Solves clustering contradictions by high-dimensional embedding with wide gaps.
problem Kleinberg's clustering axioms are contradictory.
method Embedding in high-dimensional space with wide gaps between clusters.
result Handles clustering contradictions by design.
SA-REMBO adapts to nonstationary high-dimensional optimization.
problem Bayesian Optimization in high-dimensional spaces is limited by the curse of dimensionality and rigidity of global assumptions.
method SA-REMBO uses multiple random Gaussian embeddings and an index variable to adaptively select the best embedding for the optimization problem.
result SA-REMBO outperforms traditional REMBO and other low-rank BO methods across synthetic and real-world benchmarks.
Bayesian optimization for high-dimensional combinatorial spaces using embeddings.
problem Optimizing expensive functions over large, complex input spaces.
method Dictionary-based ordinal embeddings for high-dimensional combinatorial structures, using Gaussian process models.
result The proposed method outperforms state-of-the-art BO methods on diverse real-world benchmarks.
EGORSE optimizes high-dimensional problems using random and supervised embeddings.
problem Efficiently solving computationally expensive high-dimensional optimization problems.
method EGORSE combines random and supervised linear embeddings for adaptive optimization.
result EGORSE outperforms state-of-the-art methods in high-dimensional optimization.
Topological manifolds can be embedded flatly in high-dimensional Euclidean space and are locally retracts.
problem Embedding and retraction of topological manifolds in Euclidean spaces.
method Locally flat embedding and retraction of manifolds in high-dimensional Euclidean space.
result Every topological n-manifold can be embedded locally flatly in R2n+1 and is a retract of some neighborhood in R2n+1. Bayesian optimization (BO) is a popular approach to optimize expensive-to-evaluate black-box functions. A significant challenge in BO is to scale to high-dimensional parameter spaces while retaining sample efficiency. A solution considered in existing literature is to embed the high-dimensional space in a lower-dimensi…
A novel method extracts topological features from word embeddings for text classification.
problem High dimensional and noisy text representations in natural language processing.
method Persistent homology for topological data analysis on word embeddings.
result Topological features outperform conventional text mining features on long textual documents.
A new BO method tackles high-dimensional optimization without reconstruction.
problem Optimizing high-dimensional black-box functions is challenging, especially when low-dimensional structures are assumed.
method Tackles the problem in the original high-dimensional space using learned low-dimensional structure.
result Our method explores the high-dimensional space more effectively than existing approaches.
Enhances forecasting of complex systems using FKMD.
problem Forecasting high-dimensional dynamical systems with unknown features.
method Featurized Koopman Mode Decomposition (FKMD) using delay embedding and learned Mahalanobis distance.
result Improves prediction accuracy for various complex systems.
Proposes MamBO for efficient high-dimensional large-scale optimization.
problem High-dimensional and large-scale optimization problems in machine learning and simulation.
method Combines subsampling and subspace embeddings with model aggregation to address uncertainty in surrogate models.
result Improves robustness of Bayesian optimization algorithm and achieves superior performance.
ReliefE ranks features faster and better in high-dimensional data.
problem Feature ranking in high-dimensional spaces.
method Adapting Relief algorithms to manifold embeddings.
result ReliefE outperforms traditional Relief algorithms in feature ranking.
SOLAR improves search efficiency and accuracy with sparse, orthogonal embeddings.
problem Bottleneck of indexing large dense vectors and NNS for query efficiency and accuracy.
method Proposes SOLAR embeddings: sparse, orthogonal, learned, and random vectors across multiple GPUs.
result Successfully trains 500K dimensional SOLAR embeddings for 1.6M books and multi-label classification.
Paper proves embedding theorem for conformally compact manifolds.
problem Embedding conformally compact manifolds into hyperbolic spaces.
method Proves analogous Nash Embedding Theorem for conformally compact manifolds.
result Conformally compact manifolds can be isometrically embedded into hyperbolic spaces.
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.
This paper finds a linear relationship between t-SNE perplexity and data set size.
problem Choosing the right perplexity for t-SNE embeddings.
method Analyzed the relationship between perplexity and data set size.
result Embeddings remain structurally consistent when perplexity is adjusted accordingly.
PERCEPT detects changes in high-dimensional data streams using topological data analysis.
problem Detecting changes in high-dimensional data streams, especially when embedded in a low-dimensional space.
method Leverages topological data analysis to learn embedded topology as a point cloud via persistence diagrams, then applies non-parametric monitoring for detecting changes.
result Demonstrates efficient detection of online changes from high-dimensional data streams.
