16. A method for relational analysis of data, comprising: (a) receiving an input data set represented as a set of exponential family distributions {{F (j) } j=1 m ,{S (j) } j=1 m ,{R (ij) } i,j=1 m }; (b) storing an initial estimate of a set of matrices {tilde over (Ω)}, comprising cluster membership matrices {Λ (j) } j=1 m , attribute matrices F (j) , attribute expectation matrices {Θ (j) } j=1 m for the attribute matrices, homogeneous relation matrices S (j) , homogeneous relation expectation matrices {Γ (j) } j=1 m for the homogeneous relation matrices S (j) , heterogeneous relation matrices R (ij) , and heterogeneous relation expectation matrices { (ij) } i,j=1 m for the heterogeneous relation matrices R (ij) ; (c) automatically iteratively computing a posterior function Pr({C (j) }|F (j) } j=1 m ,{S (j) } j=1 m ,{R (ij) } i,j=1 m ,{tilde over (Ω)}) using a Monte Carlo approach, which maximizes a fitness of at least the cluster membership matrices {Λ (j)} j=1 m ; (d) comparing the stored set of matrices {tilde over (Ω)} with a resulting set of matrices Ω of an iteration of the posterior function to determine if convergence is achieved; and (e) storing a result after convergence is achieved.
17. The method according to claim 16 , wherein the posterior function Pr({C (j) }|F (j) } j=1 m ,{S (j) } j=1 m ,{R (ij) } i,j=1 m ,{tilde over (Ω)}) is computer using a Gibbs sampler, wherein: C (j) is a cluster indicator matrix: Λ (j) is computed using Λ hp (1) =Pr(C hp (1) =1|F,S,R,{tilde over (Ω)}), ⁢ Θ ( j ) ⁢ ⁢ is ⁢ ⁢ computed ⁢ ⁢ using ⁢ ⁢ Θ · g = ∑ p = 1 n 1 ⁢ F · p ⁢ Pr ⁡ ( C gp ( 1 ) = 1 | F , S , R , Ω ~ ) ∑ p = 1 n 1 ⁢ Pr ⁡ ( C gp ( 1 ) = 1 | F , S , R , Ω ~ ) , ⁢ Γ ( j ) ⁢ ⁢ is ⁢ ⁢ computed ⁢ ⁢ using ⁢ ⁢ Γ gh = ∑ p , q = 1 n 1 ⁢ S pq ⁢ Pr ⁡ ( C gp ( 1 ) = 1 , C hq ( 1 ) = 1 | F , S , R , Ω ~ ) ∑ p , q = 1 n 1 ⁢ Pr ⁡ ( C gp ( 1 ) = 1 , C hq ( 1 ) = 1 | F , S , R , Ω ~ ) , ⁢ ( ij ) ⁢ ⁢ is ⁢ ⁢ computed ⁢ ⁢ using ⁢ ⁢ ∑ p = 1 n 1 ⁢ ∑ q = 1 n 2 ⁢ R pq ⁢ Pr ⁡ ( C gp ( 1 ) = 1 , C hq ( 2 ) = 1 | F , S , R , Ω ~ ) ∑ p = 1 n 1 ⁢ ∑ q = 1 n 2 ⁢ Pr ⁡ ( C gp ( 1 ) = 1 , C hq ( 2 ) = 1 | F , S , R , Ω ~ ) .