前面一篇介绍了用tensorflow实现线性回归模型预测sklearn内置的波士顿房价，现在这一篇就记一下用逻辑回归分类sklearn提供的乳腺癌数据集，该数据集有569个样本，每个样本有30维，为二分类数据集，212个正样本，357个负样本。
首先，加载数据，并划分训练集和测试集：
# 加载乳腺癌数据集，该数据及596个样本，每个样本有30维，共有两类
cancer = skd.load_breast_cancer()
# 将数据集的数据和标签分离
X_data = cancer.data
Y_data = cancer.target
x_train,x_test,y_train,y_test = train_test_split(X_data,Y_data,test_size=0.3,random_state=0)这里还要注意一下，因为后面要用到的损失函数为交叉熵，而数据集的标签是一维的，所以我们需要将其转换为位数来表示类别，也就是[0,1]=>[[0,1],[1,0]]这种形式的标签：
y_train_new = np.zeros([y_train.shape[0], 2], dtype='int32')
y_test_new = np.zeros([y_test.shape[0], 2], dtype='int32')
for i in range(y_train.shape[0]):
if y_train[i] == 0:
y_train_new[i,0] = 0
y_train_new[i,1] = 1
else:
y_train_new[i,0] = 1
y_train_new[i,1] = 0
for i in range(y_test.shape[0]):
if y_test[i] == 0:
y_test_new[i,0] = 0
y_test_new[i,1] = 1
else:
y_test_new[i,0] = 1
y_test_new[i,1] = 0接着就是老套路，初始化训练参数，设置模型输入输出，然后是构建模型，二分类逻辑回归模型的数学表达式为：
用tensorflow实现代码如下：
pred = tf.nn.sigmoid(tf.matmul(X, W) + b) # sigmoid然后是构建交叉熵表达式，其数学公式为：
用tensorflow实现代码如下：
cost = tf.reduce_mean(-tf.reduce_sum(Y*tf.log(pred), reduction_indices=1))对于训练好的模型的测试性能的评价，这里我采用计算ROC曲线的方式来展现。首先是模型对于输入数据的预测会得到一个对应的1*2的输出，这个输出不一定是很好的[0 1]或者[1 0]，而是一个类似于概率的量，也就是类似于这样[0.9527， 0.0473]，所以我们需要判断，如果第一位小于第二位，依照前面的设定应该是0，反之为1，当然可能会有第一位等于第二位的情况，那就只能是存在误差了：
y_test_pred = sess.run(pred, feed_dict={X: x_test})
y_scores = np.empty((y_test_pred.shape[0]))
for i in range(y_scores.shape[0]):
if y_test_pred[i,0]<y_test_pred[i,1]:
y_scores[i]=0
else:
y_scores[i]=1然后roc曲线和其AUC值这里调用的是sklearn提供的函数：
fpr, tpr, thresholds = roc_curve((y_test), y_scores)
AUC_ROC = roc_auc_score(y_test, y_scores)然后是画出precision recall curve(精确率-召回率曲线)，同样也是调用sklearn的函数:
precision, recall, thresholds = precision_recall_curve(y_test, y_scores)
precision = np.fliplr([precision])[0] #so the array is increasing (you won't get negative AUC)
recall = np.fliplr([recall])[0] #so the array is increasing (you won't get negative AUC) AUC_prec_rec = np.trapz(precision,recall)接着是计算置信度矩阵，得到矩阵后顺带的就可以计算准确率、灵敏性、特异性等几个参数了，同样的，还是调用sklearn的函数即可：
confusion = confusion_matrix(y_test, y_pred)
accuracy = float(confusion[0,0]+confusion[1,1])/float(np.sum(confusion))
specificity = float(confusion[0,0])/float(confusion[0,0]+confusion[0,1])
sensitivity = float(confusion[1,1])/float(confusion[1,1]+confusion[1,0])
precision = float(confusion[1,1])/float(confusion[1,1]+confusion[0,1])同样的衡量指标还有Jaccard系数和F1分数：
jaccard_index = jaccard_similarity_score(y_test, y_pred, normalize=True)
F1_score = f1_score(y_test, y_pred, labels=None, average='binary', sample_weight=None)这里涉及到了很多模型性能的评价指标，具体的含义就不细究了，下一次专门写一篇来总结吧。完整的代码如下：
from __future__ import print_function
import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets as skd
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import scale
from sklearn.metrics import roc_curve
from sklearn.metrics import roc_auc_score
from sklearn.metrics import confusion_matrix
from sklearn.metrics import precision_recall_curve
from sklearn.metrics import jaccard_similarity_score
from sklearn.metrics import f1_score
# 加载乳腺癌数据集，该数据及596个样本，每个样本有30维，共有两类
cancer = skd.load_breast_cancer()
# 将数据集的数据和标签分离
X_data = cancer.data
Y_data = cancer.target
print("X_data.shape = ", X_data.shape)
print("Y_data.shape = ", Y_data.shape)
# 将数据和标签分成训练集和测试集
x_train,x_test,y_train,y_test = train_test_split(X_data,Y_data,test_size=0.3,random_state=0)
x_train = scale(x_train)
x_test = scale(x_test)
y_train_new = np.zeros([y_train.shape[0], 2], dtype='int32')
y_test_new = np.zeros([y_test.shape[0], 2], dtype='int32')
for i in range(y_train.shape[0]):
if y_train[i] == 0:
y_train_new[i,0] = 0
y_train_new[i,1] = 1
else:
y_train_new[i,0] = 1
y_train_new[i,1] = 0
for i in range(y_test.shape[0]):
if y_test[i] == 0:
y_test_new[i,0] = 0
y_test_new[i,1] = 1
else:
y_test_new[i,0] = 1
y_test_new[i,1] = 0
print("x_train.shape = ", x_train.shape)
print("x_test.shape = ", x_test.shape)
print("y_train.shape = ", y_train_new.shape)
print("y_test.shape = ", y_test_new.shape)
# 初始化参数
learning_rate = 0.01
training_epochs = 50000
display_step = 50
# 定义图模型输入
X = tf.placeholder(tf.float32, [None, 30]) # mnist data image of shape 28*28=784
Y = tf.placeholder(tf.float32, [None, 2]) # 0-9 digits recognition => 10 classes#
# 设置模型权重和偏置
W = tf.Variable(tf.random_normal([30, 2]),dtype=tf.float32, name="weight")
b = tf.Variable(tf.random_normal([2]),dtype=tf.float32, name="bias")
# 构建模型
#pred = tf.nn.softmax(tf.matmul(x, W) + b) # Softmax
pred = tf.nn.sigmoid(tf.matmul(X, W) + b) # sigmoid
# 使用交叉熵来最小化训练误差
cost = tf.reduce_mean(-tf.reduce_sum(Y*tf.log(pred), reduction_indices=1))
# 梯度下降法
optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(cost)#
# 初始化器
init = tf.global_variables_initializer()
# 开始训练
with tf.Session() as sess:#
# 初始化
sess.run(init)#
# 迭代训练
for epoch in range(training_epochs):
avg_cost = 0.
