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A siamese network is a special type of neural network and it is one of the simplest and most popularly used one-shot learning algorithms. One-shot learning is a technique where we learn from only one training example per class. So, a siamese network is predominantly used in applications where we don’t have many data points in each class. For instance, let’s say we want to build a face recognition model for our organization and about 500 people are working in our organization.

If we want to build our face recognition model using a Convolutional Neural Network (CNN) from scratch, then we need many images of all of these 500 people for training the network and attaining good accuracy. But apparently, we will not have many images for all of these 500 people and so it is not feasible to build a model using a CNN or any deep learning algorithm unless we have sufficient data points. So, in these kinds of scenarios, we can resort to a sophisticated one-shot learning algorithm such as a siamese network, which can learn from fewer data points.

Siamese networks basically consist of two symmetrical neural networks both sharing the same weights and architecture and both joined together at the end using some energy function, E. The objective of our siamese network is to learn whether two input values are similar or dissimilar.

We will understand the siamese network by building a face recognition model. The objective of our network is to understand whether two faces are similar or dissimilar. We use the AT&T Database of Faces, which can be downloaded from the Cambridge University Computer Laboratory website.


This article is an excerpt from a book written by Sudharsan Ravichandiran titled Hands-On Meta-Learning with Python. In this book, you will learn how to build relation networks and matching networks from scratch.

Once you have downloaded and extracted the archive, you can see the folders s1, s2, up to s40, as shown here:

 

Each of these folders has 10 different images of a single person taken from various angles. For instance, let’s open folder s1. As you can see, there are 10 different images of a single person:

 

We open and check folder s13:

Siamese networks require input values as a pair along with the label, so we have to create our data in such a way. So, we will take two images randomly from the same folder and mark them as a genuine pair and we will take single images from two different folders and mark them as an imposite pair. A sample is shown in the following screenshot; as you can see, a genuine pair has images of the same person and the imposite pair has images of different people:

Once we have our data as pairs along with their labels, we train our siamese network. From the image pair, we feed one image to network A and another image to network B. The role of these two networks is only to extract the feature vectors. So, we use two convolution layers with rectified linear unit (ReLU) activations for extracting the features. Once we have learned the features, we feed the resultant feature vector from both of the networks to the energy function, which measures the similarity; we use Euclidean distance as our energy function. So, we train our network by feeding the image pair to learn the semantic similarity between them. Now, we will see this step by step.

For better understanding, you can check the complete code, which is available as a Jupyter Notebook with an explanation from GitHub.

First, we will import the required libraries:

import re
import numpy as np
from PIL import Image

from sklearn.model_selection import train_test_split
from keras import backend as K
from keras.layers import Activation
from keras.layers import Input, Lambda, Dense, Dropout, Convolution2D, MaxPooling2D, Flatten
from keras.models import Sequential, Model
from keras.optimizers import RMSprop

Now, we define a function for reading our input image. The read_image function takes as input an image and returns a NumPy array:

def read_image(filename, byteorder='>'):
    
    #first we read the image, as a raw file to the buffer
    with open(filename, 'rb') as f:
        buffer = f.read()
    
    #using regex, we extract the header, width, height and maxval of the image
    header, width, height, maxval = re.search(
        b"(^P5\s(?:\s*#.*[\r\n])*"
        b"(\d+)\s(?:\s*#.*[\r\n])*"
        b"(\d+)\s(?:\s*#.*[\r\n])*"
        b"(\d+)\s(?:\s*#.*[\r\n]\s)*)", buffer).groups()
    
    #then we convert the image to numpy array using np.frombuffer which interprets buffer as one dimensional array
    return np.frombuffer(buffer,
                            dtype='u1' if int(maxval) 

For an example, let’s open one image:

Image.open("data/orl_faces/s1/1.pgm")

When we feed this image to our read_image function, it will return as a NumPy array:

img = read_image('data/orl_faces/s1/1.pgm')
img.shape
(112, 92)

Now, we define another function, get_data, for generating our data. As we know, for the siamese network, data should be in the form of pairs (genuine and imposite) with a binary label.

