相关论文: nSimplex Zen: A Novel Dimensionality Reduction for…

Sufficient dimension reduction (SDR) is continuing an active research field nowadays for high dimensional data. It aims to estimate the central subspace (CS) without making distributional assumption. To overcome the large-$p$-small-$n$…

We introduce a dimension reduction method for visualizing the clustering structure obtained from a finite mixture of Gaussian densities. Information on the dimension reduction subspace is obtained from the variation on group means and,…

Empirically, Deep Learning (DL) has demonstrated unprecedented success in practical applications. However, DL remains by and large a mysterious "black-box", spurring recent theoretical research to build its mathematical foundations. In this…

Euclidean representation learning methods have achieved promising results in image fusion tasks, which can be attributed to their clear advantages in handling with linear space. However, data collected from a realistic scene usually has a…

Dimensionality reduction (DR) techniques map high-dimensional data into lower-dimensional spaces. Yet, current DR techniques are not designed to explore semantic structure that is not directly available in the form of variables or class…

Dimensionality reduction can distort vector space properties such as orthogonality and linear independence, which are critical for tasks including cross-modal retrieval, clustering, and classification. We propose a Relationship Preserving…

Dimensionality reduction (DR) techniques help analysts to understand patterns in high-dimensional spaces. These techniques, often represented by scatter plots, are employed in diverse science domains and facilitate similarity analysis among…

Starting from the vector multipliers, the inner product, norm, distance, as well as addition of two vectors of different dimensions are proposed, which makes the spaces into a topological vector space, called the Euclidean space of…

We have designed a new efficient dimensionality reduction algorithm in order to investigate new ways of accurately characterizing the biodiversity, namely from a geometric point of view, scaling with large environmental sets produced by NGS…

With the recent surge in big data analytics for hyper-dimensional data there is a renewed interest in dimensionality reduction techniques for machine learning applications. In order for these methods to improve performance gains and…

Pairwise Euclidean distance calculation is a fundamental step in many machine learning and data analysis algorithms. In real-world applications, however, these distances are frequently distorted by heteroskedastic noise$\unicode{x2014}$a…

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…

Dimensionality reduction is a fundamental task in modern data science. Several projection methods specifically tailored to take into account the non-linearity of the data via local embeddings have been proposed. Such methods are often based…

Dimension reduction (DR) is inherently non-unique: multiple embeddings can preserve the structure of high-dimensional data equally well while differing in layout or geometry. In this paper, we formally define the Rashomon set for DR -- the…

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…

Multi-connected Universe models with space idenfication scales smaller than the size of the observable universe produce topological images in the catalogs of cosmic sources. In this review, we present the recent developments for the search…

Dimensionality reduction (DR) on the manifold includes effective methods which project the data from an implicit relational space onto a vectorial space. Regardless of the achievements in this area, these algorithms suffer from the lack of…

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…

The discovering of low-dimensional manifolds in high-dimensional data is one of the main goals in manifold learning. We propose a new approach to identify the effective dimension (intrinsic dimension) of low-dimensional manifolds. The scale…

Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…