数据集：鸢尾花卉

数据集：鸢尾花卉

进阶分析：【$k$近邻法】

数据集介绍

数据集来源	UCI 数据库 Iris
概述	UCI Iris 数据集原始数据，根据鸢花萼片和花瓣4项指标对花的种类进行分类。
数据介绍	UCI Iris是常用分类建模数据集，通过花萼长度，花萼宽度，花瓣长度，花瓣宽度4个属性预测鸢尾花卉属于（Setosa，Versicolour，Virginica）三个种类中的哪一类。
属性数	5
记录数	150
无缺失值记录数	150

数据集元数据

名称	数据类型
萼片宽度	float
萼片长度	float
花瓣长度	float
花瓣宽度	float
鸢花种类	string

专有名词

中文	英文
萼片	$Calyx$
花瓣	$Petal$
长度	$Length$
宽度	$Width$
鸢花	$Iris$

预处理

# 导包
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

# 读取文件
fname = 'iris.data'
with open(fname,'r+',encoding='utf-8') as f:
    s = [i[:-1].split(',') for i in f.readlines()]

# pandas读取数据，样本数各50个
names = ['slength','swidth','plength','pwidth','name']
iris = pd.DataFrame(data=s,columns=names)
iris

数据预览

索引	slength	swidth	plength	pwidth	name
0	5.1	3.5	1.4	0.2	Iris-setosa
1	4.9	3.0	1.4	0.2	Iris-setosa
2	4.7	3.2	1.3	0.2	Iris-setosa
3	4.6	3.1	1.5	0.2	Iris-setosa
4	5.0	3.6	1.4	0.2	Iris-setosa
…	…	…	…	…	…
146	6.3	2.5	5.0	1.9	Iris-virginica
147	6.5	3.0	5.2	2.0	Iris-virginica
148	6.2	3.4	5.4	2.3	Iris-virginica
149	5.9	3.0	5.1	1.8	Iris-virginica
150	None	None	None	None	None

151 rows × 5 columns

分组统计

# 三种类别
Setosa = iris.iloc[0:50,0:4].astype('float')
Versicolour = iris.iloc[50:100,0:4].astype('float')
Virginica = iris.iloc[100:150,0:4].astype('float')

# 统计每个品种有多少个样本
iris['name'].value_counts()

整体样本数：

Iris-versicolor    50
Iris-virginica     50
Iris-setosa        50
Name: name, dtype: int64

统计每个类别每个数据点出现的个数：

# setosa
Setosa.loc[:,'slength'].value_counts(),Setosa.loc[:,'swidth'].value_counts(),Setosa.loc[:,'plength'].value_counts(),Setosa.loc[:,'pwidth'].value_counts()
# versicolour
Versicolour.loc[:,'slength'].value_counts(),Versicolour.loc[:,'swidth'].value_counts(),Versicolour.loc[:,'plength'].value_counts(),Versicolour.loc[:,'pwidth'].value_counts()
# virginica
Virginica.loc[:,'slength'].value_counts(),Virginica.loc[:,'swidth'].value_counts(),Virginica.loc[:,'plength'].value_counts(),Virginica.loc[:,'pwidth'].value_counts()

分组样本数：

# Setosa:
(5.0    8
 5.1    8
 4.8    5
 5.4    5
 4.9    4
 4.6    4
 5.2    3
 4.4    3
 4.7    2
 5.7    2
 5.5    2
 4.5    1
 5.8    1
 4.3    1
 5.3    1
 Name: slength, dtype: int64,
 3.4    9
 3.5    6
 3.0    6
 3.1    5
 3.2    5
 3.8    4
 3.7    3
 3.9    2
 3.3    2
 3.6    2
 2.9    1
 4.1    1
 4.4    1
 4.2    1
 2.3    1
 4.0    1
 Name: swidth, dtype: int64,
 1.5    14
 1.4    12
 1.6     7
 1.3     7
 1.7     4
 1.9     2
 1.2     2
 1.1     1
 1.0     1
 Name: plength, dtype: int64,
 0.2    28
 0.4     7
 0.3     7
 0.1     6
 0.5     1
 0.6     1
 Name: pwidth, dtype: int64)

