Initializing FWSA K-Means With Feature Level Constraints

Weighted K-Means (WKM) algorithms are increasingly important with the increase of data dimension. WKM faces an initialization problem that is more complicated than K-Means’ because in addition to picking initial cluster centers, it should also provide feature weights. Moreover, the one-dimensional solution to WKM’s widely used objective function is unacceptable in most cases. Yet, the initialization of WKM, especially the initialization of feature weight, has been largely ignored. This paper studies the problem by analyzing Feature weight self-adjustment K-Means(FWSA K-Means), a popular WKM proposed to avoid the one-dimensional solution. Experimental results suggest that the algorithm is actually easy to cluster mainly based on a single feature information when it is not well initialized. Moreover, the paper argues that initial feature weights and cluster centers are equally important in determining the final partition. Therefore it suggests using feature level constraints to improve the initialization and proposes a semi-supervised algorithm Constrained FWSA K-Means (CFWSA K-Means). The algorithm uses constraints in evaluating feature weights and clusters to guide their evolution at the stage of initialization. Experimental results suggest that it is effective and robust in utilizing constraints. In addition, if its initialization process is started by the cluster centers provided by BRIk, an initialization approach for K-Means, the performance can be further improved.