JORC-UMAP improves UMAP by incorporating geometric and topological priors.
problem UMAP's local Euclidean distance assumption fails to capture intrinsic manifold geometry, leading to topological tearing and structural collapse.
method JORC-UMAP introduces Ollivier-Ricci curvature as a geometric prior and Jaccard similarity as a topological prior to reinforce edges and reduce redundant links.
result JORC-UMAP reduces tearing and collapse more effectively than standard UMAP and other DR methods, as measured by SVM accuracy and triplet preservation scores.
UMAP connects to Information Geometry principles.
problem None explicitly stated; focuses on connections.
method None explicitly stated; focuses on connections.
result UMAP has a natural geometric interpretation.
UMAP compared to other methods for dimensionality reduction.
problem Comparing UMAP to other dimensionality reduction techniques.
method Comprehensive evaluation of UMAP and other methods.
result Supervised UMAP performs well for classification but not for regression.
UMAP's true loss function differs from what was previously thought, focusing on nearest neighbor graph similarities.
problem Understanding the true effectiveness and mechanism of UMAP for high-dimensional data visualization.
method Deriving UMAP's effective loss function in closed form and analyzing its optimization scheme.
result UMAP aims to reproduce similarities encoded in the nearest neighbor graph, not the full high-dimensional similarities.
Parametric UMAP learns a mapping from data to embeddings.
problem Representing and learning from structured data.
method Parametric optimization over neural network weights for UMAP.
result Parametric UMAP performs comparably to non-parametric UMAP with faster online embeddings.
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 practical scalable algorithm that applies to real world data. The UMAP algorithm is c…
This paper corrects errors in UMAP's derivation and explains its properties.
problem Errors in UMAP's derivation by McInnes et al.
method Full derivation of Spivak's functors and McInnes et al.'s finite variant.
result Corrected errors and provided an explicit description of the metric realization.
UMAP speeds up significantly with GPU acceleration.
problem Efficient GPU implementation of UMAP.
method Various techniques to optimize UMAP for GPU, including data partitioning and parallelization.
result Up to 100x speedup in practice.
Paper interprets UMAP and t-SNE as probabilistic MAP inference.
problem Understanding and interpreting UMAP and t-SNE.
method Interprets UMAP and t-SNE as MAP inference methods corresponding to a probabilistic model of the graph Laplacian.
result Shows UMAP and t-SNE can be understood as probabilistic inference methods.
Unified probabilistic foundation for fuzzy simplicial sets in dimensionality reduction.
problem Lack of clear probabilistic interpretation in fuzzy simplicial sets.
method Introducing a probabilistic framework explaining fuzzy simplicial sets as marginals of probability measures on simplicial sets.
result Unified probabilistic theoretical foundation for fuzzy simplicial sets.
A new approach clusters data first, then embeds each cluster, improving transparency.
problem Visualizing data with latent clusters while preserving global geometry.
method First cluster, then embed each cluster, aligning the clusters.
result The approach is competitive with existing methods and more transparent.
Sep-SpectralNet improves SE for broader applicability and scalability.
problem Three main drawbacks of current SE implementations: generalizability, scalability, and eigenvectors separation.
method Sep-SpectralNet extends SpectralNet with an eigenvector separation post-processing step.
result Sep-SpectralNet achieves consistent SE approximation and generalization, enhancing scalability and applicability.
Improved performance in shape identification tasks using elastic metrics in t-SNE and UMAP.
problem Improper metrics in dimensionality reduction techniques lead to poor performance in machine learning applications.
method Incorporating elastic metrics into t-SNE and UMAP for functional data.
result Improved F1 scores on shape identification tasks for three benchmark datasets.
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 accuracy of the embedding, we introduce a score that roughly reflects the relat…
Neighbor embeddings balance attraction and repulsion to visualize data.
problem Visualizing high-dimensional datasets with trade-offs between continuous and discrete structures.
method Neighbor embeddings combine attractive and repulsive forces to visualize data.
result Changing the exaggeration parameter in t-SNE yields a spectrum of embeddings with a trade-off between continuous and discrete structures.
Efficient auto-tuning for DR hyperparameters with BO.
problem Hyperparameter selection in DR for large-scale datasets.
method Bayesian optimization with surrogate model, normalization, subsampling.
result Robust and efficient hyperparameter selection for DR algorithms.
