We derive the linear union-of-subspaces (UoS) model for subspace clustering (SC) from the nonlinear mixture model (NMM) used in blind source separation (BSS) to represent a D-dimensional observation vector as an unknown multivariate nonlinear mapping of C latent variables. Assuming the mapping is differentiable up to an unknown order K, we approximate NMM by a K-th order Taylor expansion, yielding a model equivalent to the linear UoS framework underlying SC. This establishes that: (i) the smoothness order K corresponds to the unknown subspace dimension d; (ii) KC equals the number of anchors; and (iii) the sparsity of the representation vector equals K (i.e., d). These relationships enable estimation of bounds on subspace dimension, and that is validated on six benchmark datasets using five established SC algorithms. Established theoretical results are important for post-processing of self-representation matrices estimated by SC algorithms.
Adapting deep learning models to profound clinical heterogeneity typically relies on parameter-efficient fine-tuning (PEFT) to avoid the severe overfitting associated with full end-to-end network updates. Although PEFT successfully navigates limited data scenarios, it inherently…
Visual anomaly detection requires adaptive representations and reliable decision boundaries, particularly when anomalous training samples are scarce and class distributions are highly imbalanced. Classical kernel-based methods yield principled geometric decision regions but typic…
Computed tomography angiography (CTA) is crucial for preprocedural TAVI planning, providing the anatomical information required for prosthesis sizing and vascular access assessment. As the volume of TAVI procedure increases, improving efficiency and standardizing annotations is b…
Agentic assistants capable of proactive, personalized interactions require structured models of user intent and workflow. However, building these models from raw, unstructured screen activity remains an open challenge. We present SERUM, a multi-pass framework that extracts finite…
Synthetic face datasets are increasingly used to reduce privacy exposure and data access constraints in biometric recognition. Yet the generators that produce these datasets are trained on real faces, so synthetic data may still reveal their real source data. We study this risk t…
Effective multi-organ segmentation in surgical data requires learning the intricate anatomical features and alleviating the challenge of class imbalance, which results from relatively lower proportions of small and limitedly exposed structures. Recent works on laparoscopic multi-…