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Dimensionality reduction methods such as UMAP and t-SNE are central tools for visualising high-dimensional data, but their local-neighborhood objectives can preserve sampling noise while distorting global topology. We show that standard…
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…
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…
Dimensionality reduction is crucial both for visualization and preprocessing high dimensional data for machine learning. We introduce a novel method based on a hierarchy built on 1-nearest neighbor graphs in the original space which is used…
Dimensionality reduction techniques are widely used for visualizing high-dimensional data in two dimensions. Existing methods are typically designed to preserve either local (e.g., $t$-SNE, UMAP) or global (e.g., MDS, PCA) structure of the…
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…
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…
Low-dimensional embeddings and visualizations are an indispensable tool for analysis of high-dimensional data. State-of-the-art methods, such as tSNE and UMAP, excel in unveiling local structures hidden in high-dimensional data and are…
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…
Data are not only ubiquitous in society, but are increasingly complex both in size and dimensionality. Dimension reduction offers researchers and scholars the ability to make such complex, high dimensional data spaces simpler and more…
Dimensionality Reduction (DR) techniques such as t-SNE and UMAP are popular for transforming complex datasets into simpler visual representations. However, while effective in uncovering general dataset patterns, these methods may introduce…
With the increasing availability of high-dimensional data, analysts often rely on exploratory data analysis to understand complex data sets. A key approach to exploring such data is dimensionality reduction, which embeds high-dimensional…
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…
Nowadays, as data becomes increasingly complex and distributed, data analyses often involve several related datasets that are stored on different servers and probably owned by different stakeholders. While there is an emerging need to…
Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have…
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…
This paper shows that dimensionality reduction methods such as UMAP and t-SNE, can be approximately recast as MAP inference methods corresponding to a model introduced in Ravuri et al. (2023), that describes the graph Laplacian (an estimate…
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…
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…
In Dataset Condensation, the goal is to synthesize a small dataset that replicates the training utility of a large original dataset. Existing condensation methods synthesize datasets with significant redundancy, so there is a dire need to…