【Python机器学习】实验04 多分类实践(基于逻辑回归)3-阿里云开发者社区

【Python机器学习】实验04 多分类实践(基于逻辑回归)3

2023-10-12 57

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简介： 【Python机器学习】实验04 多分类实践(基于逻辑回归)3

2. 训练数据的准备

data=np.insert(data_x,data_x.shape[1],data_y,axis=1)

data=pd.DataFrame(data,columns=["F1","F2","F3","F4","F5","F6","target"])
data

	F1	F2	F3	F4	F5	F6	target
0	2.116632	7.972800	-9.328969	-8.224605	-12.178429	5.498447	2.0

1	1.886449	4.621006	2.841595	0.431245	-2.471350	2.507833	0.0
2	2.391329	6.464609	-9.805900	-7.289968	-9.650985	6.388460	2.0

3	-1.034776	6.626886	9.031235	-0.812908	5.449855	0.134062	1.0
4	-0.481593	8.191753	7.504717	-1.975688	6.649021	0.636824	1.0
...	...	...	...	...	...	...	...

195	5.434893	7.128471	9.789546	6.061382	0.634133	5.757024	3.0
196	-0.406625	7.586001	9.322750	-1.837333	6.477815	-0.992725	1.0

197	2.031462	7.804427	-8.539512	-9.824409	-10.046935	6.918085	2.0
198	4.081889	6.127685	11.091126	4.812011	-0.005915	5.342211	3.0

199

0.985744

7.285737

-8.395940

-6.586471

-9.651765

6.651012

2.0

200 rows × 7 columns

data["target"]=data["target"].astype("int32")

data

	F1	F2	F3	F4	F5	F6	target
0	2.116632	7.972800	-9.328969	-8.224605	-12.178429	5.498447	2

1	1.886449	4.621006	2.841595	0.431245	-2.471350	2.507833	0
2	2.391329	6.464609	-9.805900	-7.289968	-9.650985	6.388460	2

3	-1.034776	6.626886	9.031235	-0.812908	5.449855	0.134062	1
4	-0.481593	8.191753	7.504717	-1.975688	6.649021	0.636824	1

...	...	...	...	...	...	...	...
195	5.434893	7.128471	9.789546	6.061382	0.634133	5.757024	3

196	-0.406625	7.586001	9.322750	-1.837333	6.477815	-0.992725	1
197	2.031462	7.804427	-8.539512	-9.824409	-10.046935	6.918085	2

198	4.081889	6.127685	11.091126	4.812011	-0.005915	5.342211	3
199	0.985744	7.285737	-8.395940	-6.586471	-9.651765	6.651012	2

200 rows × 7 columns

data.insert(0,"ones",1)

data

	ones	F1	F2	F3	F4	F5	F6	target
0	1	2.116632	7.972800	-9.328969	-8.224605	-12.178429	5.498447	2
1	1	1.886449	4.621006	2.841595	0.431245	-2.471350	2.507833	0

2	1	2.391329	6.464609	-9.805900	-7.289968	-9.650985	6.388460	2
3	1	-1.034776	6.626886	9.031235	-0.812908	5.449855	0.134062	1

4	1	-0.481593	8.191753	7.504717	-1.975688	6.649021	0.636824	1
...	...	...	...	...	...	...	...	...
195	1	5.434893	7.128471	9.789546	6.061382	0.634133	5.757024	3

196	1	-0.406625	7.586001	9.322750	-1.837333	6.477815	-0.992725	1
197	1	2.031462	7.804427	-8.539512	-9.824409	-10.046935	6.918085	2

198	1	4.081889	6.127685	11.091126	4.812011	-0.005915	5.342211	3
199	1	0.985744	7.285737	-8.395940	-6.586471	-9.651765	6.651012	2

200 rows × 8 columns

#第一个类别的数据
data1=data.copy()
data1.loc[data["target"]==0,"target"]=1
data1.loc[data["target"]!=0,"target"]=0
data1

	ones	F1	F2	F3	F4	F5	F6	target
0	1	2.116632	7.972800	-9.328969	-8.224605	-12.178429	5.498447	0
1	1	1.886449	4.621006	2.841595	0.431245	-2.471350	2.507833	1

2	1	2.391329	6.464609	-9.805900	-7.289968	-9.650985	6.388460	0
3	1	-1.034776	6.626886	9.031235	-0.812908	5.449855	0.134062	0

4	1	-0.481593	8.191753	7.504717	-1.975688	6.649021	0.636824	0
...	...	...	...	...	...	...	...	...
195	1	5.434893	7.128471	9.789546	6.061382	0.634133	5.757024	0

196	1	-0.406625	7.586001	9.322750	-1.837333	6.477815	-0.992725	0
197	1	2.031462	7.804427	-8.539512	-9.824409	-10.046935	6.918085	0

