Related papers: Conformal dimensionality reduction / increase

Data augmentation is commonly used to encode invariances in learning methods. However, this process is often performed in an inefficient manner, as artificial examples are created by applying a number of transformations to all points in the…

In this paper, we propose and analyse a family of generalised stochastic composite mirror descent algorithms. With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem. Combined with an…

With the advancement of computer technology, there is a surge of interest in effective mapping methods for objects in higher-dimensional spaces. To establish a one-to-one correspondence between objects, higher-dimensional quasi-conformal…

This paper addresses the problem of mapping high-dimensional data to a low-dimensional space, in the presence of other known features. This problem is ubiquitous in science and engineering as there are often controllable/measurable features…

We study adaptive data-dependent dimensionality reduction in the context of supervised learning in general metric spaces. Our main statistical contribution is a generalization bound for Lipschitz functions in metric spaces that are…

Clustering high-dimensional datasets is hard because interpoint distances become less informative in high-dimensional spaces. We present a clustering algorithm that performs nonlinear dimensionality reduction and clustering jointly. The…

Recently, with the help of Parisi-Sourlas supersymmetry an intriguing relation was found expressing the four-point scalar conformal block of a (d-2)-dimensional CFT in terms of a five-term linear combination of blocks of a d-dimensional…

We introduce the notion of t-restricted doubling dimension of a point set in Euclidean space as the local intrinsic dimension up to scale t. In many applications information is only relevant for a fixed range of scales. We present an…

Channel Charting is a dimensionality reduction technique that learns to reconstruct a low-dimensional, physically interpretable map of the radio environment by taking advantage of similarity relationships found in high-dimensional channel…

With the proliferation of increasingly complicated Deep Learning architectures, data synthesis is a highly promising technique to address the demand of data-hungry models. However, reliably assessing the quality of a 'synthesiser' model's…

This paper presents an extension and an elaboration of the theory of differential similarity, which was originally proposed in arXiv:1401.2411 [cs.LG]. The goal is to develop an algorithm for clustering and coding that combines a geometric…

In this paper we present a mathematical framework on linking of embeddings of compact topological spaces into Euclidean spaces and separability of linked embeddings under a specific class of dimension reduction maps. As applications of the…

Sufficient dimension reduction aims for reduction of dimensionality of a regression without loss of information by replacing the original predictor with its lower-dimensional subspace. Partial (sufficient) dimension reduction arises when…

'Big' high-dimensional data are commonly analyzed in low-dimensions, after performing a dimensionality-reduction step that inherently distorts the data structure. For the same purpose, clustering methods are also often used. These methods…

Dimensionality reduction is a crucial technique in data analysis, as it allows for the efficient visualization and understanding of high-dimensional datasets. The circular coordinate is one of the topological data analysis techniques…

We present a simple set of data structures, and a collection of methods for constructing and updating the structures, designed to support the use of cohesive elements in simulations of fracture and fragmentation. Initially all interior…

The conformal method is a technique for finding Cauchy data in general relativity solving the Einstein constraint equations, and its parameters include a conformal class, a conformal momentum (as measured by a densitized lapse), and a mean…

Image alignment and image restoration are classical computer vision tasks. However, there is still a lack of datasets that provide enough data to train and evaluate end-to-end deep learning models. Obtaining ground-truth data for image…

Most dimensionality reduction methods employ frequency domain representations obtained from matrix diagonalization and may not be efficient for large datasets with relatively high intrinsic dimensions. To address this challenge, Correlated…

We consider Hamiltonians associated with 3 dimensional conformally flat spaces, possessing 2, 3 and 4 dimensional isometry algebras. We use the conformal algebra to build additional {\em quadratic} first integrals, thus constructing a large…