# Versicolour:
(5.6    5
 5.7    5
 5.5    5
 6.0    4
 6.1    4
 6.3    3
 6.7    3
 5.8    3
 6.2    2
 5.0    2
 6.4    2
 6.6    2
 5.9    2
 5.2    1
 5.4    1
 5.1    1
 7.0    1
 6.8    1
 4.9    1
 6.5    1
 6.9    1
 Name: slength, dtype: int64,
 3.0    8
 2.9    7
 2.8    6
 2.7    5
 2.5    4
 2.6    3
 2.4    3
 3.1    3
 2.3    3
 3.2    3
 2.2    2
 2.0    1
 3.3    1
 3.4    1
 Name: swidth, dtype: int64,
 4.5    7
 4.7    5
 4.0    5
 4.4    4
 4.2    4
 3.9    3
 4.1    3
 4.6    3
 3.5    2
 4.9    2
 4.8    2
 4.3    2
 3.3    2
 3.8    1
 3.7    1
 5.1    1
 3.6    1
 5.0    1
 3.0    1
 Name: plength, dtype: int64,
 1.3    13
 1.5    10
 1.0     7
 1.4     7
 1.2     5
 1.6     3
 1.1     3
 1.8     1
 1.7     1
 Name: pwidth, dtype: int64)

# Virginica:
(6.3    6
 6.7    5
 6.4    5
 7.7    4
 6.5    4
 6.9    3
 7.2    3
 5.8    3
 6.1    2
 6.8    2
 6.2    2
 6.0    2
 5.6    1
 7.3    1
 7.6    1
 7.9    1
 7.1    1
 5.7    1
 4.9    1
 5.9    1
 7.4    1
 Name: slength, dtype: int64,
 3.0    12
 2.8     8
 3.2     5
 2.5     4
 3.1     4
 2.7     4
 3.3     3
 2.6     2
 3.8     2
 2.9     2
 3.4     2
 2.2     1
 3.6     1
 Name: swidth, dtype: int64,
 5.1    7
 5.6    6
 5.8    3
 4.9    3
 6.1    3
 5.7    3
 5.0    3
 5.5    3
 4.8    2
 5.4    2
 5.3    2
 6.0    2
 5.9    2
 5.2    2
 6.7    2
 6.6    1
 6.4    1
 4.5    1
 6.3    1
 6.9    1
 Name: plength, dtype: int64,
 1.8    11
 2.3     8
 2.0     6
 2.1     6
 1.9     5
 2.4     3
 2.5     3
 2.2     3
 1.5     2
 1.6     1
 1.7     1
 1.4     1
 Name: pwidth, dtype: int64)

统计量操作

求和：

# 分组求和
print('Setosa: ',np.sum(np.array(Setosa), axis=0))
print('Versicolour: ',np.sum(np.array(Versicolour), axis=0))
print('Virginica: ',np.sum(np.array(Virginica), axis=0))

Setosa:  [250.3 170.9  73.2  12.2]
Versicolour:  [296.8 138.5 213.   66.3]
Virginica:  [329.4 148.7 277.6 101.3]

均值：

# 分组求均值
print('Setosa: ',np.mean(np.array(Setosa), axis=0))
print('Versicolour: ',np.mean(np.array(Versicolour), axis=0))
print('Virginica: ',np.mean(np.array(Virginica), axis=0))

Setosa:  [5.006 3.418 1.464 0.244]
Versicolour:  [5.936 2.77  4.26  1.326]
Virginica:  [6.588 2.974 5.552 2.026]

