Related papers: General Riemannian SOM

In image set classification, a considerable progress has been made by representing original image sets on Grassmann manifolds. In order to extend the advantages of the Euclidean based dimensionality reduction methods to the Grassmann…

Leachates from garbage dumps can significantly compromise their surrounding area. Even if the distance between these and the populated areas could be considerable, the risk of affecting the aquifers for public use is imminent in most cases.…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

We show unsupervised machine learning techniques are a valuable tool for both visualizing and computationally accelerating the estimation of galaxy physical properties from photometric data. As a proof of concept, we use self organizing…

Self Organizing Map (SOM) has been applied into several classical modeling tasks including clustering, classification, function approximation and visualization of high dimensional spaces. The final products of a trained SOM are a set of…

The current and upcoming large data volume galaxy surveys require the use of machine learning techniques to maximize their scientific return. This study explores the use of Self-Organizing Maps (SOMs) to estimate galaxy parameters with a…

This paper defines a new learning architecture, Layered Self-Organizing Maps (LSOMs), that uses the SOM and supervised-SOM learning algorithms. The architecture is validated with the MNIST database of hand-written digit images. LSOMs are…

We identify a region $\Bbb{W}_{\f{1}{3}}$ in a Grassmann manifold $\grs{n}{m}$, not covered by a usual matrix coordinate chart, with the following important property. For a complete $n-$submanifold in $\ir{n+m} \, (n\ge 3, m\ge2)$ with…

Correlation matrices are fundamental summaries of functional brain networks, yet standard analyses often treat entries independently, ignoring the curved geometry of correlation space. Existing geometric methods frequently lack closed-form…

Dimension reduction techniques typically seek an embedding of a high-dimensional point cloud into a low-dimensional Euclidean space which optimally preserves the geometry of the input data. Based on expert knowledge, one may instead wish to…

Graph convolutional networks (GCNs) are powerful frameworks for learning embeddings of graph-structured data. GCNs are traditionally studied through the lens of Euclidean geometry. Recent works find that non-Euclidean Riemannian manifolds…

Understanding feature-outcome associations in high-dimensional data remains challenging when relationships vary across subpopulations, yet standard methods assuming global associations miss context-dependent patterns, reducing statistical…

In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…

The immersion of the string world sheet, regarded as a Riemann surface, in $R^3$ and $R^4$ is described by the generalized Gauss map. When the Gauss map is harmonic or equivalently for surfaces of constant mean curvature, we obtain…

As a generalization of slant submersions (Sahin, 2011), semi-slant submersions (Park and Prasad), and slant Riemannian maps (Sahin), we define the notion of semi-slant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds.…

The communications and interrelations between different locations on the Earth's surface have far-reaching implications for both social and natural systems. Effective spatial analytics ideally require a spatial representation, where…

We introduce slant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds as a generalization of slant immersions, invariant Riemannian maps and anti-invariant Riemannian maps. We give examples, obtain characterizations and…

Low-dimensional structure in real-world data plays an important role in the success of generative models, which motivates diffusion models defined on intrinsic data manifolds. Such models are driven by stochastic differential equations…

Interpretability is a key issue when applying deep learning models to longitudinal brain MRIs. One way to address this issue is by visualizing the high-dimensional latent spaces generated by deep learning via self-organizing maps (SOM). SOM…

Galaxy populations show bimodality in a variety of properties: stellar mass, colour, specific star-formation rate, size, and S\'ersic index. These parameters are our feature space. We use an existing sample of 7556 galaxies from the Galaxy…