14. A method of clustering data, comprising the steps of: (a) providing a data matrix representing a set of objects, the set comprising at least three different types of objects, each object having an associated feature matrix and an associated relation matrix, representing respective relations with other objects of the at least three different types; (b) collectively factorizing the data matrix, feature matrices and relation matrices, to discover hidden structures of the set of objects based on both feature information and relation information; (c) generating a symmetric matrix comprising a set of weights, which maximizes an objective function of the data matrix, feature matrices and relation matrices; and (d) deriving a set of cluster indicator matrices based on the collective factorization, to achieve adaptive dimensionality reduction for each of the different types of object, wherein the symmetric matrix is a function of at least: the data matrix, representing respective relations between distinct objects as members of a plurality of sets to be clustered into disjoint clusters; at least one feature matrix denoting feature values for an associated object; a plurality of tentative cluster characterization matrices; and a set of weights for different types of relations and features.
19. The method according to claim 14 , wherein the objective function comprises: max { ( C ( i ) ) T ⁢ C ( i ) = I k i } 1 ≤ i ≤ m ⁢ ∑ 1 ≤ i ≤ m ⁢ ⁢ w b ( i ) ⁢ tr ⁡ ( ( C ( i ) ) T ⁢ F ( i ) ⁡ ( F ( i ) ) T ⁢ C ( i ) ) + ∑ 1 ≤ i ≤ j ≤ m ⁢ ⁢ w a ( ij ) ⁢ tr ⁡ ( ( C ( i ) ) T ⁢ R ( ij ) ⁢ C ( j ) ⁡ ( C ( j ) ) T ⁢ ( R ( ij ) ) T ⁢ C ( i ) ) subject to the constraints: ∑ q = 1 k i ⁢ ⁢ C pq ( i ) = 1 , 1 ≤ i ≤ j ≤ m , where: C (i) ε{0,1} n i ×k i is a cluster indicator matrix for data object χ i such that ∑ q = 1 k i ⁢ ⁢ C pq ( i ) = 1 and C pq (i) denotes that the p th object in χ i is associated with the q th cluster of k i number of clusters; R (ij) ε n i ×n j is a set of relation matrices; F (i) ε n i ×f i is a feature matrix of χ j , the cluster structure of which being reflected in the factorization of F (i) such that F (i) ≈C (i) B (i) ; B (i) ε k i ×f i is the feature basis matrix which consists of k i basis vectors in the feature space, each a representing cluster center; n i is a number of elements in data object i; and f i is a number of features for data object i.