Related papers: Understanding and Improving UMAP with Geometric an…

Due to the intrinsic complexity of high-dimensional (HD) data, dimensionality reduction (DR) techniques cannot preserve all the structural characteristics of the original data. Therefore, DR techniques focus on preserving either local…

Mapper is an algorithm that summarizes the topological information contained in a dataset and provides an insightful visualization. It takes as input a point cloud which is possibly high-dimensional, a filter function on it and an open…

Multidimensional Projection is a fundamental tool for high-dimensional data analytics and visualization. With very few exceptions, projection techniques are designed to map data from a high-dimensional space to a visual space so as to…

The success of machine learning algorithms heavily relies on the quality of samples and the accuracy of their corresponding labels. However, building and maintaining large, high-quality datasets is an enormous task. This is especially true…

Manifold learning offers nonlinear dimensionality reduction of high-dimensional datasets. In this paper, we bring geometry processing to bear on manifold learning by introducing a new approach based on metric connection for generating a…

Visualizing high-dimensional data is essential for understanding biomedical data and deep learning models. Neighbor embedding methods, such as t-SNE and UMAP, are widely used but can introduce misleading visual artifacts. We find that the…

Supervised learning depth estimation methods can achieve good performance when trained on high-quality ground-truth, like LiDAR data. However, LiDAR can only generate sparse 3D maps which causes losing information. Obtaining high-quality…

Quantifying local structures in self-assembled systems is a central challenge in soft matter and materials science. When no a priori knowledge of the relevant structures is available, traditional order parameters often fall short.…

Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be…

Dimensionality reduction methods such as UMAP and t-SNE are central tools for visualising high-dimensional data, but their local-neighborhood objectives can preserve sampling noise while distorting global topology. We show that standard…

Recently, learning-based ego-motion estimation approaches have drawn strong interest from studies mostly focusing on visual perception. These groundbreaking works focus on unsupervised learning for odometry estimation but mostly for visual…

Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…

Motor impairments, frequently caused by neurological incidents like strokes or traumatic brain injuries, present substantial obstacles in rehabilitation therapy. This research aims to elevate the field by optimizing motor imagery…

Unsupervised deep metric learning (UDML) focuses on learning a semantic representation space using only unlabeled data. This challenging problem requires accurately estimating the similarity between data points, which is used to supervise a…

Networks with higher-order interactions, prevalent in biological, social, and information systems, are naturally represented as hypergraphs, yet their structural complexity poses fundamental challenges for geometric characterization. While…

Large-scale incremental mapping is fundamental to the development of robust and reliable autonomous systems, as it underpins incremental environmental understanding with sequential inputs for navigation and decision-making. LiDAR is widely…

Robust generalization under distribution shift remains difficult to monitor and optimize in the absence of target-domain labels, as models with similar in-distribution accuracy can exhibit markedly different out-of-distribution (OOD)…

With the proliferation of Graph Neural Network (GNN) methods stemming from contrastive learning, unsupervised node representation learning for graph data is rapidly gaining traction across various fields, from biology to molecular dynamics,…

UMAP has supplanted t-SNE as state-of-the-art for visualizing high-dimensional datasets in many disciplines, but the reason for its success is not well understood. In this work, we investigate UMAP's sampling based optimization scheme in…

Neighbor embedding methods $t$-SNE and UMAP are the de facto standard for visualizing high-dimensional datasets. Motivated from entirely different viewpoints, their loss functions appear to be unrelated. In practice, they yield strongly…