First, we read the (img1, img2) images from the same directory and store them in the x_genuine_pair array and assign y_genuine to 1. Next, we read the (img1, img2) images from the different directory and store them in the x_imposite pair and assign y_imposite to 0.

Finally, we concatenate both x_genuine_pair and x_imposite to X and y_genuine and y_imposite to Y:

size = 2
total_sample_size = 10000


def get_data(size, total_sample_size):
    #read the image
    image = read_image('data/orl_faces/s' + str(1) + '/' + str(1) + '.pgm', 'rw+')
    #reduce the size
    image = image[::size, ::size]
    #get the new size
    dim1 = image.shape[0]
    dim2 = image.shape[1]

    count = 0
    
    #initialize the numpy array with the shape of [total_sample, no_of_pairs, dim1, dim2]
    x_geuine_pair = np.zeros([total_sample_size, 2, 1, dim1, dim2]) # 2 is for pairs
    y_genuine = np.zeros([total_sample_size, 1])
    
    for i in range(40):
        for j in range(int(total_sample_size/40)):
            ind1 = 0
            ind2 = 0
            
            #read images from same directory (genuine pair)
            while ind1 == ind2:
                ind1 = np.random.randint(10)
                ind2 = np.random.randint(10)
            
            # read the two images
            img1 = read_image('data/orl_faces/s' + str(i+1) + '/' + str(ind1 + 1) + '.pgm', 'rw+')
            img2 = read_image('data/orl_faces/s' + str(i+1) + '/' + str(ind2 + 1) + '.pgm', 'rw+')
            
            #reduce the size
            img1 = img1[::size, ::size]
            img2 = img2[::size, ::size]
            
            #store the images to the initialized numpy array
            x_geuine_pair[count, 0, 0, :, :] = img1
            x_geuine_pair[count, 1, 0, :, :] = img2
            
            #as we are drawing images from the same directory we assign label as 1. (genuine pair)
            y_genuine[count] = 1
            count += 1

    count = 0
    x_imposite_pair = np.zeros([total_sample_size, 2, 1, dim1, dim2])
    y_imposite = np.zeros([total_sample_size, 1])
    
    for i in range(int(total_sample_size/10)):
        for j in range(10):
            
            #read images from different directory (imposite pair)
            while True:
                ind1 = np.random.randint(40)
                ind2 = np.random.randint(40)
                if ind1 != ind2:
                    break
                    
            img1 = read_image('data/orl_faces/s' + str(ind1+1) + '/' + str(j + 1) + '.pgm', 'rw+')
            img2 = read_image('data/orl_faces/s' + str(ind2+1) + '/' + str(j + 1) + '.pgm', 'rw+')

            img1 = img1[::size, ::size]
            img2 = img2[::size, ::size]

            x_imposite_pair[count, 0, 0, :, :] = img1
            x_imposite_pair[count, 1, 0, :, :] = img2
            #as we are drawing images from the different directory we assign label as 0. (imposite pair)
            y_imposite[count] = 0
            count += 1
            
    #now, concatenate, genuine pairs and imposite pair to get the whole data
    X = np.concatenate([x_geuine_pair, x_imposite_pair], axis=0)/255
    Y = np.concatenate([y_genuine, y_imposite], axis=0)

    return X, Y

Now, we generate our data and check our data size. As you can see, we have 20,000 data points and, out of these, 10,000 are genuine pairs and 10,000 are imposite pairs:

X, Y = get_data(size, total_sample_size)

X.shape
(20000, 2, 1, 56, 46)

Y.shape
(20000, 1)

Next, we split our data for training and testing with 75% training and 25% testing proportions:

x_train, x_test, y_train, y_test = train_test_split(X, Y, test_size=.25)

Now that we have successfully generated our data, we build our siamese network. First, we define the base network, which is basically a convolutional network used for feature extraction. We build two convolutional layers with ReLU activations and max pooling followed by a flat layer:

def build_base_network(input_shape):
    
    seq = Sequential()
    
    nb_filter = [6, 12]
    kernel_size = 3
    
    
    #convolutional layer 1
    seq.add(Convolution2D(nb_filter[0], kernel_size, kernel_size, input_shape=input_shape,
                          border_mode='valid', dim_ordering='th'))
    seq.add(Activation('relu'))
    seq.add(MaxPooling2D(pool_size=(2, 2))) 
    seq.add(Dropout(.25))
    
