  In this paper, we propose a mixture of probabilistic partial canonical
correlation analysis (MPPCCA) that extracts the Causal Patterns from two
multivariate time series. Causal patterns refer to the signal patterns within
interactions of two elements having multiple types of mutually causal
relationships, rather than a mixture of simultaneous correlations or the
absence of presence of a causal relationship between the elements. In
multivariate statistics, partial canonical correlation analysis (PCCA)
evaluates the correlation between two multivariates after subtracting the
effect of the third multivariate. PCCA can calculate the Granger Causal- ity
Index (which tests whether a time-series can be predicted from an- other
time-series), but is not applicable to data containing multiple partial
canonical correlations. After introducing the MPPCCA, we propose an
expectation-maxmization (EM) algorithm that estimates the parameters and latent
variables of the MPPCCA. The MPPCCA is expected to ex- tract multiple partial
canonical correlations from data series without any supervised signals to split
the data as clusters. The method was then eval- uated in synthetic data
experiments. In the synthetic dataset, our method estimated the multiple
partial canonical correlations more accurately than the existing method. To
determine the types of patterns detectable by the method, experiments were also
conducted on real datasets. The method estimated the communication patterns In
motion-capture data. The MP- PCCA is applicable to various type of signals such
as brain signals, human communication and nonlinear complex multibody systems.
