From Principal Component Analysis to Autoencoders: a comparison on simulated data from psychometric models

Dimensionality reduction is the search for a low-dimensional space that captures the 'essence' of the original high-dimensional data. Principal Component Analysis (PCA) is one of the most used dimensionality reduction techniques in psychology for data analysis and measure development. However, machine learning techniques manage more complex data, and they represent a valuable alternative to classical methods. In this work, we consider autoencoders, neural networks with as many inputs as outputs and a smaller number of hidden nodes, which are widely used in several study fields for dimensionality reduction. Recent literature has compared PCA and autoencoders focusing especially on differences concerning image reconstruction. In particular, recent research has proposed a PCA-Autoencoder, a neural network which embeds PCA properties. The objective of this work is to compare PCA-autoencoder, an autoencoder with uncorrelated hidden features, a simple autoencoder and Principal Component Analysis performances on artificial data that have been simulated from factor-based populations. Results show that three-layered linear autoencoders and PCA are very similar in performing dimensionality reduction in terms of accuracy and reconstruction error also on simulated data from psychometric models and could be used where traditional methods show their limits.