New DR algorithm preserves both local and global structure.
problem Trade-off between preserving local and global structure in DR methods.
method Analysis of existing DR methods and design principles for loss functions.
result Design of PaCMAP algorithm that preserves both local and global structure.
This paper addresses overfitting in dimension reduction methods by calibrating hyperparameters considering noise.
problem Overfitting in dimension reduction methods, especially t-SNE and UMAP, when data contains noise.
method Present a framework to calibrate hyperparameters in the presence of noise for t-SNE and UMAP.
result Recommended hyperparameter values for t-SNE and UMAP are too small and overfit the noise.
This study evaluates clustering algorithms on high-dimensional data.
problem Comparing clustering algorithms on high-dimensional datasets.
method Evaluation of K-means, DBSCAN, and Spectral Clustering using PCA, t-SNE, UMAP, and multiple metrics.
result UMAP preprocessing improves clustering quality across all algorithms, with Spectral Clustering excelling.
New methods improve analysis of single cell RNA sequencing data.
problem High dimensionality and complexity of scRNA-seq data.
method Topological Nonnegative Matrix Factorization (TNMF) and Robust Topological NMF (rTNMF).
result TNMF and rTNMF significantly outperform other NMF-based methods.
dtSNE preserves local densities in low-dimensional embeddings.
problem Local density differences are not accurately preserved in tSNE and UMAP.
method dtSNE, which approximately conserves local densities.
result dtSNE provides more accurate local density depictions.
Introduces a probabilistic framework for dimension reduction methods.
problem Lack of clear probabilistic foundations for popular DR methods.
method A unifying statistical framework based on the coupling of hidden graphs using cross entropy.
result Existing DR methods suffer from a statistical deficiency that affects performance.
New methods explain NE embeddings by identifying key variables.
problem Lack of interpretability in NE techniques.
method Combining PCA, Q-residuals, Hotelling's T2, and visualization.
result Identifies discriminatory features not seen in standard approaches.
Two methods factor out prior knowledge from low-dimensional embeddings.
problem Visualizing data without considering background knowledge.
method JEDI for tSNE and CONFETTI for any embedding.
result Embeddings reveal meaningful structure hidden by prior knowledge.
EmDT generates synthetic fraud data to improve detection accuracy.
problem Imbalanced datasets in fraud detection lead to poor performance on rare fraudulent transactions.
method EmDT uses UMAP clustering to identify fraudulent patterns and a Transformer denoising network to generate synthetic data.
result EmDT significantly improves classification performance compared to existing methods.
Improves visualization of high-dimensional data by correcting misleading artifacts in neighbor embedding methods.
problem Misleading visual artifacts in t-SNE and UMAP due to lack of data-independent manifold learning interpretations.
method LOO-map framework that extends embedding maps to the entire input space, identifying and correcting map discontinuities.
result Developed point-wise diagnostic scores to detect unreliable embedding points and improve hyperparameter selection.
LASE improves local network structure visualization by targeting locally low-dimensional regions.
problem Global spectral embedding fails to capture local geometric features in sparse, transitive networks.
method Local Adjacency Spectral Embedding (LASE) using weighted spectral decomposition.
result LASE reveals locally low-dimensional structure, improving local reconstruction and visualization.
Taxicab correspondence analysis visualizes sparse text data sets.
problem Visualization of extremely sparse contingency tables.
method Robust variant of correspondence analysis for sparse data.
result Visualized an 8265-dimensional textual data set.
Sequencer algorithm detects main trends in complex datasets.
problem Detecting simple phenomena in complex data.
method Constructs graphs from data similarities, identifies elongated trends.
result Sequencer outperforms t-SNE and UMAP in identifying main trends.
MEDAL converts manifold embeddings into models for rigorous validation.
problem Challenges in validating manifold embeddings without held-out validation.
method Develops MEDAL framework that distills embeddings into autoencoder models.
result Enables rigorous validation of manifold embeddings and hyperparameters.
Visual summarization of clinical data collected on patients contained within the electronic health record (EHR) may enable precise and rapid triage at the time of patient presentation to an emergency department (ED). The triage process is critical in the appropriate allocation of resources and in anticipating eventual …
IsUMap improves data visualization of complex geometries.
problem Accurately representing complex, locally distorted metric spaces.
method Integrates UMAP and Isomap with Vietoris-Rips filtrations.
result Significant improvements in data representation quality.