198	1	4.081889	6.127685	11.091126	4.812011	-0.005915	5.342211	0
199	1	0.985744	7.285737	-8.395940	-6.586471	-9.651765	6.651012	0

200 rows × 8 columns

data1_x=data1.iloc[:,:data1.shape[1]-1].values
data1_y=data1.iloc[:,data1.shape[1]-1].values
data1_x.shape,data1_y.shape

((200, 7), (200,))

#第二个类别的数据
data2=data.copy()
data2.loc[data["target"]==1,"target"]=1
data2.loc[data["target"]!=1,"target"]=0
data2

	ones	F1	F2	F3	F4	F5	F6	target
0	1	2.116632	7.972800	-9.328969	-8.224605	-12.178429	5.498447	0
1	1	1.886449	4.621006	2.841595	0.431245	-2.471350	2.507833	0

2	1	2.391329	6.464609	-9.805900	-7.289968	-9.650985	6.388460	0
3	1	-1.034776	6.626886	9.031235	-0.812908	5.449855	0.134062	1

4	1	-0.481593	8.191753	7.504717	-1.975688	6.649021	0.636824	1
...	...	...	...	...	...	...	...	...
195	1	5.434893	7.128471	9.789546	6.061382	0.634133	5.757024	0

196	1	-0.406625	7.586001	9.322750	-1.837333	6.477815	-0.992725	1
197	1	2.031462	7.804427	-8.539512	-9.824409	-10.046935	6.918085	0

198	1	4.081889	6.127685	11.091126	4.812011	-0.005915	5.342211	0
199	1	0.985744	7.285737	-8.395940	-6.586471	-9.651765	6.651012	0

200 rows × 8 columns

data2_x=data2.iloc[:,:data2.shape[1]-1].values
data2_y=data2.iloc[:,data2.shape[1]-1].values

#第三个类别的数据
data3=data.copy()
data3.loc[data["target"]==2,"target"]=1
data3.loc[data["target"]!=2,"target"]=0
data3

	ones	F1	F2	F3	F4	F5	F6	target
0	1	2.116632	7.972800	-9.328969	-8.224605	-12.178429	5.498447	1
1	1	1.886449	4.621006	2.841595	0.431245	-2.471350	2.507833	0

2	1	2.391329	6.464609	-9.805900	-7.289968	-9.650985	6.388460	1
3	1	-1.034776	6.626886	9.031235	-0.812908	5.449855	0.134062	0

4	1	-0.481593	8.191753	7.504717	-1.975688	6.649021	0.636824	0
...	...	...	...	...	...	...	...	...
195	1	5.434893	7.128471	9.789546	6.061382	0.634133	5.757024	0

196	1	-0.406625	7.586001	9.322750	-1.837333	6.477815	-0.992725	0
197	1	2.031462	7.804427	-8.539512	-9.824409	-10.046935	6.918085	1

198	1	4.081889	6.127685	11.091126	4.812011	-0.005915	5.342211	0
199	1	0.985744	7.285737	-8.395940	-6.586471	-9.651765	6.651012	1

200 rows × 8 columns

data3_x=data3.iloc[:,:data3.shape[1]-1].values
data3_y=data3.iloc[:,data3.shape[1]-1].values

#第四个类别的数据
data4=data.copy()
data4.loc[data["target"]==3,"target"]=1
data4.loc[data["target"]!=3,"target"]=0
data4

	ones	F1	F2	F3	F4	F5	F6	target
0	1	2.116632	7.972800	-9.328969	-8.224605	-12.178429	5.498447	0
1	1	1.886449	4.621006	2.841595	0.431245	-2.471350	2.507833	0

2	1	2.391329	6.464609	-9.805900	-7.289968	-9.650985	6.388460	0
3	1	-1.034776	6.626886	9.031235	-0.812908	5.449855	0.134062	0

4	1	-0.481593	8.191753	7.504717	-1.975688	6.649021	0.636824	0
...	...	...	...	...	...	...	...	...
195	1	5.434893	7.128471	9.789546	6.061382	0.634133	5.757024	1

196	1	-0.406625	7.586001	9.322750	-1.837333	6.477815	-0.992725	0
197	1	2.031462	7.804427	-8.539512	-9.824409	-10.046935	6.918085	0

198	1	4.081889	6.127685	11.091126	4.812011	-0.005915	5.342211	1
199	1	0.985744	7.285737	-8.395940	-6.586471	-9.651765	6.651012	0

200 rows × 8 columns

data4_x=data4.iloc[:,:data4.shape[1]-1].values
data4_y=data4.iloc[:,data4.shape[1]-1].values

