  We develop a supervised machine learning algorithm that is able to learn
topological phases of finite condensed matter systems from bulk data in real
lattice space. The algorithm employs diagonalization in real space together
with any supervised learning algorithm to learn topological phases through an
eigenvector ensembling procedure. We combine our algorithm with decision trees
and random forests to successfully recover topological phase diagrams of
Su-Schrieffer-Heeger (SSH) models from bulk lattice data in real space and show
how the Shannon information entropy of ensembles of lattice eigenvectors can be
used to retrieve a signal detailing how topological information is distributed
in the bulk. We further use insights obtained from these information entropy
signatures to engineer global topological features from real space lattice data
that still carry most of the topological information in the lattice, while
greatly diminishing the size of feature space, thus effectively amounting to a
topological lattice compression. Finally, we explore the theoretical
possibility of interpreting the information entropy topological signatures in
terms of emergent information entropy wave functions, which lead us to
Heisenberg and Hirschman uncertainty relations for topological phase
transitions. The discovery of Shannon information entropy signals associated
with topological phase transitions from the analysis of data from several
thousand SSH systems illustrates how model explainability in machine learning
can advance the research of exotic quantum materials with properties that may
power future technological applications such as qubit engineering for quantum
computing.
