Related papers: Tutorial: Classifying Photonic Topology Using the …
This paper introduces a simple but highly efficient ensemble for robust texture classification, which can effectively deal with translation, scale and changes of significant viewpoint problems. The proposed method first inherits the spirit…
Topological photonics is developed based on the analogy of Schr\"{o}dinger equation which is mathematically reduced to a standard eigenvalue equation. Notably, several photonic systems are beyond the standard topological band theory as they…
The topology of periodic spaces has attracted a lot of interest in recent years in order to study and classify crystalline structures and other large homogeneous data sets, such as the distribution of galaxies in cosmology. In practice,…
Persistent topological properties of an image serve as an additional descriptor providing an insight that might not be discovered by traditional neural networks. The existing research in this area focuses primarily on efficiently…
Regionalization is the task of dividing up a landscape into homogeneous patches with similar properties. Although this task has a wide range of applications, it has two notable challenges. First, it is assumed that the resulting regions are…
Neural networks represent more features than they have dimensions via superposition, forcing features to share representational space. Current methods decompose activations into sparse linear features but discard geometric structure. We…
This paper presents a structured dictionary-based model for hyperspectral data that incorporates both spectral and contextual characteristics of a spectral sample, with the goal of hyperspectral image classification. The idea is to…
Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of…
Spatio-temporal forecasting is challenging attributing to the high nonlinearity in temporal dynamics as well as complex location-characterized patterns in spatial domains, especially in fields like weather forecasting. Graph convolutions…
We define pseudo-Riemannian spectral triples, an analytic context broad enough to encompass a spectral description of a wide class of pseudo-Riemannian manifolds, as well as their noncommutative generalisations. Our main theorem shows that…
We construct localization cofiber sequences for the topological Hochschild homology (THH) and topological cyclic homology (TC) of spectral categories. Using a global construction of the THH and TC of a scheme in terms of the perfect…
Topological phononic crystals, alike their electronic counterparts, are characterized by a bulk-edge correspondence where the interior of a material dictates the existence of stable surface or boundary modes. In the mechanical setup, such…
Topology in photonics comes in two distinct flavors: global and local. Global topology considers invariants that are obtained by integrating over the energy band, whereas local topology considers defects, typically vortices, in the…
Regularization plays a crucial role in supervised learning. Most existing methods enforce a global regularization in a structure agnostic manner. In this paper, we initiate a new direction and propose to enforce the structural simplicity of…
In this article, we develop and investigate a new classifier based on features extracted using spatial depth. Our construction is based on fitting a generalized additive model to the posterior probabilities of the different competing…
Image matching that finding robust and accurate correspondences across images is a challenging task under extreme conditions. Capturing local and global features simultaneously is an important way to mitigate such an issue but recent…
Spatial transcriptomics clustering is pivotal for identifying cell subpopulations by leveraging spatial location information. While recent graph-based methods modeling cell-cell interactions have improved clustering accuracy, they remain…
Spectral Clustering (SC) is widely used for clustering data on a nonlinear manifold. SC aims to cluster data by considering the preservation of the local neighborhood structure on the manifold data. This paper extends Spectral Clustering to…
This contribution describes the mathematical theory of topological indices in solid state systems composed of non-interacting Fermions. In particular, this covers the spectral localizer and the bulk-boundary correspondence.
The local histogram transform of an image is a data cube that consists of the histograms of the pixel values that lie within a fixed neighborhood of any given pixel location. Such transforms are useful in image processing applications such…