9. A method for relational analysis of data, comprising: (a) receiving an input data set is 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: membership matrices {Λ (j) } j=1 m , attribute expectation matrices {Θ (j) } j=1 m for attribute matrices F (j) , homogeneous relation expectation matrices {Γ (j) } j=1 m for homogeneous relation matrices S (j) , and heterogeneous relation expectation matrices {γ (ij) } i,j=1 m , for heterogeneous relation matrices R (ij) ; (c) with an automated processor, iteratively computing, for each respective value of i and j, a posterior function , wherein Pr({C (j) }|F (j) } j=1 m ,{S (j) } j=1 m ,{R (ij) } i,j=1 m ,{tilde over (Ω)}), wherein C (j) is a cluster indicator matrix: Λ ( j ) ⁢ ⁢ using ⁢ ⁢ Λ hp ( 1 ) = Pr ⁢ ( C hp ( 1 ) = 1 ❘ F , S , R , Ω ~ ) , Θ ( j ) ⁢ ⁢ 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 ) ⁢ ⁢ 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 ~ ) , Υ ( ij ) ⁢ ⁢ using ⁢ ⁢ Υ gh = ∑ 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 ~ ) ; (d) comparing the stored set of matrices {tilde over (Ω)} with a resulting set of matrices Ω of an iteration of said computing to determine a convergence; and (e) outputting a converged result Ω.
9. A method for relational analysis of data, comprising: (a) receiving an input data set is 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: membership matrices {Λ (j) } j=1 m , attribute expectation matrices {Θ (j) } j=1 m for attribute matrices F (j) , homogeneous relation expectation matrices {Γ (j) } j=1 m for homogeneous relation matrices S (j) , and heterogeneous relation expectation matrices {γ (ij) } i,j=1 m , for heterogeneous relation matrices R (ij) ; (c) with an automated processor, iteratively computing, for each respective value of i and j, a posterior function , wherein Pr({C (j) }|F (j) } j=1 m ,{S (j) } j=1 m ,{R (ij) } i,j=1 m ,{tilde over (Ω)}), wherein C (j) is a cluster indicator matrix: Λ ( j ) ⁢ ⁢ using ⁢ ⁢ Λ hp ( 1 ) = Pr ⁢ ( C hp ( 1 ) = 1 ❘ F , S , R , Ω ~ ) , Θ ( j ) ⁢ ⁢ 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 ) ⁢ ⁢ 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 ~ ) , Υ ( ij ) ⁢ ⁢ using ⁢ ⁢ Υ gh = ∑ 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 ~ ) ; (d) comparing the stored set of matrices {tilde over (Ω)} with a resulting set of matrices Ω of an iteration of said computing to determine a convergence; and (e) outputting a converged result Ω. 15. The method according to claim 9 , further comprising using at least the computed values Ω to determine a clustering of objects represented in the input data set.