In this paper, we address the challenges inherent in Sparse Subspace Clustering (SSC), a technique central to the field of data analysis, particularly in high-dimensional datasets. SSC's efficacy in uncovering complex feature patterns is well-established, yet it grapples with issues of over-sparsification due to the L1-norm penalty, which can lead to sub-optimal clustering outcomes. To overcome this, we introduce a novel sparsity regularization approach, named Elastic Stars (ES), which synergizes the benefits of sparsity and connectivity within clusters. ES minimizes the distance between variables and a dynamically evolving set of centroids, including a zero centroid, to ensure a balanced representation matrix. We further enhance our methodology with an L2 norm penalty to mitigate noise and outlier distortions. Despite the non-convex and non-smooth nature of our model, we propose an effective optimization solution using the Alternating Direction Method of Multipliers (ADMM), tailored for SSC with ES. Our empirical results demonstrate that ES regularization significantly improves the accuracy of cluster formations in comparison to existing methods, especially in the context of Hyperspectral Imaging (HSI) Datasets.