Ml (machine learning) softmax function to realize the classification of simple movie categories

I'll share a wave with you softmax function . The expression is as follows ：

y = exp(input_data) / sum(exp(input_data))

A brief explanation , Is to index the input data , Then divide by the sum of the input data after indexation .

The code implementation is as follows ：

import numpy as np
import matplotlib.pyplot as plt
import os
import time

def softmax(inx):
    exp_input = np.exp(inx)
    sum_exp = np.sum(exp_input)
    y = exp_input / sum_exp
    print(y)

if __name__ == '__main__':
    inx = np.array([0.2,3,10])
    softmax(inx)

Running results ：

Let's change to a larger data input , Find the following problems ：

if __name__ == '__main__':
    inx = np.array([1000,5000,10000])
    softmax(inx)

In order to solve the problem of large input data nan Value problem （ Value overflow ）, Introduce a constant C, The expression becomes ：
y = exp(input_data)*C / sum(exp(input_data))*C
take C Move in , obtain y = exp(input_data+log（C）) / sum(exp(input_data+log（C）))
Make θ = log（C）, be y = exp(input_data+θ) / sum(exp(input_data+θ)).
here , because θ You can choose any value , However, in order to prevent numerical overflow ,θ Value will be selected input_data Maximum of , And because θ The value itself is a large positive number , therefore , We need to θ The value becomes negative , Introduce bias b=-θ
that , The final expression can be written as y = exp(input_data+b) / sum(exp(input_data+b))[ When θ Positive number ].

that , The above code is modified to ：

import numpy as np
import matplotlib.pyplot as plt
import os
import time

def softmax(inx):
    theta = np.max(inx)
    b = -theta# bias 
    exp_input = np.exp(inx+b)
    sum_exp = np.sum(exp_input)
    y = exp_input / sum_exp
    print(y)

if __name__ == '__main__':
    inx = np.array([1000,5000,10000])
    softmax(inx)

Running results ：

For our convenience, we will call softmax(inx) function , modify print by return, Here's the picture ：



We find that this calculation result is very similar to probability , The sum is 1（ Because of the accuracy error of the computer itself , So it's not 1）. therefore , We can use softmax(inx) Function calculation probability ,softmax(inx) Function can be used in machine learning classification problems .

I use softmax(inx) Function implements a simple binary classification problem . The data set I set is as follows ：

def Data_load():
    dataset = {
    
        " Action movies ":{
    " The fight scenes ":105," Kissing scene ":15},
        " Love story ":{
    " The fight scenes ":5," Kissing scene ":85}
    }
    return  dataset
    
def classification(dataset):
    DataSet = Data_load()
    labels = [k for k in DataSet.keys()]  # [' Action movies ',' Love story ']
    result_array = softmax(dataset)
    result_ls = list(result_array)
    # print(result_ls)
    Max = max(result_ls)
    Max_Index = result_ls.index(Max)
    # print(Max_Index)
    movie = labels[Max_Index]
    print(' The film is :', movie)
    
if __name__ == '__main__':
    # testset = np.array([14,37])# Test set 
    # testset2 = np.array([78,15])
    # classification(testset)
    # classification(testset2)
    testset_ls = [np.array([78,15]),np.array([14,37]),np.array([57,21]),np.array([31,87])
                  ,np.array([23,65]),np.array([26,73])]
    for testset in testset_ls:
        classification(testset)

Running results ：

In this way, we have completed the simple two classification according to our needs .

Last , Thank you for coming to watch my article , There may be many inadequacies in the text , I also hope to point out and sea culvert .