This paper studies clustering and embedding in high-dimensional Gaussian mixture block models.
problem Clustering and embedding in high-dimensional Gaussian mixture block models.
method Spectral clustering and embedding algorithms for graphs sampled from Gaussian mixture block models.
result Performance analysis of spectral clustering and embedding algorithms for 2-component spherical Gaussian mixtures.
BOIDS optimizes high-dimensional problems by guiding optimization with one-dimensional lines.
problem Scaling Bayesian Optimization to high-dimensional problems.
method BOIDS uses a sequence of one-dimensional direction lines guided by an adaptive selection technique and incorporates subspace embedding for efficiency.
result BOIDS outperforms state-of-the-art methods on various synthetic and real-world problems.
SILBO optimizes high-dimensional Bayesian optimization using semi-supervised embedding learning.
problem Bayesian optimization struggles with high-dimensional search spaces.
method SILBO uses semi-supervised dimension reduction to find a low-dimensional space for iterative optimization.
result SILBO outperforms existing methods on high-dimensional Bayesian optimization tasks.
Proposes EOT eigenmaps for aligning and embedding multiple datasets.
problem Aligning and embedding multiple datasets with shared structures but individual distortions.
method Entropic Optimal Transport (EOT) eigenmaps, leveraging leading singular vectors of EOT plan matrix.
result Proves theoretical guarantees and favorable properties for aligning and embedding datasets.
While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods are not amenable to the analysis of such manifolds. This is mainly due to the necessary spectral decomposition step, which limits control over the…
Survey of embedding methods for high-dimensional and network data.
problem Embedding high-dimensional and nonlinear data structures in a lower-dimensional space.
method Survey of various embedding methods including principal curves, multidimensional scaling, graph-based methods, and topological embeddings.
result Discussion of the pros and cons of algorithmic machine learning and statistical modeling approaches.
Proposes a boundary detection method inspired by LLE for high-dimensional data.
problem Identifying boundary points from data on an embedded manifold.
method Inspired by locally linear embedding, uses nearest neighbor search schemes and spectral properties of local covariance matrix.
result Enhanced boundary detection in noisy data.
New BO method efficiently optimizes high-dimensional functions by automatically selecting variables.
problem Efficiently optimizing functions with high-dimensional domains.
method Exploits variable selection to automatically learn sub-spaces without pre-specified dimensions.
result Empirically validated on synthetic and real problems, demonstrating efficiency.
Kernel-spectral embedding learns low-dim. structures from noisy data.
problem Learning low-dimensional nonlinear structures from high-dimensional noisy data.
method Adaptive bandwidth spectral embedding using integral operators.
result Convergence to noiseless embeddings and eigenfunctions of integral operators.
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.
Mercat preserves angles to create accurate low-dimensional embeddings.
problem Reconstructing global relationships in low-dimensional embeddings.
method Reconstructing angles between data points to preserve both local and global structures.
result Mercat yields good reconstruction across various experiments and metrics.
In the advent of big data era, interactive visualization of large data sets consisting of M*10^5+ high-dimensional feature vectors of length N (N ~ 10^3+), is an indispensable tool for data exploratory analysis. The state-of-the-art data embedding (DE) methods of N-D data into 2-D (3-D) visually perceptible space (e.g.…
Combines OT and PCA for DR, preserving clusters.
problem Analyzing high-dimensional data with global dependencies.
method Optimal transport (OT) for minimizing reconstruction error, combined with PCA.
result Effective preservation of high-dimensional clusters in embeddings.
Framework uses RL with dynamic embedding to outperform benchmarks in volatile markets.
problem Challenges in high-dimensional, non-stationary, and noisy market information.
method Dynamic embedding of market information using generative autoencoders and online meta-learning in a reinforcement learning framework.
result Framework outperforms common portfolio benchmarks and PTO approach during market stress.
A new method optimizes slicing directions for SW distances to improve high-dimensional probability measure comparison.
problem Challenging identification of informative slicing directions for SW distances.
method Constrained learning approach to optimize slicing directions, using continuous relaxations and gradient-based primal-dual approach.
result Demonstrated efficacy in learning more informative slicing directions on various high-dimensional data.
Modern techniques simplify complex high-dimensional data.
problem Complex, high-dimensional data.
method Unsupervised dimension reduction techniques.
result Simplified representation of high-dimensional data.
