數據集
- 數據集 ：ris鳶尾花數據集，它包含3個不同品種的鳶尾花：[Setosa，Versicolour，and Virginica]數據，特征：[‘sepal length’, ‘sepal width’, ‘petal length’, ‘petal width’],一共150個數據。由于這是2分類問題，所以選擇前兩類數據進行算法測試。
代碼實現
import
numpy
as
np
import
pandas
as
pd
from
sklearn
.
datasets
import
load_iris
from
sklearn
.
model_selection
import
train_test_split
import
matplotlib
.
pyplot
as
plt
#加載數據
def
create_data
(
)
:
iris
=
load_iris
(
)
#選取前兩類作為數據
Data
=
np
.
array
(
iris
[
"data"
]
)
[
:
100
]
Label
=
np
.
array
(
iris
[
"target"
]
)
[
:
100
]
Label
=
Label
*
2
-
1
print
(
"dara shape:"
,
Data
.
shape
)
print
(
"label shape:"
,
Label
.
shape
)
return
Data
,
Label
class
SVM
:
def
__init__
(
self
,
max_iter
=
100
,
kernel
=
'linear'
)
:
self
.
max_iter
=
max_iter
self
.
_kernel
=
kernel
#參數初始化
def
init_args
(
self
,
features
,
labels
)
:
self
.
m
,
self
.
n
=
features
.
shape
self
.
X
=
features
self
.
Y
=
labels
self
.
b
=
0.0
self
.
alpha
=
np
.
ones
(
self
.
m
)
self
.
computer_product_matrix
(
)
#為了加快訓練速度創建一個內積矩陣
# 松弛變量
self
.
C
=
1.0
# 將Ei保存在一個列表里
self
.
create_E
(
)
#KKT條件判斷
def
judge_KKT
(
self
,
i
)
:
y_g
=
self
.
function_g
(
i
)
*
self
.
Y
[
i
]
if
self
.
alpha
[
i
]
==
0
:
return
y_g
>=
1
elif
0
<
self
.
alpha
[
i
]
<
self
.
C
:
return
y_g
==
1
else
:
return
y_g
<=
1
#計算內積矩陣#如果數據量較大，可以使用系數矩陣
def
computer_product_matrix
(
self
)
:
self
.
product_matrix
=
np
.
zeros
(
(
self
.
m
,
self
.
m
)
)
.
astype
(
np
.
float
)
for
i
in
range
(
self
.
m
)
:
for
j
in
range
(
self
.
m
)
:
if
self
.
product_matrix
[
i
]
[
j
]
==
0.0
:
self
.
product_matrix
[
i
]
[
j
]
=
self
.
product_matrix
[
j
]
[
i
]
=
self
.
kernel
(
self
.
X
[
i
]
,
self
.
X
[
j
]
)
# 核函數
def
kernel
(
self
,
x1
,
x2
)
:
if
self
.
_kernel
==
'linear'
:
return
np
.
dot
(
x1
,
x2
)
elif
self
.
_kernel
==
'poly'
:
return
(
np
.
dot
(
x1
,
x2
)
+
1
)
**
2
return
0
#將Ei保存在一個列表里
def
create_E
(
self
)
:
self
.
E
=
(
np
.
dot
(
(
self
.
alpha
*
self
.
Y
)
,
self
.
product_matrix
)
+
self
.
b
)
-
self
.
Y
# 預測函數g(x)
def
function_g
(
self
,
i
)
:
return
self
.
b
+
np
.
dot
(
(
self
.
alpha
*
self
.
Y
)
,
self
.
product_matrix
[
i
]
)
#選擇變量
def
select_alpha
(
self
)
:
# 外層循環首先遍歷所有滿足0
index_list
=
[
i
for
i
in
range
(
self
.
m
)
if
0
<
self
.
alpha
[
i
]
<
self
.
C
]
# 否則遍歷整個訓練集
non_satisfy_list
=
[
i
for
i
in
range
(
self
.
m
)
if
i
not
in
index_list
]
index_list
.
extend
(
non_satisfy_list
)
for
i
in
index_list
:
if
self
.
judge_KKT
(
i
)
:
continue
E1
=
self
.
E
[
i
]
# 如果E2是+，選擇最小的；如果E2是負的，選擇最大的
if
E1
>=
0
:
j
=
np
.
argmin
(
self
.
E
)
else
:
j
=
np
.
argmax
(
self
.
