| US 7,461,073 B2 | ||
| Co-clustering objects of heterogeneous types | ||
| Bin Gao, Beijing (China); Tie-Yan Liu, Beijing (China); and Wei-Ying Ma, Beijing (China) | ||
| Assigned to Microsoft Corporation, Redmond, Wash. (US) | ||
| Filed on Feb. 14, 2006, as Appl. No. 11/354,208. | ||
| Prior Publication US 2007/0192350 A1, Aug. 16, 2007 | ||
| Int. Cl. G06F 17/00 (2006.01); G06F 17/30 (2006.01) | ||
| U.S. Cl. 707—100 [707/10; 707/102; 707/104.1; 707/101; 715/530] | 18 Claims |
| 10. A computing system with a processor and memory for solving an objective function for consistent bipartite graph co-partitioning,
comprising:
a component that provides object matrices, each representing a bipartite graph representing relationships between objects
of different types where vertices represent objects and edges represent relationships;
a component that generates diagonal and Laplacian matrices for the object matrices;
a component that generates extended matrices based on the diagonal and Laplacian matrices;
a component that solves a cut-based objective function represents relationships across cuts for each of the bipartite graphs
using the extended matrices using semi-definite programming;
a component that identifies clusters of objects from the solution; and
wherein the objective function is represented as:
 where A is a matrix representing the first bipartite graph and aij is element i and j of
A, B is a matrix representing the second bipartite graph and bij is element i and j of
B, D(1) is a diagonal matrix represented as
D(1)ii=Σkaik,
D(2) is a diagonal matrix represented as
D(2)ii=Σkbik,
L(1) is a Laplacian matrix represented as
L(1)=D−A,
L(2) is a Laplacian matrix represented as
L(2)=D−B,
e is a column vector with all its elements equal to 1, q is a column vector with qi=c1 when i is an object in one cluster and qi=−c2 when i is an object in a second cluster, pi=c1 when i is an object in one cluster and pi=−c2 when i is an object in a second cluster, and β represents a weight of the relationships of the first bipartite graph and the
second bipartite graph.
|