? ? ? 本文引用Brendon Hall在2016年《The Leading Edge》上發表的題為“Facies classfication using machine learning”文章，Hall(2016)在文中介紹了SVM方法在巖相分類中的應用。本文實現了利用神經網絡方法實現巖相分類。

模型：（引用吳恩達老師深度學習微專業編程作業2.3.2-利用TensorFlow搭建神經網絡模型）

?LINEAR -> RELU -> LINEAR -> RELU -> LINEAR -> SOFTMAX

劃分數據集：

training_data = pd.read_csv('training_data.csv')

test_data? ? ? = training_data[training_data['Well Name'] == 'SHANKLE']??#從訓練數據集中抽出一口井用于測試

training_data = training_data[training_data['Well Name'] != 'SHANKLE']? #從訓練數據剔除這口井

all_vectors = training_data.drop(['Facies','Formation', 'Well Name', 'Depth'], axis=1)

all_labels? = training_data['Facies'].values

nan_idx = np.any(np.isnan(all_vectors), axis=1)??# 剔除NaNs

training_vectors = all_vectors[np.logical_not(nan_idx)]

training_labels? = all_labels [np.logical_not(nan_idx)]

test_vectors = test_data.drop(['Facies','Formation', 'Well Name', 'Depth'], axis=1)

test_labels? = np.ones(test_vectors.shape[0], dtype=np.int)

test_labels_true? = test_data['Facies'].values

scaler = preprocessing.StandardScaler().fit(training_vectors)

scaled_training_vectors = scaler.transform(training_vectors)

scaled_test_vectors = scaler.transform(test_vectors)? #據我了解，測試集應該與訓練集采用相同的均值和方差用于標準化

X_train, X_cv, Y_train, Y_cv = train_test_split(scaled_training_vectors, training_labels, test_size=0.05, random_state=42)

轉換數據集矩陣：

X_train = X_train.T? #處理完后每一列代表一樣樣本

Y_train = Y_train.T

X_cv = X_cv.T

Y_cv = Y_cv.T

將巖相類別轉換為tensorflow需要的one-hot向量：

Y_train = convert_to_one_hot(Y_train-1, 9)? #其中的“-1”是因為類別標簽是1-9，而程序中one-hot對應為0-8

Y_cv = convert_to_one_hot(Y_cv-1, 9)

創建placeholder：

X=tf.placeholder(tf.float32,shape=[n_x,None],name='X')

Y=tf.placeholder(tf.float32,shape=[n_y,None],name='Y')

初始化模型參數：

W1 = tf.get_variable("W1", [65, 7], initializer = tf.contrib.layers.xavier_initializer(seed=1))

b1 = tf.get_variable("b1", [65, 1], initializer = tf.zeros_initializer())

W2 = tf.get_variable("W2", [25, 65], initializer = tf.contrib.layers.xavier_initializer(seed=1))

b2 = tf.get_variable("b2", [25, 1], initializer = tf.zeros_initializer())

W3 = tf.get_variable("W3", [9, 25], initializer = tf.contrib.layers.xavier_initializer(seed=1))

b3 = tf.get_variable("b3", [9, 1], initializer = tf.zeros_initializer())

前向傳播：

Z1 = tf.add(tf.matmul(W1,X),b1)

A1 = tf.nn.relu(Z1)

Z2 = tf.add(tf.matmul(W2,A1),b2)? ? ? ? ? ? ? ? ? ? ? ?

A2 = tf.nn.relu(Z2)

Z3 = tf.add(tf.matmul(W3,A2),b3)

計算損失函數：

logits = tf.transpose(Z3)

labels = tf.transpose(Y)

cost = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits=logits,labels=labels))

反向傳播及參數更新：

反向傳播

optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate).minimize(cost)

參數優化

_ , minibatch_cost = sess.run([optimizer, cost], feed_dict={X: minibatch_X, Y: minibatch_Y})

建立整體模型：

def model(X_train, Y_train, X_test, Y_test, learning_rate = 0.0001,num_epochs = 4000, minibatch_size = 512,?

? ? ? ? ? ? ? ? ? print_cost = True):

? ? """
? ? Implements a three-layer tensorflow neural network: LINEAR->RELU->LINEAR->RELU->LINEAR->SOFTMAX.
? ??
? ? Arguments:
? ? X_train -- training set, of shape (input size = 7, number of training examples = 2783)
? ? Y_train -- test set, of shape (output size = 9, number of training examples = 2783)
? ? X_test -- training set, of shape (input size = 7, number of training examples = 449)
? ? Y_test -- test set, of shape (output size = 9, number of test examples = 449)
? ? learning_rate -- learning rate of the optimization
? ? num_epochs -- number of epochs of the optimization loop
? ? minibatch_size -- size of a minibatch
? ? print_cost -- True to print the cost every 100 epochs
? ??
? ? Returns:
? ? parameters -- parameters learnt by the model. They can then be used to predict.
? ? """
? ??
? ? ops.reset_default_graph()? ? ? ? ? ? ? ? ? ? ? ? ?# to be able to rerun the model without overwriting tf variables
? ? tf.set_random_seed(1)? ? ? ? ? ? ? ? ? ? ? ? ? ? ?# to keep consistent results
? ? seed = 3? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? # to keep consistent results
? ? (n_x, m) = X_train.shape? ? ? ? ? ? ? ? ? ? ? ? ? # (n_x: input size, m : number of examples in the train set)
? ? n_y = Y_train.shape[0]? ? ? ? ? ? ? ? ? ? ? ? ? ? # n_y : output size
? ? costs = []? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? # To keep track of the cost
? ??
? ? # Create Placeholders of shape (n_x, n_y)
? ? ### START CODE HERE ### (1 line)
? ? X, Y = create_placeholders(n_x, n_y)
? ? ### END CODE HERE ###


