相关论文: Atlas-based Manifold Representations for Interpret…

Majority of the current dimensionality reduction or retrieval techniques rely on embedding the learned feature representations onto a computable metric space. Once the learned features are mapped, a distance metric aids the bridging of gaps…

Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in…

Under the data manifold hypothesis, high-dimensional data are concentrated near a low-dimensional manifold. We study the problem of Riemannian optimization over such manifolds when they are given only implicitly through the data…

The analysis of manifold-valued data requires efficient tools from Riemannian geometry to cope with the computational complexity at stake. This complexity arises from the always-increasing dimension of the data, and the absence of…

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…

Multi-Task Learning (MTL) seeks to boost statistical power and learning efficiency by discovering structure shared across related tasks. State-of-the-art MTL representation methods, however, usually treat the latent representation matrix as…

Data for face analysis often exhibit highly-skewed class distribution, i.e., most data belong to a few majority classes, while the minority classes only contain a scarce amount of instances. To mitigate this issue, contemporary deep…

This article introduces a new data-driven approach that leverages a manifold embedding generated by the invertible neural network to improve the robustness, efficiency, and accuracy of the constitutive-law-free simulations with limited…

Real world data often lie on low-dimensional Riemannian manifolds embedded in high-dimensional spaces. This motivates learning degenerate normalizing flows that map between the ambient space and a low-dimensional latent space. However, if…

Deep learning models have gained great popularity in statistical modeling because they lead to very competitive regression models, often outperforming classical statistical models such as generalized linear models. The disadvantage of deep…

Several first order stochastic optimization methods commonly used in the Euclidean domain such as stochastic gradient descent (SGD), accelerated gradient descent or variance reduced methods have already been adapted to certain Riemannian…

System identification has greatly benefited from deep learning techniques, particularly for modeling complex, nonlinear dynamical systems with partially unknown physics where traditional approaches may not be feasible. However, deep…

In the realm of robotics, numerous downstream robotics tasks leverage machine learning methods for processing, modeling, or synthesizing data. Often, this data comprises variables that inherently carry geometric constraints, such as the…

Deep generative models are tremendously successful in learning low-dimensional latent representations that well-describe the data. These representations, however, tend to much distort relationships between points, i.e. pairwise distances…

The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing…

Point cloud analysis (such as 3D segmentation and detection) is a challenging task, because of not only the irregular geometries of many millions of unordered points, but also the great variations caused by depth, viewpoint, occlusion, etc.…

The increasing use of machine-learning (ML) enabled systems in critical tasks fuels the quest for novel verification and validation techniques yet grounded in accepted system assurance principles. In traditional system development,…

Data augmentation is a widely used technique and an essential ingredient in the recent advance in self-supervised representation learning. By preserving the similarity between augmented data, the resulting data representation can improve…

Object recognition is a key enabler across industry and defense. As technology changes, algorithms must keep pace with new requirements and data. New modalities and higher resolution sensors should allow for increased algorithm robustness.…

Modeling non-Euclidean data is drawing extensive attention along with the unprecedented successes of deep neural networks in diverse fields. Particularly, a symmetric positive definite matrix is being actively studied in computer vision,…