In this video, we will learn about deep learning algorithms. We will start with supervised deep learning algorithms, and in this video, we will learn about convolutional neural networks. Convolutional neural networks are very similar to the neural networks that we have seen so far in this course. They are made up of neurons, which need to have the weights and biases optimized. Each neuron combines the inputs that it receives by computing the dot product between each input and the corresponding weight before it fits the resulting total input into an activation function, ReLU most likely. So then, what is different with these networks and why are they called convolutional neural networks? Well convolutional neural networks, or CNNs for short, make the explicit assumption that the inputs are images, which allows us to incorporate certain properties into their architecture. These properties make the forward propagation step much more efficient and vastly reduces the amount of parameters in the network. Therefore, CNNs are best for solving problems related to image recognition, object detection, and other computer vision applications. Here is a typical architecture of a convolutional neural network. As you can see, the network consists of a series of convolutional, ReLU,  and pooling layers as well as a number of fully connected layers which are necessary before the output is generated. Now, let's study what happens in each layer. So far, we have dealt only with conventional neural networks that take an ( n x 1) vector as their input. The input to a convolutional neural network, on the other hand, is mostly an (n x m x 1) for grayscale images or an (n x m x 3) for colored images, where the number 3 represents the red, green, and blue components of each pixel in the image. In the convolutional layer, we basically define filters and we compute the convolution between the defined filters and each of the three images. If we take the red image for example, let's assume these are the pixel values. Now for a (2 x 2) filter with these values, let's create an empty matrix to save the results of the convolution process. We start by sliding the filter over the image and computing the dot product between the filter and the overlapping pixel values and storing the result in the empty matrix. We repeat this step moving our filter one cell, or one stride is the proper terminology, at a time, and we repeat this until we cover the entire image and fill the empty matrix. Here, I just showed one filter and only one of the three images. The same thing would be applied to the green and blue images and you can apply more than one filter. The more filters we use, the more we are able to preserve the spatial dimensions better. But one question you must be asking yourself at this point is, why would we need to use convolution? Why not flatten the input image into an (n x m) x 1 vector and use that as our input? Well, if we do that, we will end up with a massive number of parameters that will need to be optimized, and it will be super computationally expensive. Also, decreasing the number of parameters would definitely help in preventing the model from overfitting the training data. It is worth mentioning that a convolutional layer also consists of ReLU's which filter the output of the convolutional step passing only positive values and turning any negative values to 0. The next layer in our convolutional neural network is the pooling layer. The pooling layer's main objective is to reduce the spatial dimensions of the data propagating through the network. There are two types of pooling that are widely used in convolutional neural networks. Max- pooling and average pooling. In max-pooling which is the most common of the two, for each section of the image we scan we keep the highest value, like so. Here our filter is moving two strides at a time. Similarly, with average pooling, we compute the average of each area we scan. In addition to reducing the dimension of the data, pooling, or max pooling in particular, provides spatial variance which enables the neural network to recognize objects in an image even if the object does not exactly resemble the original object. Finally, in the fully connected layer, we flatten the output of the last convolutional layer and connect every node of the current layer with every other node of the next layer. This layer basically takes as input the output from the preceding layer, whether it is a convolutional layer, ReLU, or pooling layer, and outputs an n-dimensional vector, where n is the number of classes pertaining to the problem at hand. For example, if you are building a network to classify images of digits, the dimension n would be 10, since there are 10 digits. You will be covering convolutional neural networks in much more details in the other courses in this specialization, but this information is more than enough to give you a general understanding of convolutional neural networks. Now let's see how we can use the Keras library to build a convolutional neural network. Here I will show you how you can use the Keras library to build a convolutional neural network. Training and testing of a convolutional neural network are the same as what we have seen so far. So to begin with, we use the sequential constructor to create our model. Then, we define our input to be the size of the input images. Assuming the input images are 128 by 128 color images, we define the input shape to be a tuple of (128, 128, 3). Next, we start adding layers to the network. We start with a convolutional layer, with 16 filters, each filter being of size 2x2 and slides through the image with a stride of magnitude 1 in the horizontal direction, and of magnitude 1 in the vertical direction. And the layer uses the ReLU activation function. Then, we add a pooling layer and we're using max-pooling here with a filter or pooling size of 2 and the filter slides through the image with a stride of magnitude 2. Next, we add another set of convolutional and pooling layers. The only difference here is we are using more filters in the convolutional layer, actually twice as many filters as the first convolutional layer. Finally, we flatten the output from these layers so that the data can proceed to the fully connected layers. We add another dense layer with 100 nodes and an output layer that has nodes equal to the number of classes in the problem at hand. And we use the softmax activation function in order to convert the outputs into probabilities. With this, we conclude this video on convolutional neural networks. In the lab, we will implement a complete convolutional neural network, where we will use the Keras library to build the network, train it, and then validate it. So make sure to complete this module's lab on convolution learning networks.