求解逻辑回归—-梯度下降

# 根据result把数据分为两类
positive = pdData[pdData['result'] == 1]  # 返回result为1的数据
negative = pdData[pdData['result'] == 0]# 设置图片大小，分辨率
fig, ax = plt.subplots(figsize=(20,8),dpi=80)
# 绘制散点图----s:标量，默认为20；c:散点颜色；marker:散点形状；label：标签
ax.scatter(positive['test1'], positive['test2'], s=30, c='b', marker='o', label='合格')
ax.scatter(negative['test1'], negative['test2'], s=30, c='r', marker='v', label='不合格')
# 设置图例
ax.legend(prop=my_font)
ax.set_xlabel('test1 Score')  # 横坐标
ax.set_ylabel('test2 Score')  # 纵坐标
# 展示图片
plt.show()

建立分类器
sigmoid函数：映射到概率的函数

sigmoid 函数介绍

def sigmoid(z):
    return 1/(1 + np.exp(-z))
# 画出sigmoid图
nums = np.arange(-10, 10, step=1)
# 生成-10到10的向量（含头不含尾），步进为1，即[-10,-9,...,8,9]print(nums)
fig, ax = plt.subplots(figsize=(12,4))
ax.plot(nums, sigmoid(nums), 'r')
plt.show()

[-10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7
   8   9]

model 函数: 返回预测结果值

def model(X,theta):
    return sigmoid(np.matmul(X,theta))
pdData.insert(0,'Ones',1)
pdData.head()
orig_data = pdData.as_matrix()
print(orig_data)
cols = orig_data.shape[1]print(cols)
X = orig_data[:,0:cols-1]y = orig_data[:,cols-1:cols]theta = np.zeros([cols-1,1])

[[  1.          30.28671077  43.89499752   0.        ] [  1.          35.84740877  72.90219803   0.        ] [  1.          60.18259939  86.3085521    1.        ] [  1.          79.03273605  75.34437644   1.        ] [  1.          45.08327748  56.31637178   0.        ] [  1.          61.10666454  96.51142588   1.        ] [  1.          75.02474557  46.55401354   1.        ] [  1.          76.0987867   87.42056972   1.        ] [  1.          84.43281996  43.53339331   1.        ] [  1.          95.86155507  38.22527806   0.        ] [  1.          75.01365839  30.60326323   0.        ] [  1.          82.30705337  76.4819633    1.        ] [  1.          69.36458876  97.71869196   1.        ] [  1.          39.53833914  76.03681085   0.        ] [  1.          53.97105215  89.20735014   1.        ] [  1.          69.07014406  52.74046973   1.        ] [  1.          67.94685548  46.67857411   0.        ] [  1.          70.66150955  92.92713789   1.        ] [  1.          76.97878373  47.57596365   1.        ] [  1.          67.37202755  42.83843832   0.        ] [  1.          89.67677575  65.79936593   1.        ] [  1.          50.53478829  48.85581153   0.        ] [  1.          34.21206098  44.2095286    0.        ] [  1.          77.92409145  68.97235999   1.        ] [  1.          62.27101367  69.95445795   1.        ] [  1.          80.19018075  44.82162893   1.        ] [  1.          93.1143888   38.80067034   0.        ] [  1.          61.83020602  50.25610789   0.        ] [  1.          38.7858038   64.99568096   0.        ] [  1.          61.37928945  72.80788731   1.        ] [  1.          85.40451939  57.05198398   1.        ] [  1.          52.10797973  63.12762377   0.        ] [  1.          52.04540477  69.43286012   1.        ] [  1.          40.23689374  71.16774802   0.        ] [  1.          54.63510555  52.21388588   0.        ] [  1.          33.91550011  98.86943574   0.        ] [  1.          64.17698887  80.90806059   1.        ] [  1.          74.78925296  41.57341523   0.        ] [  1.          34.18364003  75.23772034   0.        ] [  1.          83.90239366  56.30804622   1.        ] [  1.          51.54772027  46.85629026   0.        ] [  1.          94.44336777  65.56892161   1.        ] [  1.          82.36875376  40.61825516   0.        ] [  1.          51.04775177  45.82270146   0.        ] [  1.          62.22267576  52.06099195   0.        ] [  1.          77.19303493  70.4582       1.        ] [  1.          97.77159928  86.72782233   1.        ] [  1.          62.0730638   96.76882412   1.        ] [  1.          91.5649745   88.69629255   1.        ] [  1.          79.94481794  74.16311935   1.        ] [  1.          99.27252693  60.999031     1.        ] [  1.          90.54671411  43.39060181   1.        ] [  1.          34.52451385  60.39634246   0.        ] [  1.          50.28649612  49.80453881   0.        ] [  1.          49.58667722  59.80895099   0.        ] [  1.          97.64563396  68.86157272   1.        ] [  1.          32.57720017  95.59854761   0.        ] [  1.          74.24869137  69.82457123   1.        ] [  1.          71.79646206  78.45356225   1.        ] [  1.          75.39561147  85.75993667   1.        ] [  1.          35.28611282  47.02051395   0.        ] [  1.          56.2538175   39.26147251   0.        ] [  1.          30.05882245  49.59297387   0.        ] [  1.          44.66826172  66.45008615   0.        ] [  1.          66.56089447  41.09209808   0.        ] [  1.          40.45755098  97.53518549   1.        ] [  1.          49.07256322  51.88321182   0.        ] [  1.          80.27957401  92.11606081   1.        ] [  1.          66.74671857  60.99139403   1.        ] [  1.          32.72283304  43.30717306   0.        ] [  1.          64.03932042  78.03168802   1.        ] [  1.          72.34649423  96.22759297   1.        ] [  1.          60.45788574  73.0949981    1.        ] [  1.          58.84095622  75.85844831   1.        ] [  1.          99.8278578   72.36925193   1.        ] [  1.          47.26426911  88.475865     1.        ] [  1.          50.4581598   75.80985953   1.        ] [  1.          60.45555629  42.50840944   0.        ] [  1.          82.22666158  42.71987854   0.        ] [  1.          88.91389642  69.8037889    1.        ] [  1.          94.83450672  45.6943068    1.        ] [  1.          67.31925747  66.58935318   1.        ] [  1.          57.23870632  59.51428198   1.        ] [  1.          80.366756    90.9601479    1.        ] [  1.          68.46852179  85.5943071    1.        ] [  1.          42.07545454  78.844786     0.        ] [  1.          75.47770201  90.424539     1.        ] [  1.          78.63542435  96.64742717   1.        ] [  1.          52.34800399  60.76950526   0.        ] [  1.          94.09433113  77.15910509   1.        ] [  1.          90.44855097  87.50879176   1.        ] [  1.          55.48216114  35.57070347   0.        ] [  1.          74.49269242  84.84513685   1.        ] [  1.          89.84580671  45.35828361   1.        ] [  1.          83.48916274  48.3802858    1.        ] [  1.          42.26170081  87.10385094   1.        ] [  1.          99.31500881  68.77540947   1.        ] [  1.          55.34001756  64.93193801   1.        ] [  1.          74.775893    89.5298129    1.        ]]4
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