? ? # Initialize parameters
? ? ### START CODE HERE ### (1 line)
? ? parameters = initialize_parameters()
? ? ### END CODE HERE ###
? ??
? ? # Forward propagation: Build the forward propagation in the tensorflow graph
? ? ### START CODE HERE ### (1 line)
? ? Z3 = forward_propagation(X, parameters)
? ? ### END CODE HERE ###
? ??
? ? # Cost function: Add cost function to tensorflow graph
? ? ### START CODE HERE ### (1 line)
? ? cost = compute_cost(Z3, Y)
? ? ### END CODE HERE ###
? ??
? ? # Backpropagation: Define the tensorflow optimizer. Use an AdamOptimizer.
? ? ### START CODE HERE ### (1 line)
? ? optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate).minimize(cost)
? ? ### END CODE HERE ###
? ??
? ? # Initialize all the variables
? ? init = tf.global_variables_initializer()


? ? # Start the session to compute the tensorflow graph
? ? with tf.Session() as sess:
? ? ? ??
? ? ? ? # Run the initialization
? ? ? ? sess.run(init)
? ? ? ??
? ? ? ? # Do the training loop
? ? ? ? for epoch in range(num_epochs):


? ? ? ? ? ? epoch_cost = 0.? ? ? ? ? ? ? ? ? ? ? ?# Defines a cost related to an epoch
? ? ? ? ? ? num_minibatches = int(m / minibatch_size) # number of minibatches of size minibatch_size in the train set
? ? ? ? ? ? seed = seed + 1
? ? ? ? ? ? minibatches = random_mini_batches(X_train, Y_train, minibatch_size, seed)


? ? ? ? ? ? for minibatch in minibatches:


? ? ? ? ? ? ? ? # Select a minibatch
? ? ? ? ? ? ? ? (minibatch_X, minibatch_Y) = minibatch
? ? ? ? ? ? ? ??
? ? ? ? ? ? ? ? # IMPORTANT: The line that runs the graph on a minibatch.
? ? ? ? ? ? ? ? # Run the session to execute the "optimizer" and the "cost", the feedict should contain a minibatch for (X,Y).
? ? ? ? ? ? ? ? ### START CODE HERE ### (1 line)
? ? ? ? ? ? ? ? _ , minibatch_cost = sess.run([optimizer, cost], feed_dict={X: minibatch_X, Y: minibatch_Y})
? ? ? ? ? ? ? ? ### END CODE HERE ###
? ? ? ? ? ? ? ??
? ? ? ? ? ? ? ? epoch_cost += minibatch_cost / num_minibatches


? ? ? ? ? ? # Print the cost every epoch
? ? ? ? ? ? if print_cost == True and epoch % 100 == 0:
? ? ? ? ? ? ? ? print ("Cost after epoch %i: %f" % (epoch, epoch_cost))
? ? ? ? ? ? if print_cost == True and epoch % 5 == 0:
? ? ? ? ? ? ? ? costs.append(epoch_cost)
? ? ? ? ? ? ? ??
? ? ? ? # plot the cost
? ? ? ? plt.plot(np.squeeze(costs))
? ? ? ? plt.ylabel('cost')
? ? ? ? plt.xlabel('iterations (per tens)')
? ? ? ? plt.title("Learning rate =" + str(learning_rate))
? ? ? ? plt.show()


? ? ? ? # lets save the parameters in a variable
? ? ? ? parameters = sess.run(parameters)
? ? ? ? print("Parameters have been trained!")


? ? ? ? # Calculate the correct predictions
? ? ? ? correct_prediction = tf.equal(tf.argmax(Z3), tf.argmax(Y))


? ? ? ? # Calculate accuracy on the test set
? ? ? ? accuracy = tf.reduce_mean(tf.cast(correct_prediction, "float"))


? ? ? ? print("Train Accuracy:", accuracy.eval({X: X_train, Y: Y_train}))
? ? ? ? print("Test Accuracy:", accuracy.eval({X: X_test, Y: Y_test}))
? ? ? ??

? ? ? ? return parameters

預測：

X_test = scaled_test_vectors.T

Y_test_orig= test_labels_true.T

test_prediction = predict(X_test, parameters)? ? #一列代表一個樣本，用向量化速度快

def predict(X, parameters):
? ??
? ? W1 = tf.convert_to_tensor(parameters["W1"])
? ? b1 = tf.convert_to_tensor(parameters["b1"])
? ? W2 = tf.convert_to_tensor(parameters["W2"])
? ? b2 = tf.convert_to_tensor(parameters["b2"])
? ? W3 = tf.convert_to_tensor(parameters["W3"])
? ? b3 = tf.convert_to_tensor(parameters["b3"])
? ??
? ? params = {"W1": W1,
? ? ? ? ? ?"b1": b1,
? ? ? ? ? ?"W2": W2,
? ? ? ? ? ?"b2": b2,
? ? ? ? ? ?"W3": W3,
? ? ? ? ? ?"b3": b3}
? ??
? ? x = tf.placeholder("float", [X.shape[0], X.shape[1]])
? ??
? ? z3 = forward_propagation_for_predict(x, params)
? ? p = tf.argmax(z3)
? ??
? ? sess = tf.Session()
? ? prediction = sess.run(p, feed_dict = {x: X})
? ? ? ??
? ? return prediction

本人的測試結果如下：

參考Brendon Hall論文、Andrew Ng深度學習課程以及OliverChrist博客，向他們表示感謝！

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