LOT framework embeds high-dimensional cell data into interpretable Euclidean space.
problem Lack of interpretable methods for high-dimensional cell data.
method Adapts Linear Optimal Transport (LOT) to irregular point clouds.
result Accurate and interpretable classification and synthetic data generation.
This paper introduces an acceleration structure for hyperbolic embeddings.
problem Efficiently embedding and visualizing high-dimensional data in hyperbolic spaces.
method Building upon a polar quadtree, the paper introduces a new acceleration structure for hyperbolic embeddings.
result The new method computes embeddings in significantly less time compared to existing methods.
Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold learning algorithm based on deep learning to create an encoder, which maps a high-dimensional dataset and its low-dimensional embedding, and …
A new method identifies critical transitions in high-dimensional data.
problem Challenges in identifying critical transitions in high-dimensional time-series data.
method Spatial-temporal Principal Component Analysis (stPCA)
result Identifies tipping points before critical transitions reliably.
Kernel method embeds noisy datasets, capturing shared structures.
problem Limited power in capturing nonlinear structures, noisiness, high-dimensionality, and interpretability issues.
method Kernel spectral joint embeddings using duo-landmark integral operators.
result Consistent recovery of low-dimensional noiseless signals and convergence to eigenfunctions of integral operators.
Improved multi-task averaging reduces mean squared error in high-dimensional data.
problem Joint estimation of multiple distributions using independent data sets.
method Exploits similarities between tasks by shrinking naive estimators towards local averages.
result The method provides a significant reduction in mean squared error, especially in high-dimensional spaces.
The widespread availability of electronic health records (EHRs) promises to usher in the era of personalized medicine. However, the problem of extracting useful clinical representations from longitudinal EHR data remains challenging. In this paper, we explore deep neural network models with learned medical feature embe…
New families of embeddings in 4-manifolds, topologically trivial but smoothly non-trivial.
problem Constructing non-trivial smooth embeddings of 3-manifolds in 4-manifolds.
method Parameterized families of embeddings, using high-dimensional spheres.
result Embeddings of homology spheres and any 3-manifold in blown-up K3 surfaces.
The neural architecture search (NAS) algorithm with reinforcement learning can be a powerful and novel framework for the automatic discovering process of neural architectures. However, its application is restricted by noncontinuous and high-dimensional search spaces, which result in difficulty in optimization. To resol…
CAMEL enhances manifold embedding and learning with curvature metrics.
problem High-dimensional data classification, dimension reduction, and visualization.
method CAMEL uses a Riemannian manifold with curvature metrics for enhanced expressibility and interpretability.
result CAMEL outperforms state-of-the-art methods on high-dimensional datasets.
Survey of SDR methods for high-dimensional regression and embedding.
problem Reducing dimensionality in high-dimensional data.
method Involves both statistical and machine learning approaches, covering inverse and forward regression methods.
result Supervised Kernel Dimension Reduction is equivalent to supervised PCA.
This paper proposes a variant of the method of Guédon and Verhynin for estimating the cluster matrix in the Mixture of Gaussians framework via Semi-Definite Programming. A clustering oriented embedding is deduced from this estimate. The procedure is suitable for very high dimensional data because it is based on pairwis…
A fast binary embedding method preserves Euclidean distances in high-dimensional data.
problem Preserving Euclidean distances in high-dimensional datasets.
method Stable noise-shaping quantization of Ax with A a sparse Gaussian random matrix, followed by a linear transformation. result Euclidean distances are approximated by the ℓ1 norm on binary sequences, leading to accurate binary codes. We present function preserving projections (FPP), a scalable linear projection technique for discovering interpretable relationships in high-dimensional data. Conventional dimension reduction methods aim to maximally preserve the global and/or local geometric structure of a dataset. However, in practice one is often mo…
Enhances medical code predictions for multi-morbidity patients using text classification.
problem Improving accuracy in predicting medical codes for patients with multiple illnesses.
method Used machine learning techniques, including multi-label medical text classification, to enhance predictions.
result High dimensional embeddings pre-trained on health data significantly improve multi-label classification performance.
In this paper we explore the "vector semantics" problem from the perspective of "almost orthogonal" property of high-dimensional random vectors. We show that this intriguing property can be used to "memorize" random vectors by simply adding them, and we provide an efficient probabilistic solution to the set membership …