  Model order reduction has been extensively studied over the last two decades.
Projection-based methods such as the Proper Orthogonal Decomposition and the
Reduced Basis Method enjoy the important advantages of Galerkin methods in the
derivation of the reduced problem, but are limited to linear data compression
for which the reduced solution is sought as a linear combination of spatial
modes. Nonlinear data compression must be used when the solution manifold is
not embedded in a low-dimensional subspace. Early methods involve piecewise
linear data compression, by constructing a dictionary of reduced-order models
tailored to a partition of the solution manifold. In this work, we introduce
the concept of optimal partition of the solution manifold in terms of
normalized Kolmogorov widths, and prove that the optimal partitions can be
found by means of a representative-based clustering algorithm using the sine
dissimilarity measure on the solution manifold.
