Related papers: GeoMM: On Geodesic Perspective for Multi-modal Lea…
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…
Geospatial data has been transformative for the monitoring of the Earth, yet, as in the case of (geo)physical monitoring, the measurements can have variable spatial and temporal sampling and may be associated with a significant level of…
Recent work in distance metric learning has focused on learning transformations of data that best align with provided sets of pairwise similarity and dissimilarity constraints. The learned transformations lead to improved retrieval,…
We introduce a notion of distance between supervised learning problems, which we call the Risk distance. This distance, inspired by optimal transport, facilitates stability results; one can quantify how seriously issues like sampling bias,…
We give bounds on geodesic distances on the Stiefel manifold, derived from new geometric insights. The considered geodesic distances are induced by the one-parameter family of Riemannian metrics introduced by H\"uper et al. (2021), which…
Mode connectivity is a phenomenon where trained models are connected by a path of low loss. We reframe this in the context of Information Geometry, where neural networks are studied as spaces of parameterized distributions with curved…
We propose unsupervised representation learning and feature extraction from dendrograms. The commonly used Minimax distance measures correspond to building a dendrogram with single linkage criterion, with defining specific forms of a level…
The $\mathcal{G}^0$ distribution is widely used for monopolarized SAR image modeling because it can characterize regions with different degree of texture accurately. It is indexed by three parameters: the number of looks (which can be…
We propose a novel node embedding of directed graphs to statistical manifolds, which is based on a global minimization of pairwise relative entropy and graph geodesics in a non-linear way. Each node is encoded with a probability density…
We present an efficient dynamic data structure that supports geodesic nearest neighbor queries for a set $S$ of point sites in a static simple polygon $P$. Our data structure allows us to insert a new site in $S$, delete a site from $S$,…
Distance measures play an important role in shape classification and data analysis problems. Topological distances based on Reeb graphs and persistence diagrams have been employed to obtain effective algorithms in shape matching and scalar…
In order to compare and interpolate signals, we investigate a Riemannian geometry on the space of signals. The metric allows discontinuous signals and measures both horizontal (thus providing many benefits of the Wasserstein metric) and…
Multimodal data pervades various domains, including healthcare, social media, and transportation, where multimodal graphs play a pivotal role. Machine learning on multimodal graphs, referred to as multimodal graph learning (MGL), is…
Learned local descriptors based on Convolutional Neural Networks (CNNs) have achieved significant improvements on patch-based benchmarks, whereas not having demonstrated strong generalization ability on recent benchmarks of image-based 3D…
Laplacian-based methods are popular for the dimensionality reduction of data lying in $\mathbb{R}^N$. Several theoretical results for these algorithms depend on the fact that the Euclidean distance locally approximates the geodesic distance…
Selective segmentation is an important application of image processing. In contrast to global segmentation in which all objects are segmented, selective segmentation is used to isolate specific objects in an image and is of particular…
Machine learning has been progressively generalised to operate within non-Euclidean domains, but geometrically accurate methods for learning on surfaces are still falling behind. The lack of closed-form Riemannian operators, the…
The constraint of neighborhood consistency or local consistency is widely used for robust image matching. In this paper, we focus on learning neighborhood topology consistent descriptors (TCDesc), while former works of learning descriptors,…
We consider the problem of learning distance-based Graph Convolutional Networks (GCNs) for relational data. Specifically, we first embed the original graph into the Euclidean space $\mathbb{R}^m$ using a relational density estimation…
Generative model evaluation commonly relies on high-dimensional embedding spaces to compute distances between samples. We show that dataset representations in these spaces are affected by the hubness phenomenon, which distorts…