Abstract Image Classification with Convolutional Neural Networks (CNNs)
The invention of convolutional neural networks (CNNs) applied to vision represents by far one of the most innovative achievements in the history of applied mathematics. With their multiple layers (visible and hidden), CNNs have brought artificial intelligence from machine learning to deep learning.
In Chapter 8, Solving the XOR Problem with a Feedforward Neural Network, we saw that f(x, w) is the building block of any neural network. A function f will transform an input x with weights w to produce an output. This output can be used as such or fed into another layer. In this chapter, we will generalize this principle and introduce several layers. At the same time, we will use datasets with images. We will have a dataset for training and a dataset for validation to confirm that our model works.
A CNN relies on two basic tools of linear algebra: kernels and functions, applying...