3. 定义假设函数、代价函数和梯度下降算法

def sigmoid(z):
    return 1 / (1 + np.exp(-z))

def h(X,w):
    z=X@w
    h=sigmoid(z)
    return h

#代价函数构造
def cost(X,w,y):
    #当X(m,n+1),y(m,),w(n+1,1)
    y_hat=sigmoid(X@w)
    right=np.multiply(y.ravel(),np.log(y_hat).ravel())+np.multiply((1-y).ravel(),np.log(1-y_hat).ravel())
    cost=-np.sum(right)/X.shape[0]
    return cost

def grandient(X,y,iter_num,alpha):
    y=y.reshape((X.shape[0],1))
    w=np.zeros((X.shape[1],1))
    cost_lst=[]  
    for i in range(iter_num):
        y_pred=h(X,w)-y
        temp=np.zeros((X.shape[1],1))
        for j in range(X.shape[1]):
            right=np.multiply(y_pred.ravel(),X[:,j])
            gradient=1/(X.shape[0])*(np.sum(right))
            temp[j,0]=w[j,0]-alpha*gradient
        w=temp
        cost_lst.append(cost(X,w,y.ravel()))
    return w,cost_lst

4. 学习这四个分类模型

import matplotlib.pyplot as plt

#初始化超参数
iter_num,alpha=600000,0.001

#训练第1个模型
w1,cost_lst1=grandient(data1_x,data1_y,iter_num,alpha)

plt.plot(range(iter_num),cost_lst1,"b-o")

[<matplotlib.lines.Line2D at 0x25624eb08e0>]

#训练第2个模型
w2,cost_lst2=grandient(data2_x,data2_y,iter_num,alpha)
plt.plot(range(iter_num),cost_lst2,"b-o")

[<matplotlib.lines.Line2D at 0x25631b87a60>]

#训练第3个模型
w3,cost_lst3=grandient(data3_x,data3_y,iter_num,alpha)
plt.plot(range(iter_num),cost_lst3,"b-o")

[<matplotlib.lines.Line2D at 0x2562bcdfac0>]

#训练第4个模型
w4,cost_lst4=grandient(data4_x,data4_y,iter_num,alpha)
plt.plot(range(iter_num),cost_lst4,"b-o")

[<matplotlib.lines.Line2D at 0x25631ff4ee0>]

5. 利用模型进行预测

data_x

array([[ 2.11663151e+00,  7.97280013e+00, -9.32896918e+00,
        -8.22460526e+00, -1.21784287e+01,  5.49844655e+00],
       [ 1.88644899e+00,  4.62100554e+00,  2.84159548e+00,
         4.31244563e-01, -2.47135027e+00,  2.50783257e+00],
       [ 2.39132949e+00,  6.46460915e+00, -9.80590050e+00,
        -7.28996786e+00, -9.65098460e+00,  6.38845956e+00],
       ...,
       [ 2.03146167e+00,  7.80442707e+00, -8.53951210e+00,
        -9.82440872e+00, -1.00469351e+01,  6.91808489e+00],
       [ 4.08188906e+00,  6.12768483e+00,  1.10911262e+01,
         4.81201082e+00, -5.91530191e-03,  5.34221079e+00],
       [ 9.85744105e-01,  7.28573657e+00, -8.39593964e+00,
        -6.58647097e+00, -9.65176507e+00,  6.65101187e+00]])

data_x=np.insert(data_x,0,1,axis=1)

data_x.shape

(200, 7)

w3.shape

(7, 1)

multi_pred=pd.DataFrame(zip(h(data_x,w1).ravel(),h(data_x,w2).ravel(),h(data_x,w3).ravel(),h(data_x,w4).ravel()))
multi_pred

	0	1	2	3
0	0.020436	4.556248e-15	9.999975e-01	2.601227e-27
1	0.820488	4.180906e-05	3.551499e-05	5.908691e-05

2	0.109309	7.316201e-14	9.999978e-01	7.091713e-24
3	0.036608	9.999562e-01	1.048562e-09	5.724854e-03

4	0.003075	9.999292e-01	2.516742e-09	6.423038e-05
...	...	...	...	...
195	0.017278	3.221293e-06	3.753372e-14	9.999943e-01

196	0.003369	9.999966e-01	6.673394e-10	2.281428e-03
197	0.000606	1.118174e-13	9.999941e-01	1.780212e-28

198	0.013072	4.999118e-05	9.811154e-14	9.996689e-01
199	0.151548	1.329623e-13	9.999447e-01	2.571989e-24

200 rows × 4 columns

6. 计算准确率

np.sum(np.argmax(multi_pred.values,axis=1)==data_y.ravel())/len(data)

1.0

【Python机器学习】实验04 多分类实践(基于逻辑回归)3

2. 训练数据的准备

3. 定义假设函数、代价函数和梯度下降算法

4. 学习这四个分类模型

5. 利用模型进行预测

6. 计算准确率

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