sess.run(optimizer, feed_dict={X: x_train, Y: y_train_new})
# 显示训练信息
if (epoch+1) % display_step == 0:
c = sess.run(cost, feed_dict={X: x_train, Y:y_train_new})
print("Epoch:", '%04d' % (epoch+1), "cost=", "{:.9f}".format(c))
print("完成训练!")
# 测试模型
correct_prediction = tf.equal(tf.argmax(pred, 1), tf.argmax(Y, 1))
# 计算准确度
accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))
print("Accuracy:", accuracy.eval({X: x_test, Y: y_test_new}))
# 计算模型预测
y_test_pred = sess.run(pred, feed_dict={X: x_test})
y_pred = np.empty((y_test_pred.shape[0]), dtype='int32')
# 二值化
for i in range(y_pred.shape[0]):
if y_test_pred[i,0]<y_test_pred[i,1]:
y_pred[i]=0
else:
y_pred[i]=1
# 得到ROC曲线
fpr, tpr, thresholds = roc_curve((y_test), y_pred)
AUC_ROC = roc_auc_score(y_test, y_pred)
roc_curve =plt.figure()
plt.plot(fpr,tpr,'-',label='Area Under the Curve (AUC = %0.4f)' % AUC_ROC)
plt.title('ROC curve')
plt.xlabel("FPR (False Positive Rate)")
plt.ylabel("TPR (True Positive Rate)")
plt.legend(loc="lower right")
plt.show()
# 得到precision_recall曲线
precision, recall, thresholds = precision_recall_curve(y_test, y_pred)
precision = np.fliplr([precision])[0] #so the array is increasing (you won't get negative AUC)
recall = np.fliplr([recall])[0] #so the array is increasing (you won't get negative AUC)
AUC_prec_rec = np.trapz(precision,recall)
print("\nArea under Precision-Recall curve: " +str(AUC_prec_rec))
prec_rec_curve = plt.figure()
plt.plot(recall,precision,'-',label='Area Under the Curve (AUC = %0.4f)' % AUC_prec_rec)
plt.title('Precision - Recall curve')
plt.xlabel("Recall")
plt.ylabel("Precision")
plt.legend(loc="lower right")
plt.show()
# 计算置信度矩阵
threshold_confusion = 0.5
print("\nConfusion matrix: Costum threshold (for positive) of " +str(threshold_confusion))
confusion = confusion_matrix(y_test, y_pred)
print(confusion)
accuracy = 0
if float(np.sum(confusion))!=0:
accuracy = float(confusion[0,0]+confusion[1,1])/float(np.sum(confusion))
print("Global Accuracy: " +str(accuracy))
specificity = 0
if float(confusion[0,0]+confusion[0,1])!=0:
specificity = float(confusion[0,0])/float(confusion[0,0]+confusion[0,1])
print("Specificity: " +str(specificity))
sensitivity = 0
if float(confusion[1,1]+confusion[1,0])!=0:
sensitivity = float(confusion[1,1])/float(confusion[1,1]+confusion[1,0])
print("Sensitivity: " +str(sensitivity))
precision = 0
if float(confusion[1,1]+confusion[0,1])!=0:
precision = float(confusion[1,1])/float(confusion[1,1]+confusion[0,1])
print("Precision: " +str(precision))
#Jaccard similarity index
jaccard_index = jaccard_similarity_score(y_test, y_pred, normalize=True)
print("\nJaccard similarity score: " +str(jaccard_index))
#F1 score
F1_score = f1_score(y_test, y_pred, labels=None, average='binary', sample_weight=None)
print("\nF1 score (F-measure): " +str(F1_score))
print("y_test[0:20]=", y_test[0:20])
print("y_pred[0:20]=", y_pred[0:20])最总的结果显示如下：
古人学问无遗力，少壮工夫老始成。
纸上得来终觉浅，绝知此事要躬行。
-- 陆游 《冬夜读书示子聿》
上善若水，为而不争。
