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UMAP is a popular neighborhood-preserving dimension reduction (DR) algorithm. However, its application for graph drawing has not been evaluated. Moreover, a naive application of UMAP to graph drawing would include O(nm) time all-pair…

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…

UMAP (Uniform Manifold Approximation and Projection) is among the most widely used algorithms for non linear dimensionality reduction and data visualisation. Despite its popularity, and despite being presented through the lens of algebraic…

Most popular dimension reduction (DR) methods like t-SNE and UMAP are based on minimizing a cost between input and latent pairwise similarities. Though widely used, these approaches lack clear probabilistic foundations to enable a full…

We introduce an improved unsupervised clustering protocol specially suited for large-scale structured data. The protocol follows three steps: a dimensionality reduction of the data, a density estimation over the low dimensional…

Uniform Manifold Approximation and Projection (UMAP) is one of the state-of-the-art methods for dimensionality reduction and data visualization. This is a tutorial and survey paper on UMAP and its variants. We start with UMAP algorithm…

In contrast to classical techniques for exploratory analysis of high-dimensional data sets, such as principal component analysis (PCA), neighbor embedding (NE) techniques tend to better preserve the local structure/topology of…

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…

High-dimensional imaging is becoming increasingly relevant in many fields from astronomy and cultural heritage to systems biology. Visual exploration of such high-dimensional data is commonly facilitated by dimensionality reduction.…

Nonlinear dimensionality reduction techniques, particularly UMAP, are widely used for visualizing high-dimensional data. However, UMAP's local Euclidean distance assumption often fails to capture intrinsic manifold geometry, leading to…

Stochastic Neighbor Embedding (SNE) algorithms like UMAP and tSNE often produce visualizations that do not preserve the geometry of noisy and high dimensional data. In particular, they can spuriously separate connected components of the…

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…

TSNE and UMAP are two of the most popular dimensionality reduction algorithms due to their speed and interpretable low-dimensional embeddings. However, while attempts have been made to improve on TSNE's computational complexity, no existing…

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…

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…

Complex network topologies and hyperbolic geometry seem specularly connected, and one of the most fascinating and challenging problems of recent complex network theory is to map a given network to its hyperbolic space. The Popularity…

Neighbour embeddings (NE) allow the representation of high dimensional datasets into lower dimensional spaces and are often used in data visualisation. In practice, accelerated approximations are employed to handle very large datasets.…

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 central goal of this paper is to establish two commonly available dimensionality reduction (DR) methods i.e. t-distributed Stochastic Neighbor Embedding (t-SNE) and Multidimensional Scaling (MDS) in Matlab and to observe their…

Visualizing high-dimensional data is essential for understanding biomedical data and deep learning models. Neighbor embedding methods, such as t-SNE and UMAP, are widely used but can introduce misleading visual artifacts. We find that the…