  In the last two decades, unsupervised latent variable models---blind source
separation (BSS) especially---have enjoyed a strong reputation for the
interpretable features they produce. Seldom do these models combine the rich
diversity of information available in multiple datasets. Multidatasets, on the
other hand, yield joint solutions otherwise unavailable in isolation, with a
potential for pivotal insights into complex systems.
  To take advantage of the complex multidimensional subspace structures that
capture underlying modes of shared and unique variability across and within
datasets, we present a direct, principled approach to multidataset combination.
We design a new method called multidataset independent subspace analysis (MISA)
that leverages joint information from multiple heterogeneous datasets in a
flexible and synergistic fashion.
  Methodological innovations exploiting the Kotz distribution for subspace
modeling in conjunction with a novel combinatorial optimization for evasion of
local minima enable MISA to produce a robust generalization of independent
component analysis (ICA), independent vector analysis (IVA), and independent
subspace analysis (ISA) in a single unified model.
  We highlight the utility of MISA for multimodal information fusion, including
sample-poor regimes and low signal-to-noise ratio scenarios, promoting novel
applications in both unimodal and multimodal brain imaging data.
