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To perform an exploration process over complex structured data within unsupervised settings, the so-called kernel spectral clustering (KSC) is one of the most recommended and appealing approaches, given its versatility and elegant formulation. In this work, we explore the relationship between (KSC) and other well-known approaches, namely normalized cut clustering and kernel k-means. To do so, we first deduce a generic KSC model from a primal-dual formulation based on least-squares support-vector machines (LS-SVM). For experiments, KSC as well as other consider methods are assessed on image segmentation tasks to prove their usability.