E
)
return
i
,
j
#剪切
def
clip_alpha
(
self
,
_alpha
,
L
,
H
)
:
if
_alpha
>
H
:
return
H
elif
_alpha
<
L
:
return
L
else
:
return
_alpha
#訓練函數，使用SMO算法
def
Train
(
self
,
features
,
labels
)
:
self
.
init_args
(
features
,
labels
)
#SMO算法訓練
for
t
in
range
(
self
.
max_iter
)
:
i1
,
i2
=
self
.
select_alpha
(
)
# 邊界
if
self
.
Y
[
i1
]
==
self
.
Y
[
i2
]
:
L
=
max
(
0
,
self
.
alpha
[
i1
]
+
self
.
alpha
[
i2
]
-
self
.
C
)
H
=
min
(
self
.
C
,
self
.
alpha
[
i1
]
+
self
.
alpha
[
i2
]
)
else
:
L
=
max
(
0
,
self
.
alpha
[
i2
]
-
self
.
alpha
[
i1
]
)
H
=
min
(
self
.
C
,
self
.
C
+
self
.
alpha
[
i2
]
-
self
.
alpha
[
i1
]
)
E1
=
self
.
E
[
i1
]
E2
=
self
.
E
[
i2
]
# eta=K11+K22-2K12
eta
=
self
.
kernel
(
self
.
X
[
i1
]
,
self
.
X
[
i1
]
)
+
self
.
kernel
(
self
.
X
[
i2
]
,
self
.
X
[
i2
]
)
-
2
*
self
.
kernel
(
self
.
X
[
i1
]
,
self
.
X
[
i2
]
)
if
eta
<=
0
:
# print('eta <= 0')
continue
alpha2_new_unc
=
self
.
alpha
[
i2
]
+
self
.
Y
[
i2
]
*
(
E1
-
E2
)
/
eta
# 此處有修改，根據書上應該是E1 - E2，書上130-131頁
alpha2_new
=
self
.
clip_alpha
(
alpha2_new_unc
,
L
,
H
)
alpha1_new
=
self
.
alpha
[
i1
]
+
self
.
Y
[
i1
]
*
self
.
Y
[
i2
]
*
(
self
.
alpha
[
i2
]
-
alpha2_new
)
b1_new
=
-
E1
-
self
.
Y
[
i1
]
*
self
.
kernel
(
self
.
X
[
i1
]
,
self
.
X
[
i1
]
)
*
(
alpha1_new
-
self
.
alpha
[
i1
]
)
-
self
.
Y
[
i2
]
*
self
.
kernel
(
self
.
X
[
i2
]
,
self
.
X
[
i1
]
)
*
(
alpha2_new
-
self
.
alpha
[
i2
]
)
+
self
.
b
b2_new
=
-
E2
-
self
.
Y
[
i1
]
*
self
.
kernel
(
self
.
X
[
i1
]
,
self
.
X
[
i2
]
)
*
(
alpha1_new
-
self
.
alpha
[
i1
]
)
-
self
.
Y
[
i2
]
*
self
.
kernel
(
self
.
X
[
i2
]
,
self
.
X
[
i2
]
)
*
(
alpha2_new
-
self
.
alpha
[
i2
]
)
+
self
.
b
if
0
<
alpha1_new
<
self
.
C
:
b_new
=
b1_new
elif
0
<
alpha2_new
<
self
.
C
:
b_new
=
b2_new
else
:
# 選擇中點
b_new
=
(
b1_new
+
b2_new
)
/
2
# 更新參數
self
.
alpha
[
i1
]
=
alpha1_new
self
.
alpha
[
i2
]
=
alpha2_new
self
.
b
=
b_new
self
.
create_E
(
)
#這里與書上不同，，我選擇更新全部E
def
predict
(
self
,
data
)
:
r
=
self
.
b
for
i
in
range
(
self
.
m
)
:
r
+=
self
.
alpha
[
i
]
*
self
.
Y
[
i
]
*
self
.
kernel
(
data
,
self
.
X
[
i
]
)
return
1
if
r
>
0
else
-
1
def
score
(
self
,
X_test
,
y_test
)
:
right_count
=
0
for
i
in
range
(
len
(
X_test
)
)
:
result
=
self
.
predict
(
X_test
[
i
]
)
if
result
==
y_test
[
i
]
:
right_count
+=
1
return
right_count
/
len
(
X_test
)
if
__name__
==
'__main__'
:
svm
=
SVM
(
max_iter
=
200
)
X
,
y
=
create_data
(
)
X_train
,
X_test
,
y_train
,
y_test
=
train_test_split
(
X
,
y
,
test_size
=
0.333
,
random_state
=
23323
)
svm
.
Train
(
X_train
,
y_train
)
print
(
svm
.
score
(
X_test
,
y_test
)
)
結果：
dara shape: (100, 4)
label shape: (100,)
0.9705882352941176
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