This paper gives a review and synthesis of methods of evaluating dimensionality reduction techniques. Particular attention is paid to rank-order neighborhood evaluation metrics. A framework is created for exploring dimensionality reduction quality through visualization. An associated toolkit is implemented in R. The to…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,982 papers · 148 categories
Trend · papers per month
48 results for “exploration reduction”
A novel supervised visualization technique for data exploration.
problem Lack of supervised dimensionality reduction methods considering class labels.
method Random forest proximities and diffusion-based dimensionality reduction.
result Retains local and global structures in data, emphasizing important variables.
The paper simplifies symmetries in complex geometric structures.
problem Redundancy in conditions for symmetry reduction in polysymplectic and polycosymplectic structures.
method Exploring and proving necessary and sufficient conditions for polycosymplectic reduction.
result A one-to-one relationship between polycosymplectic reduction and the reduction of a larger polysymplectic manifold.
Fuzzy clustering reduces text data dimensions effectively.
problem Sparsity and high dimensionality in document-term frequency matrices.
method Fuzzy clustering applied as a new unsupervised feature transformation method.
result Fuzzy clustering outperforms PCA and SVD in reducing text data dimensions.
NROWAN-DQN: A Stable Noisy Network with Noise Reduction and Online Weight Adjustment for Explorationcs.LG
NROWAN-DQN improves stability and exploration in noisy networks.
problem Noisy networks struggle with stable exploration in complex tasks.
method Noise reduction and online weight adjustment for stable actions.
result NROWAN-DQN outperforms prior algorithms in stability and exploration.
The paper explores polysymplectic structures and their reductions in field theories.
problem Invariance of Lagrangian and Hamiltonian field theories under symmetry groups.
method Application of polysymplectic reduction theorem for both Lagrangian and Hamiltonian field equations.
result Identification and relation of polysymplectic structures through Routhian function and Legendre transformation.
This paper extends symplectic reduction to cosymplectic groupoids and explores their properties.
problem Cosymplectic groupoids and their reductions.
method Analogous to symplectic reduction, the authors extend the Marsden-Weinstein-Meyer reduction to cosymplectic groupoids.
result Integration commutes with reduction for algebroids associated with cosymplectic groupoids.
The un-reduction procedure introduced previously in the context of Mechanics is extended to covariant Field Theory. The new covariant un-reduction procedure is applied to the problem of shape matching of images which depend on more than one independent variable (for instance, time and an additional labelling parameter)…
The paper explores reductions of self-dual conformal structure equations.
problem Integrating the general local form of self-dual conformal structure.
method Using Lax pair, hierarchy structure, and dressing scheme to discuss reductions.
result Constructs solutions for the SDCS equations and presents type B SDCS system.
This paper proposes BRIEF, a backward reduction algorithm that explores compact CNN-model designs from the information flow perspective. This algorithm can remove substantial non-zero weighting parameters (redundant neural channels) of a network by considering its dynamic behavior, which traditional model-compaction te…
Batch Thompson Sampling reduces exploration-exploitation trade-off in online decision making.
problem Balancing exploration and exploitation in online decision making.
method Introducing a batch Thompson Sampling framework for stochastic multi-arm bandit and linear contextual bandit problems.
result Achieves asymptotic regret bound with batch queries, significantly reducing interactions.
The paper compares PCA and PP for scRNA sequencing data.
problem Limitations of PCA in scRNA sequencing data.
method Applied PCA and PP (using negative Shannon's entropy) on scRNA sequencing data.
result PP outperforms PCA in scRNA sequencing data.
Framework guides user exploration of data relations.
problem Efficiently explore complex data sets with user knowledge.
method Model user knowledge as tile constraints, use constrained randomisation, find informative views.
result Framework steers exploration towards user interests, outperforms existing methods.
BlosSOM improves data visualization for large datasets.
problem Insufficient performance of dimensionality reduction methods for large datasets.
method GPU-accelerated semi-supervised EmbedSOM algorithm.
result Produces high-quality visualizations with user control.
The paper presents the application of Variational Autoencoders (VAE) for data dimensionality reduction and explorative analysis of mass spectrometry imaging data (MSI). The results confirm that VAEs are capable of detecting the patterns associated with the different tissue sub-types with performance than standard appro…
Ensemble learning has had many successes in supervised learning, but it has been rare in unsupervised learning and dimensionality reduction. This study explores dimensionality reduction ensembles, using principal component analysis and manifold learning techniques to capture linear, nonlinear, local, and global feature…
This paper explores the impact of metric choice on Fréchet regression.
problem Choosing the right metric for Fréchet regression in complex data.
method Review and extensive numerical studies of existing dimension reduction methods.
result Different metrics significantly affect the estimation of central and central mean space.
