2016/03/16 by Ravi Garg, Anders Eriksson, Garg, Ravi +3
Computer Science · Engineering · #Computer Vision and Pattern Recognition (cs.CV) #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #Medical Image Segmentation Techniques #Sparse and Compressive Sensing Techniques #cs.CV
paper · pdf · doi:10.48550/arxiv.1603.05015
arxiv created 2016/03/16 · openalex publication_date 2016/03/16 · arxiv updated 2016/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider an ill-posed inverse problem of estimating causal factors from observations, one of which is known to lie near some (un- known) low-dimensional, non-linear manifold expressed by a predefined Mercer-kernel. Solving this problem requires simultaneous estimation of these factors and learning the low-dimensional representation for them. In this work, we introduce a novel non-linear dimensionality regulariza- tion technique for solving such problems without pre-training. We re-formulate Kernel-PCA as an energy minimization problem in which low dimensionality constraints are introduced as regularization terms in the energy. To the best of our knowledge, ours is the first at- tempt to create a dimensionality regularizer in the KPCA framework. Our approach relies on robustly penalizing the rank of the recovered fac- tors directly in the implicit feature space to create their low-dimensional approximations in closed form. Our approach performs robust KPCA in the presence of missing data and noise. We demonstrate state-of-the-art results on predicting missing entries in the standard oil flow dataset. Additionally, we evaluate our method on the challenging problem of Non-Rigid Structure from Motion and our approach delivers promising results on CMU mocap dataset despite the presence of significant occlusions and noise.