  Unsupervised learning makes manifest the underlying structure of data without
curated training and specific problem definitions. However, the inference of
relationships between data points is frustrated by the `curse of
dimensionality' in high-dimensions. Inspired by replica theory from statistical
mechanics, we consider replicas of the system to tune the dimensionality and
take the limit as the number of replicas goes to zero. The result is the
intensive embedding, which is not only isometric (preserving local distances)
but allows global structure to be more transparently visualized. We develop the
Intensive Principal Component Analysis (InPCA) and demonstrate clear
improvements in visualizations of the Ising model of magnetic spins, a neural
network, and the dark energy cold dark matter ({\Lambda}CDM) model as applied
to the Cosmic Microwave Background.
