Related papers: Preserving local densities in low-dimensional embe…

Tensor decomposition of high-dimensional data often struggles to capture semantically or physically meaningful structures, particularly when relying on reconstruction objectives and fixed-rank constraints. We introduce a no-rank tensor…

Data visualizations summarize high-dimensional distributions in two or three dimensions. Dimensionality reduction entails a loss of information, and what is preserved differs between methods. Existing methods preserve the local or the…

Filtering multi-dimensional images such as color images, color videos, multispectral images and magnetic resonance images is challenging in terms of both effectiveness and efficiency. Leveraging the nonlocal self-similarity (NLSS)…

Density based representations of atomic environments that are invariant under Euclidean symmetries have become a widely used tool in the machine learning of interatomic potentials, broader data-driven atomistic modelling and the…

We propose an algorithmic framework for dataset normalization in data augmentation pipelines that preserves topological stability under non-uniform scaling transformations. Given a finite metric space \( X \subset \mathbb{R}^n \) with…

Deep Neural Networks (DNNs) have the potential to improve the quality of image-based 3D reconstructions. However, the use of DNNs in the context of 3D reconstruction from large and high-resolution image datasets is still an open challenge,…

High-dimensional data, characterized by many features, can be difficult to visualize effectively. Dimensionality reduction techniques, such as PCA, UMAP, and t-SNE, address this challenge by projecting the data into a lower-dimensional…

Spectral Embedding (SE) has often been used to map data points from non-linear manifolds to linear subspaces for the purpose of classification and clustering. Despite significant advantages, the subspace structure of data in the original…

High-dimensional clustering often relies on geometric or local-similarity structure, but the dominant separation between groups may not always be location-based. Differences in dispersion can create asymmetric local-neighborhood patterns:…

The rise of internet has resulted in an explosion of data consisting of millions of articles, images, songs, and videos. Most of this data is high dimensional and sparse. The need to perform an efficient search for similar objects in such…

We present the results of the application of locally linear embedding (LLE) to reduce the dimensionality of dereddened and continuum subtracted near-infrared spectra using a combination of models and real spectra of massive protostars…

Dimension reduction (DR) is commonly utilized to capture the intrinsic structure and transform high-dimensional data into low-dimensional space while retaining meaningful properties of the original data. It is used in various applications,…

Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions. Here we consider an alternative, which embeds data as discrete…

Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of…

Precision mapping of landslide inventory is crucial for hazard mitigation. Most landslides generally co-exist with other confusing geological features, and the presence of such areas can only be inferred unambiguously at a large scale. In…

In high-dimension, low-sample size (HDLSS) data, it is not always true that closeness of two objects reflects a hidden cluster structure. We point out the important fact that it is not the closeness, but the "values" of distance that…

In this note we discuss a common misconception, namely that embeddings are always used to reduce the dimensionality of the item space. We show that when we measure dimensionality in terms of information entropy then the embedding of sparse…

Auto-Encoder (AE)-based deep subspace clustering (DSC) methods have achieved impressive performance due to the powerful representation extracted using deep neural networks while prioritizing categorical separability. However,…

Monocular Depth and Surface Normals Estimation (MDSNE) is crucial for tasks such as 3D reconstruction, autonomous navigation, and underwater exploration. Current methods rely either on discriminative models, which struggle with transparent…

Here we introduce the Delaunay Density Estimator Method. Its purpose is rendering a fully volume-covering reconstruction of a density field from a set of discrete data points sampling this field. Reconstructing density or intensity fields…