其转置矩阵
a=m1-m2
a=np.array([a])
a=a.T
b=m1-m3
b=np.array([b])
b=b.T
c=m2-m3
c=np.array([c])
c=c.T
w12=(np.dot(np.linalg.inv(sw12),a)).T
w13=(np.dot(np.linalg.inv(sw13),b)).T
w23=(np.dot(np.linalg.inv(sw23),c)).T
#print(m1+m2) #1x4维度  invsw12 4x4维度  m1-m2 4x1维度
T12=-0.5*(np.dot(np.dot((m1+m2),np.linalg.inv(sw12)),a))
T13=-0.5*(np.dot(np.dot((m1+m3),np.linalg.inv(sw13)),b))
T23=-0.5*(np.dot(np.dot((m2+m3),np.linalg.inv(sw23)),c))
kind1=0
kind2=0
kind3=0
newiris1=[]
newiris2=[]
newiris3=[]
for i in range(30,49):
    x=Iris1[i,:]
    x=np.array([x])
    g12=np.dot(w12,x.T)+T12
    g13=np.dot(w13,x.T)+T13
    g23=np.dot(w23,x.T)+T23
    if g12>0 and g13>0:
        newiris1.extend(x)
        kind1=kind1+1
    elif g12<0 and g23>0:
        newiris2.extend(x)
    elif g13<0 and g23<0 :
        newiris3.extend(x)
#print(newiris1)
for i in range(30,49):
    x=Iris2[i,:]
    x=np.array([x])
    g12=np.dot(w12,x.T)+T12
    g13=np.dot(w13,x.T)+T13
    g23=np.dot(w23,x.T)+T23
    if g12>0 and g13>0:
        newiris1.extend(x)
    elif g12<0 and g23>0:
 
        newiris2.extend(x)
        kind2=kind2+1
    elif g13<0 and g23<0 :
        newiris3.extend(x)
for i in range(30,50):
    x=Iris3[i,:]
    x=np.array([x])
    g12=np.dot(w12,x.T)+T12
    g13=np.dot(w13,x.T)+T13
    g23=np.dot(w23,x.T)+T23
    if g12>0 and g13>0:
        newiris1.extend(x)
    elif g12<0 and g23>0:     
        newiris2.extend(x)
    elif g13<0 and g23<0 :
        newiris3.extend(x)
        kind3=kind3+1
#花瓣与花萼的长度散点图
plt.scatter(df.values[:50, 3], df.values[:50, 1], color='red', marker='o', label='setosa')
plt.scatter(df.values[50:100, 3], df.values[50: 100, 1], color='blue', marker='x', label='versicolor')
plt.scatter(df.values[100:150, 3], df.values[100: 150, 1], color='green', label='virginica')
plt.xlabel('petal length')
plt.ylabel('sepal length')
plt.title("花瓣与花萼长度的散点图")
plt.rcParams['font.sans-serif']=['SimHei'] #显示中文标签
plt.rcParams['axes.unicode_minus']=False
plt.legend(loc='upper left')
plt.show()
 
#花瓣与花萼的宽度度散点图
plt.scatter(df.values[:50, 4], df.values[:50, 2], color='red', marker='o', label='setosa')
plt.scatter(df.values[50:100, 4], df.values[50: 100, 2], color='blue', marker='x', label='versicolor')
plt.scatter(df.values[100:150, 4], df.values[100: 150, 2], color='green', label='virginica')
plt.xlabel('petal width')
plt.ylabel('sepal width')
plt.title("花瓣与花萼宽度的散点图")
plt.legend(loc='upper left')
plt.show()
 
correct=(kind1+kind2+kind3)/60
print("样本类内离散度矩阵S1：",s1,'\n')
print("样本类内离散度矩阵S2：",s2,'\n')
print("样本类内离散度矩阵S3：",s3,'\n')
print('-----------------------------------------------------------------------------------------------')
print("总体类内离散度矩阵Sw12：",sw12,'\n')
print("总体类内离散度矩阵Sw13：",sw13,'\n')
print("总体类内离散度矩阵Sw23：",sw23,'\n')
print('-----------------------------------------------------------------------------------------------')
print('判断出来的综合正确率：',correct*100,'%')

二、数据可视化

导入库

import numpy as np
import pandas as pd
import matplotlib
import matplotlib.pyplot as plt
import seaborn as sns

读取数据

data = pd.read_csv(r'F:/人工智能与机器学习/iris.csv')

1.前五行数据

data.head()