SRP: Efficient class-aware embedding learning for large-scale data via supervised random projectionscs.LG
Supervised dimensionality reduction strategies have been of great interest. However, current supervised dimensionality reduction approaches are difficult to scale for situations characterized by large datasets given the high computational complexities associated with such methods. While stochastic approximation strateg…
The process of un-reduction, a sort of reversal of reduction by the Lie group symmetries of a variational problem, is explored in the setting of field theories. This process is applied to the problem of curve matching in the plane, when the curves depend on more than one independent variable. This situation occurs in a…
Efficient algorithm for CMDPs reduces to offline density estimation.
problem Offline learning for CMDPs with horizon H.
method Reduction to offline density estimation, layerwise exploration-exploitation tradeoff.
result First efficient and near-optimal reduction from CMDPs to offline density estimation.
PCA simplifies multivariate extreme data analysis.
problem Analyzing multivariate extreme values with high-dimensional data.
method Principal Component Analysis (PCA) for dimensionality reduction.
result PCA helps preserve essential information for extreme value analysis.
In the covariate shift learning scenario, the training and test covariate distributions differ, so that a predictor's average loss over the training and test distributions also differ. In this work, we explore the potential of extreme dimension reduction, i.e. to very low dimensions, in improving the performance of imp…
Paper explores how risk-averse individuals' willingness to pay for insurance varies with risk probability.
problem Understanding how risk-averse individuals' willingness to pay for insurance varies with risk probability.
method Analyzes willingness to pay (WTP) for partial risk reduction within the dual theory of decision.
result In dual theory, reducing the probability of risk and providing insurance can be complementary if the surplus increases with risk reduction.
DRAMA detects anomalies in high dimensions via dimensionality reduction.
problem Challenges in anomaly detection for large datasets in high dimensions.
method Dimensionality reduction and unsupervised clustering.
result DRAMA is robust and competitive in high dimensions, especially for online anomaly detection.
Sensitivity Analysis for Active Sampling, with Applications to the Simulation of Analog Circuitsstat.ML
Active sampling improves design space exploration for analog circuits.
problem Efficiently exploring the space of design features in analog circuits with many parameters.
method Combining drastic dimension reduction with sensitivity analysis and Bayesian surrogate modeling for active sampling.
result The proposed active sampling flow outperforms traditional Monte-Carlo sampling.
We reframe linear dimensionality reduction as a problem of Bayesian inference on matrix manifolds. This natural paradigm extends the Bayesian framework to dimensionality reduction tasks in higher dimensions with simpler models at greater speeds. Here an orthogonal basis is treated as a single point on a manifold and is…
The paper explores Lorentzian connections with parallel skew torsion.
problem Understanding metric connections with parallel skew-symmetric torsion in Lorentzian signature.
method Analyzing holonomy algebras, torsion, and curvature; constructing examples; classifying homogeneous spaces.
result Complete classification of Lorentzian naturally reductive homogeneous spaces in low dimensions.
This thesis explores fast algorithms for large matrices and data augmentation to improve model efficiency.
problem Efficient handling of large models and data in scientific computing and machine learning.
method Randomized low-rank decomposition algorithms and data augmentation techniques.
result Improved sample efficiency and generalization of machine learning models.
The paper explores proper actions and their relation to representation theory, with new quantitative methods.
problem Understanding proper actions and their connection to representation theory.
method Geometric criteria, sharpness measure, and dynamical volume estimates.
result New quantitative methods have established temperedness criteria for unitary representations.
Paper proposes a method to estimate variance reduction in DNN training using importance sampling.
problem Challenges in assessing variance reduction during DNN training using importance sampling.
method Proposes a method for estimating variance reduction using minibatches sampled under importance sampling.
result Demonstrates consistent reduction in variance, improved training efficiency, and enhanced model accuracy.
In this study, we propose a new statical approach for high-dimensionality reduction of heterogenous data that limits the curse of dimensionality and deals with missing values. To handle these latter, we propose to use the Random Forest imputation's method. The main purpose here is to extract useful information and so r…
This study explores Kaluza-Klein reductions of new maximally supersymmetric backgrounds.
problem Exploring new maximally supersymmetric backgrounds in five dimensions.
method Classifying Kaluza-Klein reductions to four dimensions and determining preserved supersymmetry.
result Discovery of novel non-homogeneous four-dimensional Lorentzian spacetimes with supersymmetry.