最大值：

# 分组求最大值
print('Setosa: ',np.amax(np.array(Setosa), axis=0))
print('Versicolour: ',np.amax(np.array(Versicolour), axis=0))
print('Virginica: ',np.amax(np.array(Virginica), axis=0))

Setosa:  [5.8 4.4 1.9 0.6]
Versicolour:  [7.  3.4 5.1 1.8]
Virginica:  [7.9 3.8 6.9 2.5]

最小值：

# 分组求最小值
print('Setosa: ',np.amin(np.array(Setosa), axis=0))
print('Versicolour: ',np.amin(np.array(Versicolour), axis=0))
print('Virginica: ',np.amin(np.array(Virginica), axis=0))

Setosa:  [4.3 2.3 1.  0.1]
Versicolour:  [4.9 2.  3.  1. ]
Virginica:  [4.9 2.2 4.5 1.4]

平方根：

# 分组求平方根
print('Setosa: ')
print(np.sqrt(np.array(Setosa)))
print('Versicolour: ')
print(np.sqrt(np.array(Versicolour)))
print('Virginica: ')
print(np.sqrt(np.array(Virginica)))

Setosa: 
[[2.25831796 1.87082869 1.18321596 0.4472136 ]
 [2.21359436 1.73205081 1.18321596 0.4472136 ]
 [2.16794834 1.78885438 1.14017543 0.4472136 ]
 [2.14476106 1.76068169 1.22474487 0.4472136 ]
 [2.23606798 1.8973666  1.18321596 0.4472136 ]
 [2.32379001 1.97484177 1.30384048 0.63245553]
 [2.14476106 1.84390889 1.18321596 0.54772256]
 [2.23606798 1.84390889 1.22474487 0.4472136 ]
 [2.0976177  1.70293864 1.18321596 0.4472136 ]
 [2.21359436 1.76068169 1.22474487 0.31622777]
 [2.32379001 1.92353841 1.22474487 0.4472136 ]
 [2.19089023 1.84390889 1.26491106 0.4472136 ]
 [2.19089023 1.73205081 1.18321596 0.31622777]
 [2.07364414 1.73205081 1.04880885 0.31622777]
 [2.40831892 2.         1.09544512 0.4472136 ]
 [2.38746728 2.0976177  1.22474487 0.63245553]
 [2.32379001 1.97484177 1.14017543 0.63245553]
 [2.25831796 1.87082869 1.18321596 0.54772256]
 [2.38746728 1.94935887 1.30384048 0.54772256]
 [2.25831796 1.94935887 1.22474487 0.54772256]
 [2.32379001 1.84390889 1.30384048 0.4472136 ]
 [2.25831796 1.92353841 1.22474487 0.63245553]
 [2.14476106 1.8973666  1.         0.4472136 ]
 [2.25831796 1.81659021 1.30384048 0.70710678]
 [2.19089023 1.84390889 1.37840488 0.4472136 ]
 [2.23606798 1.73205081 1.26491106 0.4472136 ]
 [2.23606798 1.84390889 1.26491106 0.63245553]
 [2.28035085 1.87082869 1.22474487 0.4472136 ]
 [2.28035085 1.84390889 1.18321596 0.4472136 ]
 [2.16794834 1.78885438 1.26491106 0.4472136 ]
 [2.19089023 1.76068169 1.26491106 0.4472136 ]
 [2.32379001 1.84390889 1.22474487 0.63245553]
 [2.28035085 2.02484567 1.22474487 0.31622777]
 [2.34520788 2.04939015 1.18321596 0.4472136 ]
 [2.21359436 1.76068169 1.22474487 0.31622777]
 [2.23606798 1.78885438 1.09544512 0.4472136 ]
 [2.34520788 1.87082869 1.14017543 0.4472136 ]
 [2.21359436 1.76068169 1.22474487 0.31622777]
 [2.0976177  1.73205081 1.14017543 0.4472136 ]
 [2.25831796 1.84390889 1.22474487 0.4472136 ]
