Related papers: GiDR-DUN; Gradient Dimensionality Reduction -- Dif…
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…
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.…
The clustering and visualisation of high-dimensional data is a ubiquitous task in modern data science. Popular techniques include nonlinear dimensionality reduction methods like t-SNE or UMAP. These methods face the `scale-problem' of…
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…
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…
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…
Dimensionality reduction (DR) is characterized by two longstanding trade-offs. First, there is a global-local preservation tension: methods such as t-SNE and UMAP prioritize local neighborhood preservation, yet may distort global manifold…
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…
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 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…
We extend a well-known dimension reduction method, t-distributed stochastic neighbor embedding (t-SNE), from non-parametric to parametric by training neural networks. The main advantage of a parametric technique is the generalization of…
The vast majority of Dimensionality Reduction (DR) techniques rely on second-order statistics to define their optimization objective. Even though this provides adequate results in most cases, it comes with several shortcomings. The methods…
In this paper, the existing Scheduling Dimension Reduction (SDR) methods for Linear Parameter-Varying (LPV) models are reviewed and a Deep Neural Network (DNN) approach is developed that achieves higher model accuracy under scheduling…
The dimensionality reduction has been widely introduced to use the high-dimensional data for regression, classification, feature analysis, and visualization. As the one technique of dimensionality reduction, a stochastic neighbor embedding…
We aim to solve the problem of data-driven collision-distance estimation given 3-dimensional (3D) geometries. Conventional algorithms suffer from low accuracy due to their reliance on limited representations, such as point clouds. In…
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 methods such as t-SNE are designed to preserve local neighborhood structure but do not explicitly account for how probability mass is distributed, often leading to distortions of data density. We reformulate…
Misuses of t-SNE and UMAP in visual analytics have become increasingly common. For example, although t-SNE and UMAP projections often do not faithfully reflect the original distances between clusters, practitioners frequently use them to…
Dimensional data reduction methods are fundamental to explore and visualize large data sets. Basic requirements for unsupervised data exploration are simplicity, flexibility and scalability. However, current methods show complex…
Alternating minimization methods have recently been proposed as alternatives to the gradient descent for deep neural network optimization. Alternating minimization methods can typically decompose a deep neural network into layerwise…