FineMorphs: Affine-diffeomorphic sequences for regression
Michele Lohr Laurent Younes
A multivariate regression model of affine and diffeomorphic transformation
sequences - FineMorphs - is presented. Leveraging concepts from shape analysis,
model states are optimally "reshaped" by diffeomorphisms generated by smooth
vector fields during learning. Affine transformations and vector fields are
optimized within an optimal control setting, and the model can naturally reduce
(or increase) dimensionality and adapt to large datasets via suboptimal vector
fields. An existence proof of solution and necessary conditions for optimality
for the model are derived. Experimental results on real datasets from the UCI
repository are presented, with favorable results in comparison with
state-of-the-art in the literature and densely-connected neural networks in
TensorFlow.