 [2.23606798 1.87082869 1.14017543 0.54772256]
 [2.12132034 1.51657509 1.14017543 0.54772256]
 [2.0976177  1.78885438 1.14017543 0.4472136 ]
 [2.23606798 1.87082869 1.26491106 0.77459667]
 [2.25831796 1.94935887 1.37840488 0.63245553]
 [2.19089023 1.73205081 1.18321596 0.54772256]
 [2.25831796 1.94935887 1.26491106 0.4472136 ]
 [2.14476106 1.78885438 1.18321596 0.4472136 ]
 [2.30217289 1.92353841 1.22474487 0.4472136 ]
 [2.23606798 1.81659021 1.18321596 0.4472136 ]]
Versicolour: 
[[2.64575131 1.78885438 2.16794834 1.18321596]
 [2.52982213 1.78885438 2.12132034 1.22474487]
 [2.62678511 1.76068169 2.21359436 1.22474487]
 [2.34520788 1.51657509 2.         1.14017543]
 [2.54950976 1.67332005 2.14476106 1.22474487]
 [2.38746728 1.67332005 2.12132034 1.14017543]
 [2.50998008 1.81659021 2.16794834 1.26491106]
 [2.21359436 1.54919334 1.81659021 1.        ]
 [2.56904652 1.70293864 2.14476106 1.14017543]
 [2.28035085 1.64316767 1.97484177 1.18321596]
 [2.23606798 1.41421356 1.87082869 1.        ]
 [2.42899156 1.73205081 2.04939015 1.22474487]
 [2.44948974 1.4832397  2.         1.        ]
 [2.46981781 1.70293864 2.16794834 1.18321596]
 [2.36643191 1.70293864 1.8973666  1.14017543]
 [2.58843582 1.76068169 2.0976177  1.18321596]
 [2.36643191 1.73205081 2.12132034 1.22474487]
 [2.40831892 1.64316767 2.02484567 1.        ]
 [2.48997992 1.4832397  2.12132034 1.22474487]
 [2.36643191 1.58113883 1.97484177 1.04880885]
 [2.42899156 1.78885438 2.19089023 1.34164079]
 [2.46981781 1.67332005 2.         1.14017543]
 [2.50998008 1.58113883 2.21359436 1.22474487]
 [2.46981781 1.67332005 2.16794834 1.09544512]
 [2.52982213 1.70293864 2.07364414 1.14017543]
 [2.56904652 1.73205081 2.0976177  1.18321596]
 [2.60768096 1.67332005 2.19089023 1.18321596]
 [2.58843582 1.73205081 2.23606798 1.30384048]
 [2.44948974 1.70293864 2.12132034 1.22474487]
 [2.38746728 1.61245155 1.87082869 1.        ]
 [2.34520788 1.54919334 1.94935887 1.04880885]
 [2.34520788 1.54919334 1.92353841 1.        ]
 [2.40831892 1.64316767 1.97484177 1.09544512]
 [2.44948974 1.64316767 2.25831796 1.26491106]
 [2.32379001 1.73205081 2.12132034 1.22474487]
 [2.44948974 1.84390889 2.12132034 1.26491106]
 [2.58843582 1.76068169 2.16794834 1.22474487]
 [2.50998008 1.51657509 2.0976177  1.14017543]
 [2.36643191 1.73205081 2.02484567 1.14017543]
 [2.34520788 1.58113883 2.         1.14017543]
 [2.34520788 1.61245155 2.0976177  1.09544512]
 [2.46981781 1.73205081 2.14476106 1.18321596]
 [2.40831892 1.61245155 2.         1.09544512]
 [2.23606798 1.51657509 1.81659021 1.        ]
 [2.36643191 1.64316767 2.04939015 1.14017543]