GTSNE improves data visualization for high-dimensional data.
problem Visualizing high-dimensional data points in a 2D map.
method GTSNE is a variation of t-SNE that captures both local and macro structures.
result GTSNE produces better visualizations of high-dimensional data compared to other methods.
New model uses financial news to predict stock returns.
problem Predicting stock returns based on financial news.
method Derive company embedding vectors from news, select basis assets, and use statistical methods.
result NEUS model outperforms Fama-French 5-factor model.
Paper proposes a new method for supervised manifold learning using random forest proximities.
problem Existing supervised manifold learning methods fail to uncover meaningful embeddings due to using class-conditional distances.
method Proposes a data-geometry-preserving variant of random forest proximities as an initialization for manifold learning methods.
result Local and global structure preservation is near universal across manifold learning approaches using diffusion-based algorithms.
Geodesic distance is the shortest path between two points in a Riemannian manifold. Manifold learning algorithms, such as Isomap, seek to learn a manifold that preserves geodesic distances. However, such methods operate on the ambient dimensionality, and are therefore fragile to noise dimensions. We developed an unsupe…
A new method, tree-SNE, solves the scale problem in t-SNE.
problem Clustering and visualizing high-dimensional data, especially MNIST digits.
method Revisits t-SNE idea to create a 2+1 dimensional embedding with a scale parameter.
result The optimal embedding depends continuously on the scale parameter for all initial conditions.
Adapts category theory to manifold learning for better understanding and stability.
problem Understanding and improving manifold learning algorithms.
method Develops a functorial perspective on manifold learning, proving bounds and constructing new algorithms.
result Derives new manifold learning algorithms that are competitive with existing methods.
SinSim improves self-supervised learning by integrating optimal transport into contrastive learning.
problem Lack of explicit regularization in contrastive learning methods leads to suboptimal generalization.
method Integrates Sinkhorn regularization from optimal transport theory into SimCLR.
result SinSim outperforms SimCLR and other self-supervised methods on various datasets.
Centroid-Encoder reduces high-dimensional data for better visualization.
problem Visualizing high-dimensional data efficiently and accurately.
method Centroid-Encoder integrates label information to keep similar objects close in reduced space.
result Centroid-Encoder outperforms other techniques in visualizing high-dimensional data.
DEN creates interpretable visualizations using Siamese networks.
problem Creating interpretable visualizations of complex datasets.
method Differentiating Embedding Networks (DEN) using Siamese neural networks and loss functions.
result DEN outperforms existing techniques on FashionMNIST and interpretable features are identified.
ProbDR framework interprets DR algorithms as probabilistic inference.
problem Efficiently compressing high-dimensional data into lower dimensions.
method ProbDR variational framework that treats DR as probabilistic inference.
result ProbDR unifies various DR algorithms and enables probabilistic reasoning.
A new DDR framework learns low-dimensional data representations using dynamical systems.
problem Learning efficient low-dimensional data representations.
method DDR framework based on nonlinear dynamical systems, using linear combinations of functions and regularization.
result DDR method outperforms other methods on synthetic and real datasets.
Deep clustering has increasingly been demonstrating superiority over conventional shallow clustering algorithms. Deep clustering algorithms usually combine representation learning with deep neural networks to achieve this performance, typically optimizing a clustering and non-clustering loss. In such cases, an autoenco…
We present ShapeVis, a scalable visualization technique for point cloud data inspired from topological data analysis. Our method captures the underlying geometric and topological structure of the data in a compressed graphical representation. Much success has been reported by the data visualization technique Mapper, th…
Parametric t-SNE improves generalization for streaming data.
problem Training neural networks for t-SNE objective function fails due to gradient exploding.
method Applied gradient clipping to solve gradient exploding problem.
result Parametric t-SNE achieves quality compatible with non-parametric t-SNE while generalizing to new data.
Proposes a method to visualize finer cluster structures in high-dimensional data.
problem Visualization of high-dimensional data with complex cluster structures.
method Introduces a generalized sigmoid function with a parameter b to adjust the tail heaviness for better visualization.
result The method can generate visualization results comparable to UMAP, revealing finer cluster structures.
CAMEL embeds data into a manifold using curvature-augmented forces.
problem Data visualization and dimensionality reduction.
method Formulates DR as a physics model with curvature-augmented forces.
result CAMEL outperforms existing methods on benchmark datasets.