	Id	SepalLength	SepalWidth	PetalLength	PetalWidth	Species
0	1	5.1	3.5	1.4	0.2	setosa
1	2	4.9	3.0	1.4	0.2	setosa
2	3	4.7	3.2	1.3	0.2	setosa
3	4	4.6	3.1	1.5	0.2	setosa
4	5	5.0	3.6	1.4	0.2	setosa

2.后五行数据

data.tail()

	Id	SepalLength	SepalWidth	PetalLength	PetalWidth	Species
145	146	6.7	3.0	5.2	2.3	virginica
146	147	6.3	2.5	5.0	1.9	virginica
147	148	6.5	3.0	5.2	2.0	virginica
148	149	6.2	3.4	5.4	2.3	virginica
149	150	5.9	3.0	5.1	1.8	virginica

3.数据描述

data.describe()

	Id	SepalLength	SepalWidth	PetalLength	PetalWidth
count	150.000000	150.000000	150.000000	150.000000	150.000000
mean	75.500000	5.843333	3.057333	3.758000	1.199333
std	43.445368	0.828066	0.435866	1.765298	0.762238
min	1.000000	4.300000	2.000000	1.000000	0.100000
25%	38.250000	5.100000	2.800000	1.600000	0.300000
50%	75.500000	5.800000	3.000000	4.350000	1.300000
75%	112.750000	6.400000	3.300000	5.100000	1.800000
max	150.000000	7.900000	4.400000	6.900000	2.500000

4.对每种特征计数

data.Species.value_counts()

virginica 50
setosa 50
versicolor 50
Name: Species, dtype: int64

可视化操作

1.绘制花萼的长度与宽度的散点图与直方图

sns.jointplot(x="SepalLength",y="SepalWidth",data=data,kind='scatter');
plt.show()

2.绘制花瓣的长度与宽度的散点图与直方图

sns.jointplot(x="PetalLength",y="PetalWidth",data=data,kind='scatter');
plt.show()

3.绘制花萼的长度与宽度的折线图

sns.lineplot(x="SepalLength",y="SepalWidth",hue='Species',data=data)
plt.show()

4.绘制花瓣的长度与宽度的折线图

sns.lineplot(x="PetalLength",y="PetalWidth",hue='Species',data=data)
plt.show()

5.绘制花萼的长度与宽度的散点图

sns.relplot(x="SepalLength",y="SepalWidth",hue='Species',data=data)
plt.show()

6.绘制花瓣的长度与宽度的散点图

sns.relplot(x="PetalLength",y="PetalWidth",hue='Species',data=data)
plt.show()

7.绘制花萼长度的直方图

sns.distplot(data.SepalLength,bins=8,hist=True,kde=False)

8.绘制花萼宽度的直方图

sns.distplot(data.SepalWidth,bins=8,hist=True,kde=False)

9.绘制花瓣长度的直方图

sns.distplot(data.PetalLength,bins=5,hist=True,kde=False)

10.绘制花瓣宽度的直方图

sns.distplot(data.PetalWidth,bins=5,hist=True,kde=False)

11.绘制箱线图

sns.boxplot(x='SepalLength',data=data)

为了更加直观的观察四个属性的关系，将其放入一个图中

#对于每个属性的data创建一个新的DataFrame
Iris1 = pd.DataFrame({"Id": np.arange(1,151), 'Attribute': 'SepalLengthCm', 'Data':data.SepalLength, 'Species':data.Species})
Iris2 = pd.DataFrame({"Id": np.arange(151,301), 'Attribute': 'SepalWidthCm', 'Data':data.SepalWidth, 'Species':data.Species})
Iris3 = pd.DataFrame({"Id": np.arange(301,451), 'Attribute': 'PetalLengthCm', 'Data':data.PetalLength, 'Species':data.Species})
Iris4 = pd.DataFrame({"Id": np.arange(451,601), 'Attribute': 'PetalWidthCm', 'Data':data.PetalWidth, 'Species':data.Species})
#将四个DataFrame合并为一个.
Iris = pd.concat([Iris1, Iris2, Iris3, Iris4])
#绘制箱线图
sns.boxplot(x='Attribute', y='Data', data=Iris)

将三种鸢尾花进行对比

sns.boxplot(x='Attribute', y='Data',hue='Species', data=Iris)

12.绘制分布图

sns.pairplot(data.drop('Id',axis=1),hue='Species')
plt.show()

参考文章

http://bob0118.club/?p=268