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Deep subspace clustering (DSC) algorithms face several challenges that hindertheir widespread adoption across variois application domains. First, clusteringquality is typically assessed using only the encoder's output layer,disregarding valuable information present in the intermediate layers. Second,most DSC approaches treat representation learning and subspace clustering asindependent tasks, limiting their effectiveness. Third, they assume theavailability of a held-out dataset for hyperparameter tuning, which is oftenimpractical in real-world scenarios. Fourth, learning termination is commonlybased on clustering error monitoring, requiring external labels. Finally, theirperformance often depends on post-processing techniques that rely on labeleddata. To address this limitations, we introduce a novel single-view DSCapproach that: (i) minimizes a layer-wise self expression loss using a jointrepresentation matrix; (ii) optimizes a subspace-structured norm to enhanceclustering quality; (iii) employs a multi-stage sequential learning framework,consisting of pre-training and fine-tuning, enabling the use of multipleregularization terms without hyperparameter tuning; (iv) incorporates arelative error-based self-stopping mechanism to terminate training withoutlabels; and (v) retains a fixed number of leading coefficients in the learnedrepresentation matrix based on prior knowledge. We evaluate the proposed methodon six datasets representing faces, digits, and objects. The results show thatour method outperforms most linear SC algorithms with careffulyl tunedhyperparameters while maintaining competitive performance with the bestperforming linear appoaches.

Label-independent hyperparameter-free self-supervised single-view deep subspace clustering