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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…
Neighbor embeddings are a family of methods for visualizing complex high-dimensional datasets using $k$NN graphs. To find the low-dimensional embedding, these algorithms combine an attractive force between neighboring pairs of points with 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…
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…
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…
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…
Dimension reduction and visualization of high-dimensional data have become very important research topics because of the rapid growth of large databases in data science. In this paper, we propose using a generalized sigmoid function 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…
Quantifying local structures in self-assembled systems is a central challenge in soft matter and materials science. When no a priori knowledge of the relevant structures is available, traditional order parameters often fall short.…
Neighbor embedding is widely employed to visualize high-dimensional data; however, it frequently overlooks the global structure, e.g., intercluster similarities, thereby impeding accurate visualization. To address this problem, this paper…
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…
Dimensionality reduction methods are employed to decrease data dimensionality, either to enhance machine learning performance or to facilitate data visualization in two or three-dimensional spaces. These methods typically fall into two…
Neighbor embedding methods $t$-SNE and UMAP are the de facto standard for visualizing high-dimensional datasets. Motivated from entirely different viewpoints, their loss functions appear to be unrelated. In practice, they yield strongly…
Universal adversarial perturbation (UAP), also known as image-agnostic perturbation, is a fixed perturbation map that can fool the classifier with high probabilities on arbitrary images, making it more practical for attacking deep models in…
Stochastic neighbor embedding (SNE) methods $t$-SNE, UMAP are two most popular dimensionality reduction methods for data visualization. Contrastive learning, especially self-supervised contrastive learning (SSCL), has showed great success…
Spectral clustering is one of the most popular clustering approaches with the capability to handle some challenging clustering problems. Most spectral clustering methods provide a nonlinear map from the data manifold to a subspace. Only a…
In the BCI field, introspection and interpretation of brain signals are desired for providing feedback or to guide rapid paradigm prototyping but are challenging due to the high noise level and dimensionality of the signals. Deep neural…
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 study the elasto-plastic behavior of dense attractive emulsions under mechanical perturbation. The attraction is introduced through non-specific depletion interactions between the droplets and is controlled by changing the concentration…
We numerically studied active Brownian particles with attractive interactions. Contrary to our intuition, the attractive force between particles disrupts the formation of a single cluster observed in motility-induced phase separation,…