Related papers: HUMAP: Hierarchical Uniform Manifold Approximation…

Nonlinear dimension reduction (NLDR) techniques such as tSNE, and UMAP provide a low-dimensional representation of high-dimensional data ($p\text{-}D$) by applying a nonlinear transformation. NLDR often exaggerates random patterns. But NLDR…

Different unsupervised models for dimensionality reduction like PCA, LLE, Shannon's mapping, tSNE, UMAP, etc. work on different principles, hence, they are difficult to compare on the same ground. Although they are usually good for…

We introduce "TriMap"; a dimensionality reduction technique based on triplet constraints, which preserves the global structure of the data better than the other commonly used methods such as t-SNE, LargeVis, and UMAP. To quantify the global…

Dimensional reduction~(DR) maps high-dimensional data into a lower dimensions latent space with minimized defined optimization objectives. The DR method usually falls into feature selection~(FS) and feature projection~(FP). FS focuses on…

We explore two primary classes of approaches to dimensionality reduction (DR): Independent Dimensionality Reduction (IDR) and Simultaneous Dimensionality Reduction (SDR). In IDR methods, of which Principal Components Analysis is a…

Dimension reduction (DR) methods provide systematic approaches for analyzing high-dimensional data. A key requirement for DR is to incorporate global dependencies among original and embedded samples while preserving clusters in the…

Dimensionality reduction methods are unsupervised approaches which learn low-dimensional spaces where some properties of the initial space, typically the notion of "neighborhood", are preserved. Such methods usually require propagation on…

Nonlinear dimensional reduction with the manifold assumption, often called manifold learning, has proven its usefulness in a wide range of high-dimensional data analysis. The significant impact of t-SNE and UMAP has catalyzed intense…

Nonlinear dimensionality reduction methods are a popular tool for data scientists and researchers to visualize complex, high dimensional data. However, while these methods continue to improve and grow in number, it is often difficult to…

Recent advances in machine learning allow us to analyze and describe the content of high-dimensional data like text, audio, images or other signals. In order to visualize that data in 2D or 3D, usually Dimensionality Reduction (DR)…

Diffusion maps (DMAP) are often used as a dimensionality-reduction tool, but more precisely they provide a spectral representation of the intrinsic geometry rather than a complete charting method. To illustrate this distinction, we study a…

Data augmentation techniques play an important role in enhancing the performance of deep learning models. Despite their proven benefits in computer vision tasks, their application in the other domains remains limited. This paper proposes a…

Visual analytics now plays a central role in decision-making across diverse disciplines, but it can be unreliable: the knowledge or insights derived from the analysis may not accurately reflect the underlying data. In this dissertation, we…

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…

This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of…

Diffusion Map is a spectral dimensionality reduction technique which is able to uncover nonlinear submanifolds in high-dimensional data. And, it is increasingly applied across a wide range of scientific disciplines, such as biology,…

Dimensionality reduction (DR) of image features plays an important role in image retrieval and classification tasks. Recently, two types of methods have been proposed to improve the both the accuracy and efficiency for the dimensionality…

The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…

Hierarchical Reinforcement Learning (HRL) agents often struggle with long-horizon visual planning due to their reliance on error-prone distance metrics. We propose Discrete Hierarchical Planning (DHP), a method that replaces continuous…

In a world abundant with diverse data arising from complex acquisition techniques, there is a growing need for new data analysis methods. In this paper we focus on high-dimensional data that are organized into several hierarchical datasets.…