這是西瓜書第一道實踐題，感覺書裡對於原理講解過於生硬，有點難以理解，所以我更多採用從andrew ng的深度學習中學到的logistic regression來描述
資料如下
編號密度
糖分好瓜
00.697
0.46011
0.774
0.37612
0.634
0.26413
0.608
0.31814
0.556
0.21515
0.403
0.23716
0.481
0.14917
0.437
0.21118
0.666
0.09109
0.243
0.267010
0.245
0.057011
0.343
0.099012
0.639
0.161013
0.657
0.198014
0.360
0.370015
0.593
0.042016
0.719
0.103
0
import pandas as pd
import numpy as np
from sklearn.model_selection import train_test_split
df = pd.
dataframe()
x= df[
['midu'
,'tang']]
.values
y = df[
'hao'
].values
#為了使資料形式符合需要演示需要，將其進行轉置x=
x.reshape([
2,17]
)y = y.
reshape([
1,17]
)
'''
initialize parameter
'''def init_params()
: #根據x資料的形狀來確定生成w和b
w = np.random.
randn(2
,1) b =
0return w, b
'''sigmoid activation func
'''def sigmoid(z
):s =1/
(1+np.
exp(-z
))return s
由cost func對w 和b分別求導:
∂ j∂
w=1m
x(a−
y)
t(7)
\frac = \fracx(a-y)^t\tag
∂w∂j=
m1x
(a−y
)t(7)∂j
∂b=1
m∑i=
1m(a
(i)−
y(i)
)(8)
\frac = \frac \sum_^m (a^-y^)\tag
∂b∂j=
m1i
=1∑m
(a(
i)−y
(i))(8)
'''
forward prop and compute cost and back prop
'''def f_prop
(w, b,
x, y)
: m =
x.shape[
1]#一共有m個例項
a=sigmoid
(np.
dot(w.t,
x)+ b)
#計算cost函式
cost =-1
/m * np.
sum(y*np.
log(a)
+(1-y)
*np.
log(1-
a)) #對w和b求導數
dw =
1/m * np.
dot(x,
(a-y).t)
db =
1/m * np.
sum(
a- y)
#組合到乙個字典
grads =
return cost, grads
'''optimize parameters--gradient descent
'''def op_params
(w, b,
x, y, num_iter, learning_rate)
: costs =
for i in
range
(num_iter)
: cost ,grads =
f_prop
(w, b,
x, y)
dw = grads[
'dw'
] db = grads[
'db'
] #引數最優化
w = w - learning_rate * dw
b = b - learning_rate * db
costs.
(cost)
params =
return costs, params
'''
predict
'''def predict
(params,x)
: m =
x.shape[1]
y_prediction = np.
zeros((
1,m)
)
w = params[
'w']
b = params[
'b']a=
sigmoid
(np.
dot(w.t,
x)+b)
#大於0.5就是真，小於等於0.5就是假
for i in
range
(m):ifa
[0, i]
>
0.5:
y_prediction[
0, i]=1
ifa[0
, i]
<=
0.5:
y_prediction[
0, i]=0
return y_prediction
%matplotlib notebook
import matplotlib.pyplot as plt
'''merge all the func
'''w, b =
init_params()
cost, grads =
f_prop
(w, b,
x, y)
costs, params =
op_params
(w, b,
x, y,
1000
,0.9
)plt.
plot
(costs)
'''
make prediction
'''y_prediction =
predict
(params,x)
count =
0for i in
range(x
.shape[1]
):if y_perdiction[
0, i]
== y[
0, i]
: count +=
1precision = count/
x.shape[1]
print
('準確率是：'
,precision)
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