import matplotlib.pyplot as plt import numpy as np import tensorflow as tf import tensorflow.keras.backend as K from sklearn.metrics import accuracy_score from tensorflow.keras import layers from tensorflow.keras import metrics from tensorflow.keras.datasets import mnist from tensorflow.keras.models import Model

def preprocess(array): """ Normalizes the supplied array and reshapes it into the appropriate format. """ array = array.astype('float32') / 255. array = np.reshape(array, (len(array), 28, 28, 1)) return array def display_pairs(images, labels, correct=None): """ Displays the first ten pairs from the supplied array. Args: - images: An array containing the pair of images. - labels: An array containing the corresponding label (0 if both pairs are different, and 1 if both pairs are the same.) - correct (optional): An array of boolean values indicating whether the supplied labels correctly represent the image pairs. """ n = 10 plt.figure(figsize=(20, 6)) for i, (image1, image2) in enumerate(zip(images[:n, 0], images[:n, 1])): label = int(labels[:n][i][0]) text = "Label" color = "silver" # If we know whether the supplied labels are correct, let's change the # text and the face color of the annotation on the chart. if correct is not None: text = "Prediction" color = "mediumseagreen" if correct[:n][i][0] else "indianred" ax = plt.subplot(3, n, i + 1) ax.text(1, -3 ,f"{text}: {label}", style="italic", bbox={ "facecolor": color, "pad": 4 }) plt.imshow(image1.reshape(28, 28)) plt.gray() ax.get_xaxis().set_visible(False) ax.get_yaxis().set_visible(False) ax = plt.subplot(3, n, i + 1 + n) plt.imshow(image2.reshape(28, 28)) plt.gray() ax.get_xaxis().set_visible(False) ax.get_yaxis().set_visible(False) plt.show() def plot_history(history): """ Plots the training and validation loss. """ plt.plot(history['loss']) plt.plot(history['val_loss']) plt.title('Training and Validation Loss') plt.ylabel('loss') plt.xlabel('epoch') plt.legend(['train', 'val'], loc='upper right') plt.show() def generate_pairs(images, labels): """ Creates a collection of positive and negative image pairs from the supplied array of images. A positive pair contains two images of the same digit. A negative pair contains two images representing different digits. """ x_pairs = [] y_pairs = [] for i in range(len(images)): label = labels[i] j = np.random.choice(np.where(labels == label)[0]) x_pairs.append([images[i], images[j]]) y_pairs.append([1]) k = np.random.choice(np.where(labels != label)[0]) x_pairs.append([images[i], images[k]]) y_pairs.append([0]) indices = np.arange(len(x_pairs)) np.random.shuffle(indices) return np.array(x_pairs)[indices], np.array(y_pairs)[indices]

(x_train, y_train), (x_test, y_test) = mnist.load_data() VALIDATION_SIZE = int(len(x_train) * 0.2) x_val = x_train[:VALIDATION_SIZE] y_val = y_train[:VALIDATION_SIZE] x_train = x_train[VALIDATION_SIZE:] y_train = y_train[VALIDATION_SIZE:] x_train = preprocess(x_train) x_val = preprocess(x_val) x_test = preprocess(x_test) print(f"Train: {len(x_train)}") print(f"Validation: {len(x_val)}") print(f"Test: {len(x_test)}")

x_pairs_train, y_pairs_train = generate_pairs(x_train, y_train) x_pairs_val, y_pairs_val = generate_pairs(x_val, y_val) x_pairs_test, y_pairs_test = generate_pairs(x_test, y_test)

display_pairs(x_pairs_train, y_pairs_train)

def norm(features): """ Computes the euclidean norm of the two feature vectors generated by the twins of the Siamese network. """ return tf.norm(features[0] - features[1], axis=1, keepdims=True) def accuracy(y_true, y_pred): """ Computes the accuracy of the predictions. """ # Notice that `y_true` is 0 whenever two images are not the same and 1 # otherwise, but `y_pred` is the opposite. The closer `y_pred` is to 0, # the shorter the distance between both images, therefore the more likely # it is that they are the same image. To correctly compute the accuracy we # need to substract `y_pred` from 1 so both vectors are comparable. return metrics.binary_accuracy(y_true, 1 - y_pred) def contrastive_loss(y_true, y_pred): """ Computes the contrastive loss introduced by Yann LeCun et al. in the paper "Dimensionality Reduction by Learning an Invariant Mapping," 2005. """ margin = 1 y_true = tf.cast(y_true, y_pred.dtype) # The original formula proposed by Yann LeCunn et al. assumes that Y is 0 # if both images are similar and 1 otherwise. Our implementation (where Y is # `y_true`) is the opposite, hence the modification to the formula below. loss = y_true / 2 * K.square(y_pred) + (1 - y_true) / 2 \ * K.square(K.maximum(0.0, margin - y_pred)) return loss

def siamese_twin(): """ Creates the subnetwork that represents each one of the twins of the Siamese network. """ inputs = layers.Input((28, 28, 1)) x = layers.Conv2D(128, (2, 2), activation="relu")(inputs) x = layers.MaxPooling2D((2, 2))(x) x = layers.Dropout(0.4)(x) x = layers.Conv2D(128, (2, 2), activation="relu")(x) x = layers.MaxPooling2D((2, 2))(x) x = layers.Dropout(0.4)(x) x = layers.Conv2D(64, (2, 2), activation="relu")(x) x = layers.MaxPooling2D((2, 2))(x) x = layers.Dropout(0.4)(x) x = layers.GlobalAveragePooling2D()(x) # We don't want any activation function on the final layer. This layer # will contain the embedding for the input image. outputs = layers.Dense(128, activation=None)(x) return Model(inputs, outputs) def siamese_network(): """ Creates the Siamese Network model. """ input1 = layers.Input(shape=(28, 28, 1)) input2 = layers.Input(shape=(28, 28, 1)) twin = siamese_twin() # We can use a Lambda layer to compute the euclidean distance of the # embeddings from each image. distance = layers.Lambda(norm)([ twin(input1), twin(input2) ]) # Our model has two inputs: the first input is for the anchor image and # the second input is for the second image of the pair. The output of the # model is the euclidean distance between the embeddings from each image. return Model(inputs=[input1, input2], outputs=distance)

model = siamese_network() model.compile( loss=contrastive_loss, optimizer="adam", metrics=[accuracy] ) model.summary()

history = model.fit( x=[x_pairs_train[:, 0], x_pairs_train[:, 1]], y=y_pairs_train[:], validation_data=([x_pairs_val[:, 0], x_pairs_val[:, 1]], y_pairs_val[:]), batch_size=64, epochs=15 )

plot_history(history.history)

predictions = np.round(1 - model.predict([x_pairs_test[:, 0], x_pairs_test[:, 1]])) display_pairs(x_pairs_test, predictions, predictions == y_pairs_test) accuracy = metrics.BinaryAccuracy() accuracy.update_state(y_pairs_test, predictions) print(f"\nAccuracy: {accuracy.result().numpy()}")