Alternatives of Unsupervised Representations of Variables on the Latent Space

The article addresses the application of unsupervised machine learning to represent variables on the 2D latent space by applying a variational autoencoder (beta-VAE). Representation of variables on low dimensional spaces allows for data visualization, disentanglement of variables based on underlying characteristics, finding of meaningful patterns and outliers, and supports interpretability. Five distinct methods have been introduced to represent variables on the latent space: (1) straightforward transposed, (2) univariate metadata of variables, such as variable statistics, empirical probability density and cumulative distribution functions, (3) adjacency matrices of different metrics, such as correlations, R2 values, Jaccard index, cosine similarity, and mutual information, (4) gradient mappings followed by spot cross product calculation, and (5) combined. Twenty-eight approaches of variable representations by beta-VAE have been considered. The pairwise spot cross product addresses relationships of gradients of two variables along latent space axes, such as orthogonal, confounded positive, confounded negative, and everything in between. The article addresses generalized representations of variables that cover both features and labels. Dealing with categorical variables, reinforced entanglement has been introduced to represent one-hot encoded categories. The article includes three examples: (1) synthetic data with known dependencies, (2) famous MNIST example of handwritten numbers, and (3) real-world multivariate time series of Canadian financial market interest rates. As a result, unsupervised representations of interest rates on the latent space correctly disentangled rates based on their type, such as bonds, T-bills, GICs, or conventional mortgages, positioned bonds and T-bills along a single curve, and ordered rates by their terms along that curve.