 [2.38746728 1.73205081 2.04939015 1.09544512]
 [2.38746728 1.70293864 2.04939015 1.14017543]
 [2.48997992 1.70293864 2.07364414 1.14017543]
 [2.25831796 1.58113883 1.73205081 1.04880885]
 [2.38746728 1.67332005 2.02484567 1.14017543]]
Virginica: 
[[2.50998008 1.81659021 2.44948974 1.58113883]
 [2.40831892 1.64316767 2.25831796 1.37840488]
 [2.66458252 1.73205081 2.42899156 1.44913767]
 [2.50998008 1.70293864 2.36643191 1.34164079]
 [2.54950976 1.73205081 2.40831892 1.4832397 ]
 [2.75680975 1.73205081 2.56904652 1.44913767]
 [2.21359436 1.58113883 2.12132034 1.30384048]
 [2.70185122 1.70293864 2.50998008 1.34164079]
 [2.58843582 1.58113883 2.40831892 1.34164079]
 [2.68328157 1.8973666  2.46981781 1.58113883]
 [2.54950976 1.78885438 2.25831796 1.41421356]
 [2.52982213 1.64316767 2.30217289 1.37840488]
 [2.60768096 1.73205081 2.34520788 1.44913767]
 [2.38746728 1.58113883 2.23606798 1.41421356]
 [2.40831892 1.67332005 2.25831796 1.54919334]
 [2.52982213 1.78885438 2.30217289 1.51657509]
 [2.54950976 1.73205081 2.34520788 1.34164079]
 [2.77488739 1.94935887 2.58843582 1.4832397 ]
 [2.77488739 1.61245155 2.62678511 1.51657509]
 [2.44948974 1.4832397  2.23606798 1.22474487]
 [2.62678511 1.78885438 2.38746728 1.51657509]
 [2.36643191 1.67332005 2.21359436 1.41421356]
 [2.77488739 1.67332005 2.58843582 1.41421356]
 [2.50998008 1.64316767 2.21359436 1.34164079]
 [2.58843582 1.81659021 2.38746728 1.44913767]
 [2.68328157 1.78885438 2.44948974 1.34164079]
 [2.48997992 1.67332005 2.19089023 1.34164079]
 [2.46981781 1.73205081 2.21359436 1.34164079]
 [2.52982213 1.67332005 2.36643191 1.44913767]
 [2.68328157 1.73205081 2.40831892 1.26491106]
 [2.7202941  1.67332005 2.46981781 1.37840488]
 [2.81069386 1.94935887 2.52982213 1.41421356]
 [2.52982213 1.67332005 2.36643191 1.4832397 ]
 [2.50998008 1.67332005 2.25831796 1.22474487]
 [2.46981781 1.61245155 2.36643191 1.18321596]
 [2.77488739 1.73205081 2.46981781 1.51657509]
 [2.50998008 1.84390889 2.36643191 1.54919334]
 [2.52982213 1.76068169 2.34520788 1.34164079]
 [2.44948974 1.73205081 2.19089023 1.34164079]
 [2.62678511 1.76068169 2.32379001 1.44913767]
 [2.58843582 1.76068169 2.36643191 1.54919334]
 [2.62678511 1.76068169 2.25831796 1.51657509]
 [2.40831892 1.64316767 2.25831796 1.37840488]
 [2.60768096 1.78885438 2.42899156 1.51657509]
 [2.58843582 1.81659021 2.38746728 1.58113883]
 [2.58843582 1.73205081 2.28035085 1.51657509]
 [2.50998008 1.58113883 2.23606798 1.37840488]
 [2.54950976 1.73205081 2.28035085 1.41421356]
 [2.48997992 1.84390889 2.32379001 1.51657509]
 [2.42899156 1.73205081 2.25831796 1.34164079]]

