13th International Conference on Membrane Computing - MTA Sztaki

R. Pagliarini, O. Agrigoroaiei, G. Ciobanu, V. Manca
Fig. 1. Several sets of (x i, x j) points, with the Pearson correlation of x i and x j for each
set. Note that the correlation reflects the noisiness and direction of a linear relationship
(top row), but not the slope of that relationship (bottom row).
Fig. 2. Elementary interaction patterns. (a): direct interaction between two species;
(b): regulation of two species by a common regulator; (c) regulative chain via an
intermediate regulator; (d): co-regulation of a species by two regulators.
a strong correlation of the pair (x 2 , x 3 ), which might jeopardize downstream
network analysis by putting an (non oriented) edge between x 2 and x 3 , Figure 3
(b), because there will be more weight placed to the nodes x 2 and x 3 than there
actually is.
Fig. 3. (a) Illustration of causal relationships between variables (x 1, x 2) and (x 1, x 3),
and (b) the resulting network derived by correlation analysis.
Since Pearson correlation alone cannot distinguish between direct and indirect
interactions, the use of partial correlation can be useful to analyze if a direct
interaction between two time-series exists [10]. The minimum first order partial
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