Related papers: CBMAP: Clustering-based manifold approximation and…
UMAP (Uniform Manifold Approximation and Projection) is a novel manifold learning technique for dimension reduction. UMAP is constructed from a theoretical framework based in Riemannian geometry and algebraic topology. The result is a…
Uniform Manifold Approximation and Projection (UMAP) is a widely used manifold learning technique for dimensionality reduction. This paper studies UMAP, supervised UMAP, and several competing dimensionality reduction methods, including…
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…
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…
This paper presents a comprehensive comparative analysis of prominent clustering algorithms K-means, DBSCAN, and Spectral Clustering on high-dimensional datasets. We introduce a novel evaluation framework that assesses clustering…
Topology based dimensionality reduction methods such as t-SNE and UMAP have seen increasing success and popularity in high-dimensional data. These methods have strong mathematical foundations and are based on the intuition that the topology…
Scientists in many fields have the common and basic need of dimensionality reduction: visualizing the underlying structure of the massive multivariate data in a low-dimensional space. However, many dimensionality reduction methods confront…
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…
Dimension reduction (DR) algorithms have proven to be extremely useful for gaining insight into large-scale high-dimensional datasets, particularly finding clusters in transcriptomic data. The initial phase of these DR methods often…
Understanding the global organization of complicated and high dimensional data is of primary interest for many branches of applied sciences. It is typically achieved by applying dimensionality reduction techniques mapping the considered…
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…
Dimension reduction (DR) techniques such as t-SNE, UMAP, and TriMAP have demonstrated impressive visualization performance on many real world datasets. One tension that has always faced these methods is the trade-off between preservation of…
Dimensionality reduction is a fundamental technique in machine learning and data analysis, enabling efficient representation and visualization of high-dimensional data. This paper explores five key methods: Principal Component Analysis…
Subspace clustering refers to the problem of clustering unlabeled high-dimensional data points into a union of low-dimensional linear subspaces, whose number, orientations, and dimensions are all unknown. In practice one may have access to…
A fundamental problem in supervised learning is to find a good set of features or distance measures. If the new set of features is of lower dimensionality and can be obtained by a simple transformation of the original data, they can make…
Dimensionality Reduction (DR) techniques can generate 2D projections and enable visual exploration of cluster structures of high-dimensional datasets. However, different DR techniques would yield various patterns, which significantly affect…
We present a new nonlinear dimensionality reduction method, MAPLE, that enhances UMAP by improving manifold modeling. MAPLE employs a self-supervised learning approach to more efficiently encode low-dimensional manifold geometry. Central to…
Dimensionality reduction methods such as t-SNE and UMAP are popular methods for visualizing data with a potential (latent) clustered structure. They are known to group data points at the same time as they embed them, resulting in…
Manifold learning (ML) aims to seek low-dimensional embedding from high-dimensional data. The problem is challenging on real-world datasets, especially with under-sampling data, and we find that previous methods perform poorly in this case.…
We discuss topological aspects of cluster analysis and show that inferring the topological structure of a dataset before clustering it can considerably enhance cluster detection: theoretical arguments and empirical evidence show that…