softmax（多分类算法）实践

深藏阁楼爱情的钟 2022-03-09 03:14 313阅读 0赞

1.训练集规模：

![20190312103045104.png][]

数据（第一行为维度，每个字段的名字）：

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzI4Mjg2MDI3_size_16_color_FFFFFF_t_70][]

第二行为具体真是样本数据：第一列是标签，后面是特征（0-9的数字识别）

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzI4Mjg2MDI3_size_16_color_FFFFFF_t_70 1][]

样本格式（10分类，每个类别的样本数较均匀）：

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzI4Mjg2MDI3_size_16_color_FFFFFF_t_70 2][]

图像：28\*28：

![20190312103811275.png][]

softmax代码：

\# encoding=utf8

import sys  
import math  
import pandas as pd  
import numpy as np  
import random

from sklearn.model\_selection import train\_test\_split  
from sklearn.metrics import accuracy\_score

class Softmax(object):

def \_\_init\_\_(self):  
        self.learning\_step = 0.000001           \# 学习速率  
        self.max\_iteration = 1000             \# 最大迭代次数  
        self.weight\_lambda = 0.01               \# 衰退权重

def cal\_e(self,x,l):  
        theta\_l = self.w\[l\]  
        product = np.dot(theta\_l,x)

return math.exp(product)

def cal\_probability(self,x,j):  
        molecule = self.cal\_e(x,j)  
        denominator = sum(\[self.cal\_e(x,i) for i in range(self.k)\])

return molecule/denominator

def cal\_partial\_derivative(self,x,y,j):  
        first = int(y==j)                           \# 计算示性函数  
        second = self.cal\_probability(x,j)          \# 计算后面那个概率

\#return -x\*(first-second)  
        \#return -x\*(first-second) + self.weight\_lambda\*abs(self.w\[j\])  
        \#return -x\*(first-second) + self.weight\_lambda\*self.w\[j\]\*self.w\[j\]  
        return -x\*(first-second) + self.weight\_lambda\*self.w\[j\]\*self.w\[j\] + self.weight\_lambda\*abs(self.w\[j\])

def predict\_(self, x):  
        result = np.dot(self.w,x)  
        row, column = result.shape

\# 找最大值所在的列  
        \_positon = np.argmax(result)  
        m, n = divmod(\_positon, column)

return m

def train(self, features, labels):  
        self.k = len(set(labels))

self.w = np.zeros((self.k,len(features\[0\])+1))

time = 0

while time < self.max\_iteration:  
            print('loop %d' % time)  
            time += 1  
            index = random.randint(0, len(labels) - 1)

x = features\[index\]  
            y = labels\[index\]

x = list(x)  
            x.append(1.0)  
            x = np.array(x)

derivatives = \[self.cal\_partial\_derivative(x,y,j) for j in range(self.k)\]

for j in range(self.k):  
                self.w\[j\] -= self.learning\_step \* derivatives\[j\]

def predict(self,features):  
        labels = \[\]  
        for feature in features:  
            x = list(feature)  
            x.append(1)

x = np.matrix(x)  
            x = np.transpose(x)

labels.append(self.predict\_(x))  
        return labels

if \_\_name\_\_ == '\_\_main\_\_':

print('Start read data')

raw\_data = pd.read\_csv('./train.csv', header=0)  
    data = raw\_data.values

imgs = data\[0::, 1::\]  
    labels = data\[::, 0\]

\# 选取 2/3 数据作为训练集， 1/3 数据作为测试集  
    train\_features, test\_features, train\_labels, test\_labels = train\_test\_split(  
        imgs, labels, test\_size=0.33, random\_state=1)  
    print train\_features.shape  
    print test\_features.shape

print('Start training')  
    p = Softmax()  
    p.train(train\_features, train\_labels)

print('Start predicting')  
    test\_predict = p.predict(test\_features)

print p.w.shape  
    \#print p.w\[0\]

score = accuracy\_score(test\_labels, test\_predict)  
    print("The accruacy socre is " + str(score))

执行：

![20190312112449535.png][]

结果：![20190312112459922.png][]

[20190312103045104.png]: /images/20220309/a9df4c2e95b546108c6502d0533502d0.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzI4Mjg2MDI3_size_16_color_FFFFFF_t_70]: /images/20220309/19fd563705a441c7a3fafb4df3b57baa.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzI4Mjg2MDI3_size_16_color_FFFFFF_t_70 1]: /images/20220309/c3a432c79dee43838799b30dcec67f14.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzI4Mjg2MDI3_size_16_color_FFFFFF_t_70 2]: /images/20220309/89d20cf817034152a95c85a77ca069fd.png
[20190312103811275.png]: /images/20220309/0ad013e722bd4546bea5cb2f7b127e11.png
[20190312112449535.png]: /images/20220309/1cc90bbf3c964b9ba3d3c669761fa365.png
[20190312112459922.png]: /images/20220309/b63c9a2858a94512a8e12c50a2076457.png