Variance reduction (VR) methods boost the performance of stochastic gradient descent (SGD) by enabling the use of larger, constant stepsizes and preserving linear convergence rates. However, current variance reduced SGD methods require either high memory usage or an exact gradient computation (using the entire dataset)…
Unified model for reducing dimensions and clustering high-dimensional data.
problem High-dimensional data clustering and dimensionality reduction.
method Hierarchical mixtures of Gaussians (HMoGs) with closed-form likelihood and inference.
result Efficiently models hundreds of latent dimensions, improving clustering performance.
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.
DMT enhances deep neural networks to better preserve data structures.
problem Preserving geometric, topological, and distributional structures of data in NLDR.
method Deep manifold transformation (DMT) using cross-layer LGP constraints.
result DMT networks outperform existing NLDR methods in preserving data structures.
Novel algorithm reduces sample complexity for reinforcement learning.
problem Improving sample efficiency in reinforcement learning.
method SRVR-PG algorithm with recursive variance reduction.
result Reduces sample complexity to .
Topological comparison of some dimension reduction methods using persistent homology on EEG datamath.GT
Paper compares dimension reduction methods using topological analysis on EEG data.
problem Comparing dimension reduction methods on EEG data.
method Topological data analysis, including persistent homology, Wasserstein distance, and hypothesis tests.
result Different dimension reduction methods show significant qualitative differences across topological homologies.
We explore the geometry of the Nahm-Schmid equations, a version of Nahm's equations in split signature. Our discussion ties up different aspects of their integrable nature: dimensional reduction from the Yang--Mills anti-self-duality equations, explicit solutions, Lax-pair formulation, conservation laws and spectral cu…
This paper explores hyperkähler structures on specific orbits using different methods.
problem Investigate hyperkähler structures on adjoint orbits.
method Infinite dimensional hyperkähler reduction and symplectic geometry.
result Differences and connections between two methods are thoroughly investigated.
Deep learning improves oilfield equipment maintenance and reduces downtime.
problem Predicting equipment failure in oilrigs to minimize downtime.
method Developed and tested neural networks on oilfield datasets, using data processing and feature extraction.
result Deep learning can predict oilfield equipment failure with reduced downtime.
We introduce the bilinear bandit problem with low-rank structure in which an action takes the form of a pair of arms from two different entity types, and the reward is a bilinear function of the known feature vectors of the arms. The unknown in the problem is a by matrix that defines the reward…
We explore the plane-wave limit of homogeneous spacetimes. For plane-wave limits along homogeneous geodesics the limit is known to be homogeneous and we exhibit the limiting metric in terms of Lie algebraic data. This simplifies many calculations and we illustrate this with several examples. We also investigate the beh…
A new method for SVGD reduces variance in high dimensions.
problem High-dimensional variance in SVGD.
method Grassmann Stein Variational Gradient Descent (GSVGD) projects onto arbitrary subspaces and uses coupled Grassmann-valued diffusion.
result GSVGD explores high-dimensional problems with intrinsic low-dimensional structure efficiently.
The application of stochastic variance reduction to optimization has shown remarkable recent theoretical and practical success. The applicability of these techniques to the hard non-convex optimization problems encountered during training of modern deep neural networks is an open problem. We show that naive application…
Study explores Laplacian coflow versions on Calabi-Yau 7-manifolds.
problem Analyzing -structures on Calabi-Yau 7-manifolds.
method Reduced Ansätze for the Laplacian coflow on various Calabi-Yau 7-manifolds.
result Obtained a modified Kähler-Ricci flow.
This paper uses bandit algorithms to reduce the cost of user interface experimentation in online retail.
problem Reducing the cost of user interface experimentation in online retail.
method Modeling user interface experimentation as an opportunistic bandit problem, reducing the cost of exploration.
result Significant regret reduction and improved contextual information for testing.
Randomized ICA and LDA Dimensionality Reduction Methods for Hyperspectral Image Classificationstat.ML
Dimensionality reduction is an important step in processing the hyperspectral images (HSI) to overcome the curse of dimensionality problem. Linear dimensionality reduction methods such as Independent component analysis (ICA) and Linear discriminant analysis (LDA) are commonly employed to reduce the dimensionality of HS…