  Robot kinematics data, despite being a high dimensional process, is highly
correlated, especially when considering motions grouped in certain primitives.
These almost linear correlations within primitives allow us to interpret the
motions as points drawn close to a union of low-dimensional linear subspaces in
the space of all motions. Motivated by results of embedding theory, in
particular, generalizations of Whitney embedding theorem, we show that random
linear projection of motor sequences into low dimensional space loses very
little information about structure of kinematics data. Projected points are
very good initial guess for values of latent variables in generative model for
robot sensory-motor behaviour primitives. We conducted series of experiments
where we trained a recurrent neural network to generate sensory-motor sequences
for robotic manipulator with 9 degrees of freedom. Experimental results
demonstrate substantial improvement in generalisation abilities for unobserved
samples in the case of initialization of latent variables with random linear
projection of motor data over initialization with zero or random values.
Moreover, latent space is well-structured wherein samples belonging to
different primitives are well separated from the onset of training process.
