Subspace clustering is increasingly recognized as a useful and accurate alternative to conventional techniques. While a large number of hard subspace approaches have been introduced, only a handful of soft counterparts are developed with the common goal of obtaining the optimal cluster-specific dimension weights. These existing methods similarly extend k-means and rely on the iteratively modified cluster centers for the weight determination. As the quality of discovered centers are uncertain, the accuracy of weights may not always be maintained. Intuitively, by reducing such a dependency, the weight modification can be more effective, thus improving the goodness of data clustering. This paper presents a new soft subspace clustering method that implements the above-mentioned idea and demonstrates outstanding performance on real gene expression data, as compared to several existing algorithms found in the literature.