Fig 3. From spike trains to the cluster matrix.

(A) Given parallel spike train data and their intersection matrix I as in Fig 1, for each entry I_ij its cumulative probability P_ij is calculated analytically under the null hypothesis ${\mathcal{H}}_0$ that the spike trains are independent and marginally Poisson. (B) The l largest neighbors of I_ij in a rectangular area extending along the 45 degree direction are isolated by means of a kernel and their joint cumulative probability is assigned to the joint probability matrix J at position J_ij. (C) Chosen a significance threshold α₁ for the probability of individual entries (i.e. for entries P_ij) and a significance threshold α₂ for the joint probability of the neighbors of an entry (i.e. for entries J_ij), each entry I_ij for which P_ij > α₁ and J_ij > α₂ is classified as statistically significant. Significant entries of I are retained in the binary masked matrix M_ij, which takes value 1 at positions (i, j) where I is statistically significant and 0 elsewhere. (D) 1-valued entries in M falling close-by are clustered together (or discarded as isolated chance events) by means of a DBSCAN algorithm, which thus isolates diagonal structures.