  Humans can synchronize with musical events whilst coordinating their
movements with others. Interpersonal entrainment phenomena, such as dance,
involve multiple body parts and movement directions. Along with being
multidimensional, dance movement interaction is plurifrequential, since it can
occur at different frequencies simultaneously. Moreover, it is prone to
nonstationarity, due to, for instance, displacements around the dance floor.
Various methodological approaches have been adopted to study entrainment, but
only spectrogram-based techniques allow for an integral analysis thereof. This
article proposes an alternative approach based upon the cross-wavelet
transform, a technique for nonstationary and plurifrequential analysis of
univariate interaction. The presented approach generalizes the cross-wavelet
transform to multidimensional signals. It allows to identify, for different
frequencies of movement, interaction estimates of interaction and
leader-follower dynamics across body parts and movement directions. Further,
the generalized cross-wavelet transform can be used to quantify the
frequency-wise contribution of individual body parts and movement directions to
overall synchrony. The article provides a thorough mathematical description of
the method and includes proofs of its invariance under translation, rotation,
and reflection. Finally, its properties and performance are illustrated via
examples using simulated data and behavioral data collected through a mirror
game task and a free dance movement task.
