import tensorflow as tfimport numpy as npfrom sklearn.linear_model import LogisticRegressionfrom sklearn import preprocessing# Read x and yx_data = http://www.mamicode.com/np.loadtxt("ex4x.dat").astype(np.float32)y_data = np.loadtxt("ex4y.dat").astype(np.float32)scaler = preprocessing.StandardScaler().fit(x_data)x_data_standard = scaler.transform(x_data)# We evaluate the x and y by sklearn to get a sense of the coefficients.reg = LogisticRegression(C=999999999, solver="newton-cg")  # Set C as a large positive number to minimize the regularization effectreg.fit(x_data, y_data)print ("Coefficients of sklearn: K=%s, b=%f" % (reg.coef_, reg.intercept_))# Now we use tensorflow to get similar results.W = tf.Variable(tf.zeros([2, 1]))b = tf.Variable(tf.zeros([1, 1]))y = 1 / (1 + tf.exp(-tf.matmul(x_data_standard, W) + b))loss = tf.reduce_mean(- y_data.reshape(-1, 1) *  tf.log(y) - (1 - y_data.reshape(-1, 1)) * tf.log(1 - y))optimizer = tf.train.GradientDescentOptimizer(1.3)train = optimizer.minimize(loss)init = tf.initialize_all_variables()sess = tf.Session()sess.run(init)for step in range(100):    sess.run(train)    if step % 10 == 0:        print (step, sess.run(W).flatten(), sess.run(b).flatten())print ("Coefficients of tensorflow (input should be standardized): K=%s, b=%s" % (sess.run(W).flatten(), sess.run(b).flatten()))print ("Coefficients of tensorflow (raw input): K=%s, b=%s" % (sess.run(W).flatten() / scaler.scale_, sess.run(b).flatten() - np.dot(scaler.mean_ / scaler.scale_, sess.run(W))))# Problem solved and we are happy. But...# I‘d like to implement the logistic regression from a multi-class viewpoint instead of binary.# In machine learning domain, it is called softmax regression# In economic and statistics domain, it is called multinomial logit (MNL) model, proposed by Daniel McFadden, who shared the 2000  Nobel Memorial Prize in Economic Sciences.print ("------------------------------------------------")print ("We solve this binary classification problem again from the viewpoint of multinomial classification")print ("------------------------------------------------")# As a tradition, sklearn firstreg = LogisticRegression(C=9999999999, solver="newton-cg", multi_class="multinomial")reg.fit(x_data, y_data)print ("Coefficients of sklearn: K=%s, b=%f" % (reg.coef_, reg.intercept_))print ("A little bit difference at first glance. What about multiply them with 2?")# Then try tensorflowW = tf.Variable(tf.zeros([2, 2]))  # first 2 is feature number, second 2 is class numberb = tf.Variable(tf.zeros([1, 2]))V = tf.matmul(x_data_standard, W) + by = tf.nn.softmax(V)  # tensorflow provide a utility function to calculate the probability of observer n choose alternative i, you can replace it with `y = tf.exp(V) / tf.reduce_sum(tf.exp(V), keep_dims=True, reduction_indices=[1])`# Encode the y label in one-hot mannerlb = preprocessing.LabelBinarizer()lb.fit(y_data)y_data_trans = lb.transform(y_data)y_data_trans = np.concatenate((1 - y_data_trans, y_data_trans), axis=1)  # Only necessary for binary classloss = tf.reduce_mean(-tf.reduce_sum(y_data_trans * tf.log(y), reduction_indices=[1]))optimizer = tf.train.GradientDescentOptimizer(1.3)train = optimizer.minimize(loss)init = tf.initialize_all_variables()sess = tf.Session()sess.run(init)for step in range(100):    sess.run(train)    if step % 10 == 0:        print (step, sess.run(W).flatten(), sess.run(b).flatten())print ("Coefficients of tensorflow (input should be standardized): K=%s, b=%s" % (sess.run(W).flatten(), sess.run(b).flatten()))print ("Coefficients of tensorflow (raw input): K=%s, b=%s" % ((sess.run(W) / scaler.scale_).flatten(),  sess.run(b).flatten() - np.dot(scaler.mean_ / scaler.scale_, sess.run(W))))