Related papers: Locality preserving projection on SPD matrix Lie g…
Local Differential Privacy (LDP) is the gold standard trust model for privacy-preserving machine learning by guaranteeing privacy at the data source. However, its application to image data has long been considered impractical due to the…
We consider problems of dimensionality reduction and learning data representations for continuous spaces with two or more independent degrees of freedom. Such problems occur, for example, when observing shapes with several components that…
The common graph Laplacian regularizer is well-established in semi-supervised learning and spectral dimensionality reduction. However, as a first-order regularizer, it can lead to degenerate functions in high-dimensional manifolds. The…
Deep implicit functions have shown remarkable shape modeling ability in various 3D computer vision tasks. One drawback is that it is hard for them to represent a 3D shape as multiple parts. Current solutions learn various primitives and…
The integration of Symmetric Positive Definite (SPD) matrices into deep learning has historically relied on fixed algebraic Riemannian metrics. Analogous to hand-crafted features in classical machine learning, these static formulations…
Face recognition has been widely studied due to its importance in smart cities applications. However, the case when both training and test images are corrupted is not well solved. To address such a problem, this paper proposes a locality…
Dimensionality reduction is an integral part of data visualization. It is a process that obtains a structure preserving low-dimensional representation of the high-dimensional data. Two common criteria can be used to achieve a dimensionality…
We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices. A salient feature of the proposed factorization scheme is it decouples the…
A significant issue in training deep neural networks to solve supervised learning tasks is the need for large numbers of labelled datapoints. The goal of semi-supervised learning is to leverage ubiquitous unlabelled data, together with…
It is proven that encoding images and videos through Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, can lead to increased classification performance. Taking into account manifold…
Data visualisation helps understanding data represented by multiple variables, also called features, stored in a large matrix where individuals are stored in lines and variable values in columns. These data structures are frequently called…
Pretrained vision-language models (VLMs), such as CLIP, have shown remarkable potential in few-shot image classification and led to numerous effective transfer learning strategies. These methods leverage the pretrained knowledge of VLMs to…
This work puts forth low-complexity Riemannian subspace descent algorithms for the minimization of functions over the symmetric positive definite (SPD) manifold. Different from the existing Riemannian gradient descent variants, the proposed…
The projective shape of a configuration of k points or "landmarks" in RP(d) consists of the information that is invariant under projective transformations and hence is reconstructable from uncalibrated camera views. Mathematically, the…
A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…
Generative models have attracted considerable attention for their ability to produce novel shapes. However, their application in mechanical design remains constrained due to the limited size and variability of available datasets. This study…
Recent advances suggest that a wide range of computer vision problems can be addressed more appropriately by considering non-Euclidean geometry. This paper tackles the problem of sparse coding and dictionary learning in the space of…
Large pre-trained models (LPMs) have demonstrated exceptional performance in diverse natural language processing and computer vision tasks. However, fully fine-tuning these models poses substantial memory challenges, particularly in…
Dimensionality reduction-based dictionary learning methods in the literature have often used iterative random projections. The dimensionality of such a random projection matrix is a random number that might not lead to a separable subspace…
Low-rank decomposition (LRD) is a state-of-the-art method for visual data reconstruction and modelling. However, it is a very challenging problem when the image data contains significant occlusion, noise, illumination variation, and…