Related papers: Towards Stratified Space Learning: 2-complexes
Point cloud completion aims to recover the complete shape based on a partial observation. Existing methods require either complete point clouds or multiple partial observations of the same object for learning. In contrast to previous…
Hypergraphs provide a natural way to represent polyadic relationships in network data. For large hypergraphs, it is often difficult to visually detect structures within the data. Recently, a scalable polygon-based visualization approach was…
An unsupervised shape analysis is proposed to learn concepts reflecting shape commonalities. Our approach is two-fold: i) a spatial topology analysis of point cloud segment constellations within objects is used in which constellations are…
We introduce stratified toposes, which are toposes that are stratified by a suitable hierarchy of universes. The term `stratified topos' recalls the notion of stratified pseudotopos of Moerdijk and Palmgren (2002). However, the details of…
We study random 2-dimensional complexes in the Linial - Meshulam model and find torsion in their fundamental groups at various regimes. We find a simple algorithmically testable criterion for a subcomplex of a random 2-complex to be…
Abstraction is a desirable capability for deep learning models, which means to induce abstract concepts from concrete instances and flexibly apply them beyond the learning context. At the same time, there is a lack of clear understanding…
We present a network architecture for processing point clouds that directly operates on a collection of points represented as a sparse set of samples in a high-dimensional lattice. Naively applying convolutions on this lattice scales…
In recent years, network embedding methods have garnered increasing attention because of their effectiveness in various information retrieval tasks. The goal is to learn low-dimensional representations of vertexes in an information network…
Subspace clustering algorithms are notorious for their scalability issues because building and processing large affinity matrices are demanding. In this paper, we introduce a method that simultaneously learns an embedding space along…
Deep clustering has increasingly been demonstrating superiority over conventional shallow clustering algorithms. Deep clustering algorithms usually combine representation learning with deep neural networks to achieve this performance,…
We present network embedding algorithms that capture information about a node from the local distribution over node attributes around it, as observed over random walks following an approach similar to Skip-gram. Observations from…
Let $G$ be a strictly pseudoconvex domain in $\mathbb{C}^2$ with $C^\infty$-smooth boundary $\partial G$. Let $S$ be a 2-dimensional sphere embedded into $\partial G$. Denote by $\mathcal{E}$ the set of all complex points on $S$. We study…
Using the generalized entropies which depend on two parameters we propose a set of quantitative characteristics derived from the Information Geometry based on these entropies. Our aim, at this stage, is modest, as we are first constructing…
Autoencoding is a popular method in representation learning. Conventional autoencoders employ symmetric encoding-decoding procedures and a simple Euclidean latent space to detect hidden low-dimensional structures in an unsupervised way.…
A robot operating in a real-world environment needs to perform reasoning over a variety of sensor modalities such as vision, language and motion trajectories. However, it is extremely challenging to manually design features relating such…
Multiplex networks are complex graph structures in which a set of entities are connected to each other via multiple types of relations, each relation representing a distinct layer. Such graphs are used to investigate many complex…
We outline an algorithm to recover the canonical (or, coarsest) stratification of a given finite-dimensional regular CW complex into cohomology manifolds, each of which is a union of cells. The construction proceeds by iteratively…
We present path2vec, a new approach for learning graph embeddings that relies on structural measures of pairwise node similarities. The model learns representations for nodes in a dense space that approximate a given user-defined graph…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…
Self-supervised learning on point clouds has gained a lot of attention recently, since it addresses the label-efficiency and domain-gap problems on point cloud tasks. In this paper, we propose a novel self-supervised framework to learn…