Related papers: Parametric set-wise injective maps
We define shriek map for a finite codimensionnal embedding of fibration. We study the morphisms induced by shriek maps in the Leray-Serre spectral sequence. As a byproduct, we get two multiplicative spectral sequences of algebra wich…
Datasets with non-trivial large scale topology can be hard to embed in low-dimensional Euclidean space with existing dimensionality reduction algorithms. We propose to model topologically complex datasets using vector bundles, in such a way…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
Deep learning techniques provide a plausible route towards achieving practical imaging through multimode fibers. The results produced by these methods are often influenced by physical factors like temperature, fiber length, external…
In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and…
Representation learning is the first step in automating tasks such as research paper recommendation, classification, and retrieval. Due to the accelerating rate of research publication, together with the recognised benefits of…
We consider a general fibre of given length in a generic projection of a va- riety. Under the assumption that the fibre is of local embedding dimension 2 or less, an assumption which can be checked in many cases, we prove that the fibre is…
Autoencoders are commonly trained using element-wise loss. However, element-wise loss disregards high-level structures in the image which can lead to embeddings that disregard them as well. A recent improvement to autoencoders that helps…
We propose a new embedding method which is particularly well-suited for settings where the sample size greatly exceeds the ambient dimension. Our technique consists of partitioning the space into simplices and then embedding the data points…
Since their introduction in the shape analysis community, functional maps have met with considerable success due to their ability to compactly represent dense correspondences between deformable shapes, with applications ranging from shape…
Indoor localization systems often fuse inertial odometry with map information via hand-defined methods to reduce odometry drift, but such methods are sensitive to noise and struggle to generalize across odometry sources. To address the…
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…
Network embedding methods aim at learning low-dimensional latent representation of nodes in a network. These representations can be used as features for a wide range of tasks on graphs such as classification, clustering, link prediction,…
The current state-of-the-art for image annotation and image retrieval tasks is obtained through deep neural networks, which combine an image representation and a text representation into a shared embedding space. In this paper we evaluate…
In this paper we provide sufficient conditions in order to show that the set image of a continuous and shift-commuting map defined on a shift space over an arbitrary discrete alphabet is also a shift space; additionally, if such a map is…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
Vectorized high-definition map (HD-map) construction, which focuses on the perception of centimeter-level environmental information, has attracted significant research interest in the autonomous driving community. Most existing approaches…
Sense embedding learning methods learn multiple vectors for a given ambiguous word, corresponding to its different word senses. For this purpose, different methods have been proposed in prior work on sense embedding learning that use…
When light propagates through opaque material, the spatial information it holds becomes scrambled, but not necessarily lost. Two classes of techniques have emerged to recover this information: methods relying on optical memory effects, and…
Starting from filters over the set of indices, we introduce structures in a product of sets where the coordinate sets have the given structures.