1 research outputs found
Constrained K-means with General Pairwise and Cardinality Constraints
In this work, we study constrained clustering, where constraints are utilized
to guide the clustering process. In existing works, two categories of
constraints have been widely explored, namely pairwise and cardinality
constraints. Pairwise constraints enforce the cluster labels of two instances
to be the same (must-link constraints) or different (cannot-link constraints).
Cardinality constraints encourage cluster sizes to satisfy a user-specified
distribution. However, most existing constrained clustering models can only
utilize one category of constraints at a time. In this paper, we enforce the
above two categories into a unified clustering model starting with the integer
program formulation of the standard K-means. As these two categories provide
useful information at different levels, utilizing both of them is expected to
allow for better clustering performance. However, the optimization is difficult
due to the binary and quadratic constraints in the proposed unified
formulation. To alleviate this difficulty, we utilize two techniques:
equivalently replacing the binary constraints by the intersection of two
continuous constraints; the other is transforming the quadratic constraints
into bi-linear constraints by introducing extra variables. Then we derive an
equivalent continuous reformulation with simple constraints, which can be
efficiently solved by Alternating Direction Method of Multipliers (ADMM)
algorithm. Extensive experiments on both synthetic and real data demonstrate:
(1) when utilizing a single category of constraint, the proposed model is
superior to or competitive with state-of-the-art constrained clustering models,
and (2) when utilizing both categories of constraints jointly, the proposed
model shows better performance than the case of the single category