Demystifying Autoencoders: Understanding the Mathematics and Implementation
Introduction:
Autoencoders, a class of artificial neural networks, are celebrated for their ability to learn compact representations of data without supervision. To truly comprehend their functionality, one must delve into the mathematical underpinnings and intricacies of their implementation.
What are Autoencoders?
Autoencoders are neural networks comprised of an encoder and a decoder. The encoder compresses the input data into a latent space representation, while the decoder aims to reconstruct the original input from this compressed representation.
Encoder: The encoder function, denoted as f, maps the input data X to a latent representation h: h=f(X).
Decoder: Conversely, the decoder function, denoted as g, reconstructs the input data X′ from the latent representation: X′=g(h).
Mathematics Behind Autoencoders: Autoencoders minimize a loss function that quantifies the discrepancy between the original input data and its reconstruction. Mean Squared Error (MSE) is a commonly employed loss function:
Where:
- N is the number of samples in the dataset,
- Xi represents the i-th sample of the original data,