    #convolutional layer 2
    seq.add(Convolution2D(nb_filter[1], kernel_size, kernel_size, border_mode='valid', dim_ordering='th'))
    seq.add(Activation('relu'))
    seq.add(MaxPooling2D(pool_size=(2, 2), dim_ordering='th')) 
    seq.add(Dropout(.25))

    #flatten 
    seq.add(Flatten())
    seq.add(Dense(128, activation='relu'))
    seq.add(Dropout(0.1))
    seq.add(Dense(50, activation='relu'))
    return seq

Next, we feed the image pair to the base network, which will return the embeddings, that is, feature vectors:

input_dim = x_train.shape[2:]
img_a = Input(shape=input_dim)
img_b = Input(shape=input_dim)

base_network = build_base_network(input_dim)
feat_vecs_a = base_network(img_a)
feat_vecs_b = base_network(img_b)

feat_vecs_a and feat_vecs_b are the feature vectors of our image pair. Next, we feed these feature vectors to the energy function to compute the distance between them, and we use Euclidean distance as our energy function:

def euclidean_distance(vects):
    x, y = vects
    return K.sqrt(K.sum(K.square(x - y), axis=1, keepdims=True))


def eucl_dist_output_shape(shapes):
    shape1, shape2 = shapes
    return (shape1[0], 1)

distance = Lambda(euclidean_distance, output_shape=eucl_dist_output_shape)([feat_vecs_a, feat_vecs_b])

Now, we set the epoch length to 13, and we use the RMS prop for optimization and define our model:

epochs = 13
rms = RMSprop()

model = Model(input=[input_a, input_b], output=distance)

Next, we define our loss function as the contrastive_loss function and compile the model:

def contrastive_loss(y_true, y_pred):
    margin = 1
    return K.mean(y_true * K.square(y_pred) + (1 - y_true) * K.square(K.maximum(margin - y_pred, 0)))

model.compile(loss=contrastive_loss, optimizer=rms)

Now, we train our model:

img_1 = x_train[:, 0]
img_2 = x_train[:, 1] 

model.fit([img_1, img_2], y_train, validation_split=.25, batch_size=128, verbose=2, nb_epoch=epochs)

You can see how the loss decreases over epochs:

Train on 11250 samples, validate on 3750 samples
Epoch 1/13
 - 60s - loss: 0.2179 - val_loss: 0.2156
Epoch 2/13
 - 53s - loss: 0.1520 - val_loss: 0.2102
Epoch 3/13
 - 53s - loss: 0.1190 - val_loss: 0.1545
Epoch 4/13
 - 55s - loss: 0.0959 - val_loss: 0.1705
Epoch 5/13
 - 52s - loss: 0.0801 - val_loss: 0.1181
Epoch 6/13
 - 52s - loss: 0.0684 - val_loss: 0.0821
Epoch 7/13
 - 52s - loss: 0.0591 - val_loss: 0.0762
Epoch 8/13
 - 52s - loss: 0.0526 - val_loss: 0.0655
Epoch 9/13
 - 52s - loss: 0.0475 - val_loss: 0.0662
Epoch 10/13
 - 52s - loss: 0.0444 - val_loss: 0.0469
Epoch 11/13
 - 52s - loss: 0.0408 - val_loss: 0.0478
Epoch 12/13
 - 52s - loss: 0.0381 - val_loss: 0.0498
Epoch 13/13
 - 54s - loss: 0.0356 - val_loss: 0.0363

Now, we make predictions with test data:

pred = model.predict([x_test[:, 0], x_test[:, 1]])

Next, we define a function for computing accuracy:

def compute_accuracy(predictions, labels):
    return labels[predictions.ravel() 

Now, we compute the accuracy of model:

compute_accuracy(pred, y_test)

0.9779092702169625

In this tutorial, we have learned to build face recognition models using siamese networks. The architecture of siamese networks, basically consists of two identical neural networks both having the same weights and architecture and the output of these networks is plugged into some energy function to understand the similarity. To learn more about meta-learning with Python, check out the book Hands-On Meta-Learning with Python.

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