logistics二分类

binaryclassification

#DATASET: https://archive.ics.uci.edu/ml/datasets/Glass+Identification
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import sklearn 
import sklearn.preprocessing as pre

df=pd.read_csv('dataglassiglass.data')
df.head()

	id	RI	Na	Mg	Al	Si	K	Ca	Ba	Fe	class
0	1	1.52101	13.64	4.49	1.10	71.78	0.06	8.75	0.0	0.0	1
1	2	1.51761	13.89	3.60	1.36	72.73	0.48	7.83	0.0	0.0	1
2	3	1.51618	13.53	3.55	1.54	72.99	0.39	7.78	0.0	0.0	1
3	4	1.51766	13.21	3.69	1.29	72.61	0.57	8.22	0.0	0.0	1
4	5	1.51742	13.27	3.62	1.24	73.08	0.55	8.07	0.0	0.0	1

X,y=df.iloc[:,1:-1],df.iloc[:,-1]
X,y=np.array(X),np.array(y)

#change the value the element

for idx,class_name in enumerate(sorted(list(set(y)))):
y[y==class_name]=idx

y

array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
       4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
       5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], dtype=int64)

#make the matrix's elements 2 value
#if element doesn't equals to 1 then make it 0
#'1' stands for the '2' class

for i in range(len(y)):
    if y[i]!=1:
        y[i]=0

#split our training dataset randomly

from sklearn.model_selection import train_test_split
X_train,X_test,y_train,y_test=train_test_split(X,y,test_size=0.15,random_state=44)

X_train.shape,y_train.shape,X_test.shape,y_test.shape

((181, 9), (181,), (33, 9), (33,))

f_mean=np.mean(X_train,axis=0)
f_std=np.std(X_train,axis=0)
f_mean,f_std

(array([1.51832884e+00, 1.33736464e+01, 2.69287293e+00, 1.46425414e+00,
        7.26391160e+01, 5.17016575e-01, 8.95314917e+00, 1.71104972e-01,
        6.02762431e-02]),
 array([0.00300427, 0.79769555, 1.42353328, 0.49169919, 0.77056863,
        0.69105168, 1.42892902, 0.5002639 , 0.10131419]))

#standardize training set

X_train=(X_train-f_mean)/f_std
X_test=(X_test-f_mean)/f_std

theta = np.zeros((X_train.shape[1] + 1))
theta.shape

(10,)

#add constant parameter

X_train = np.concatenate((np.ones((X_train.shape[0], 1)), X_train), axis=1)
X_test = np.concatenate((np.ones((X_test.shape[0], 1)), X_test), axis=1)
X_train.shape,X_test.shape,theta.shape

((181, 10), (33, 10), (10,))

#initialize the parameter

np.random.seed(42)
theta = np.random.rand(*theta.shape)
theta

array([0.37454012, 0.95071431, 0.73199394, 0.59865848, 0.15601864,
       0.15599452, 0.05808361, 0.86617615, 0.60111501, 0.70807258])

#cross_entropy_loss: loss function
#h: hypothesis function
#gradient: gradient function

num_epoch=500000
for epoch in range(num_epoch):
    logist = np.dot(X_train, theta)
    h = 1 / (1 + np.exp(-logist))
    cross_entropy_loss = (-y_train * np.log(h) - (1 - y_train) * np.log(1 - h)).mean()
    gradient = np.dot((h - y_train), X_train) / y_train.size
    theta = theta -  0.01*gradient
    if epoch%100000==0:
        print('Epoch={}	Loss={}'.format(epoch,cross_entropy_loss))

Epoch=0	Loss=0.9770836920534414
Epoch=100000	Loss=0.5884129057196792
Epoch=200000	Loss=0.5828823869347305
Epoch=300000	Loss=0.5798937167992417
Epoch=400000	Loss=0.5782071252958373

h_test = 1 / (1 + np.exp(-np.dot(X_test, theta)))

#accurancy
((h_test > 0.5) == y_test).sum() / y_test.size

0.8484848484848485