Related papers: Multiple Manifolds Metric Learning with Applicatio…

Geometric representation learning in preserving the intrinsic geometric and topological properties for discrete non-Euclidean data is crucial in scientific applications. Previous research generally mapped non-Euclidean discrete data into…

Learning a distance metric from the given training samples plays a crucial role in many machine learning tasks, and various models and optimization algorithms have been proposed in the past decade. In this paper, we generalize several…

Modern machine learning systems are increasingly trained on large amounts of data embedded in high-dimensional spaces. Often this is done without analyzing the structure of the dataset. In this work, we propose a framework to study the…

The exponential growth in the number of complex datasets every year requires more enhancement in machine learning methods to provide robust and accurate data classification. Lately, deep learning approaches have achieved surpassing results…

Parametrizations of data manifolds in shape spaces can be computed using the rich toolbox of Riemannian geometry. This, however, often comes with high computational costs, which raises the question if one can learn an efficient neural…

Low rank representation (LRR) has recently attracted great interest due to its pleasing efficacy in exploring low-dimensional sub- space structures embedded in data. One of its successful applications is subspace clustering, by which data…

In this article we study the field of Hilbertian metrics and positive definit (pd) kernels on probability measures, they have a real interest in kernel methods. Firstly we will make a study based on the Alpha-Beta-divergence to have a…

In this paper we demonstrate how sub-Riemannian geometry can be used for manifold learning and surface reconstruction by combining local linear approximations of a point cloud to obtain lower dimensional bundles. Local approximations…

Supervised dimensionality reduction has emerged as an important theme in the last decade. Despite the plethora of models and formulations, there is a lack of a simple model which aims to project the set of patterns into a space defined by…

The knowledge that data lies close to a particular submanifold of the ambient Euclidean space may be useful in a number of ways. For instance, one may want to automatically mark any point far away from the submanifold as an outlier or to…

We propose a deep learning approach for discovering kernels tailored to identifying clusters over sample data. Our neural network produces sample embeddings that are motivated by--and are at least as expressive as--spectral clustering. Our…

Learning the distribution of data on Riemannian manifolds is crucial for modeling data from non-Euclidean space, which is required by many applications in diverse scientific fields. Yet, existing generative models on manifolds suffer from…

Learning in Riemannian orbifolds is motivated by existing machine learning algorithms that directly operate on finite combinatorial structures such as point patterns, trees, and graphs. These methods, however, lack statistical…

In image classification task, feature extraction is always a big issue. Intra-class variability increases the difficulty in designing the extractors. Furthermore, hand-crafted feature extractor cannot simply adapt new situation. Recently,…

Data sets tend to live in low-dimensional non-linear subspaces. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The symmetric Riemannian geometry setting can be suitable for a variety of…

Retrieving videos of a particular person with face image as a query via hashing technique has many important applications. While face images are typically represented as vectors in Euclidean space, characterizing face videos with some…

We develop a rigorous theoretical framework for principal manifold estimation that recovers a latent low-dimensional manifold from a point cloud observed in a high-dimensional ambient space. Our framework accommodates manifolds with…

Modern deep neural networks have shown remarkable performance in medical image classification. However, such networks either emphasize pixel-intensity features instead of fundamental anatomical structures (e.g., those encoded by topological…

Graph diffusion models have made significant progress in learning structured graph data and have demonstrated strong potential for predictive tasks. Existing approaches typically embed node, edge, and graph-level features into a unified…

In this paper, we present a novel deep metric learning method to tackle the multi-label image classification problem. In order to better learn the correlations among images features, as well as labels, we attempt to explore a latent space,…