  Similarity distance measure between two trajectories is an essential tool to
understand patterns in motion, for example, in Human-Robot Interaction or
Imitation Learning. The problem has been faced in many fields, from Signal
Processing, Probabilistic Theory field, Topology field or Statistics
field.Anyway, up to now, none of the trajectory similarity measurements metrics
are invariant to all possible linear transformation of the trajectories
(rotation, scaling, reflection, shear mapping or squeeze mapping). Also not all
of them are robust in front of noisy signals or fast enough for real-time
trajectory classification. To overcome this limitation this paper proposes a
similarity distance metric that will remain invariant in front of any possible
linear transformation.Based on Pearson Correlation Coefficient and the
Coefficient of Determination, our similarity metric, the Generalized Multiple
Correlation Coefficient (GMCC) is presented like the natural extension of the
Multiple Correlation Coefficient. The motivation of this paper is two fold.
First, to introduce a new correlation metric that presents the best properties
to compute similarities between trajectories invariant to linear
transformations and compare it with some state of the art similarity
distances.Second, to present a natural way of integrating the similarity metric
in an Imitation Learning scenario for clustering robot trajectories.