标准差：

# 分组求标准差
print('Setosa: ',np.std(np.array(Setosa), axis=0))
print('Versicolour: ',np.std(np.array(Versicolour), axis=0))
print('Virginica: ',np.std(np.array(Virginica), axis=0))

Setosa:  [0.34894699 0.37719491 0.17176728 0.10613199]
Versicolour:  [0.51098337 0.31064449 0.46518813 0.19576517]
Virginica:  [0.62948868 0.31925538 0.54634787 0.27188968]

方差：

# 分组求方差
print('Setosa: ',np.var(np.array(Setosa), axis=0))
print('Versicolour: ',np.var(np.array(Versicolour), axis=0))
print('Virginica: ',np.var(np.array(Virginica), axis=0))

Setosa:  [0.121764 0.142276 0.029504 0.011264]
Versicolour:  [0.261104 0.0965   0.2164   0.038324]
Virginica:  [0.396256 0.101924 0.298496 0.073924]

协方差：

# 分组求协方差
print('Setosa: ',np.cov(np.mean(np.array(Setosa), axis=0)))
print('Versicolour: ',np.cov(np.mean(np.array(Versicolour), axis=0)))
print('Virginica: ',np.cov(np.mean(np.array(Virginica), axis=0)))

Setosa:  4.427078666666667
Versicolour:  3.916518666666666
Virginica:  4.576966666666664

绘图操作

# 散点图
ax = Setosa.plot.scatter(x='slength', y='swidth', color='tab:blue', label='Calyx');
Setosa.plot.scatter(x='plength', y='pwidth', color='tab:orange', label='Petal', ax=ax);
plt.xlabel('$Length$');
plt.ylabel('$Width$');
plt.title('$Setosa$');

ax = Versicolour.plot.scatter(x='slength', y='swidth', color='tab:blue', label='Calyx');
Versicolour.plot.scatter(x='plength', y='pwidth', color='tab:orange', label='Petal', ax=ax);
plt.xlabel('$Length$');
plt.ylabel('$Width$');
plt.title('$Versicolour$');

ax = Virginica.plot.scatter(x='slength', y='swidth', color='tab:blue', label='Calyx');
Virginica.plot.scatter(x='plength', y='pwidth', color='tab:orange', label='Petal', ax=ax);
plt.xlabel('$Length$');
plt.ylabel('$Width$');
plt.title('$Virginica$');

图示：

# 直方图
plt.bar([1,2,3,4],np.mean(np.array(Setosa), axis=0),label='Setosa');
plt.bar([8,9,10,11],np.mean(np.array(Versicolour), axis=0),label='Versicolour');
plt.bar([15,16,17,18],np.mean(np.array(Virginica), axis=0),label='Virginica');
plt.legend();
plt.xticks((1,2,3,4,8,9,10,11,15,16,17,18),('sl','sw','pl','pw','sl','sw','pl','pw','sl','sw','pl','pw'));
plt.title('The different kinds of mean in three kinds of flowers');

图示：

# 盒图
blt = plt.boxplot(np.array(Setosa), notch=False, sym='o',vert=True, patch_artist=True);
colors = ['pink', 'lightblue', 'lightgreen']
for pacthes, color in zip(bplt['boxes'], colors):
    pacthes.set_facecolor(color)
    
plt.xticks((1,2,3,4),('slength','swidth','plength','pwidth'))
plt.title('Setosa')
plt.show()

blt = plt.boxplot(np.array(Versicolour), notch=False, sym='o',vert=True, patch_artist=True);
colors = ['pink', 'lightblue', 'lightgreen']
for pacthes, color in zip(bplt['boxes'], colors):
    pacthes.set_facecolor(color)
    
plt.xticks((1,2,3,4),('slength','swidth','plength','pwidth'))
plt.title('Versicolour')
plt.show()

blt = plt.boxplot(np.array(Virginica), notch=False, sym='o',vert=True, patch_artist=True);
colors = ['pink', 'lightblue', 'lightgreen']
for pacthes, color in zip(bplt['boxes'], colors):
    pacthes.set_facecolor(color)
    
plt.xticks((1,2,3,4),('slength','swidth','plength','pwidth'))
plt.title('Virginica')
plt.show()

图示：