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.
A range of methods aim to enhance the performance of vision-language models (VLMs) at test time. Among them, transduction has emerged as a promising paradigm due to its strong compatibility and efficiency. However, realistic evaluations often involve highly imbalanced class distr…
Free-viewing gaze data provides a rich, task-free window into human visual attention. Conventional exploratory data analysis of the data provides user attention patterns through fixations and areas of interest. However, despite the richness of this gaze data, its human-informatio…
Source-free universal domain adaptation (SF-UniDA) adapts a pre-trained source model to an unlabeled target domain under both covariate and label shifts, without access to source data. However, existing SF-UniDA methods rely on inefficient techniques such as threshold tuning and…
Despite strong performance on many multimodal tasks, vision-language models (VLMs) still struggle with basic object counting. We investigate whether this reflects missing internal knowledge or a gap between internal representations and verbalized outputs. Training simple probes o…
Brownian Bridge Diffusion Models (BBDM) offer an appealing framework for image restoration and inverse problems by constructing a stochastic bridge from the clean signal directly to the degraded observation, rather than to pure noise. Despite their promise, the choice of bridge s…
Video Diffusion Models (VDMs) have demonstrated superior generation quality but suffer from prohibitive computational costs. While recent few-step distillation techniques significantly accelerate inference, they typically enforce a static model architecture across all denoising s…