DiHypeSC: Data-Informed Hyperparameter Adaptation for Self-Expressive Subspace Clustering

Many subspace clustering methods require careful balancing of self-expressive reconstruction and structural regularization. Improper weighting can produce either dense cross-subspace connections or overly sparse and disconnected representations, both of which degrade clustering performance. However, the corresponding trade-off parameter is often selected through costly searches using labeled validation data, and its optimal value depends strongly on the dataset, noise level, representation, and regularizer. Label-free parameter selection remains challenging because deep clustering is stochastic and non-convex, while internal validation measures may not align with the ground-truth partition. We propose DiHypeSC, a data-informed strategy derived from subspace-preserving conditions that relate regularization strength to cross-subspace correlations and reconstruction residuals. During training, DiHypeSC estimates a proxy for the subspace dimension and uses it to adapt the regularization weight to each dataset. When integrated into two state-of-the-art deep subspace clustering methods, DiHypeSC provides a unified, dimension-aware weighting principle for both elastic-net and block-diagonal regularization. Even when using only a single hyperparameter configuration, DiHypeSC often achieves better results than conventional hyperparameter searches.