A new distributed learning method for high-dimensional linear classification.
problem Efficiently performing linear classification on large-scale, high-dimensional data.
method Feature-distributed stochastic variance reduced gradient (FD-SVRG) for high-dimensional linear classification.
result FD-SVRG outperforms other distributed methods in terms of communication cost and wall-clock time.
This paper contains all computations supporting the classification of 7-dimensional Einstein nilradicals given in the article "Classification of 7-dimensional Einstein nilradicals" (arXiv). Each algebra is analyzed in detail here.
Paper compares dimensionality reduction methods for affect classification.
problem Difficulty in obtaining labeled training samples for affect classification.
method Five dimensionality reduction approaches are compared.
result No single approach universally outperforms others in affect classification.
The paper classifies para-Kähler structures on Lie groups.
problem Classifying para-Kähler structures on Lie groups.
method Classification based on symplectic Lie algebras, finding compatible para-complex structures and pseudo-Riemannian metrics.
result Explicit forms of para-complex structures and pseudo-Riemannian metrics are found.
Study shows how to approximate and estimate high-dimensional classification functions without the curse of dimensionality.
problem Approximating and estimating classification functions in high-dimensional spaces.
method Modified existing results to show that RBV2 functions can be approximated by neural networks with bounded weights. Proved the existence of a neural network with bounded weights approximating a classification function. Leveraged these bounds to quantify estimation rates. result Neural networks can approximate RBV2 functions without the curse of dimensionality, leading to efficient estimation rates. This work refines Cover's theory for binary classification on low-dimensional data.
problem The challenge of analyzing how low-dimensional data structures affect classification models.
method Refines Cover's function-counting theory to account for low-dimensional data structure.
result Derives dichotomy counts and analyzes the impact of data structure on classification models.
Empirical Bayes method improves high-dimensional classification accuracy.
problem High-dimensional classification with sparse mean differences.
method Dirichlet process mixture model and variational Bayes algorithm.
result Effective estimation of mean difference leads to reduced misclassification.
New classification of 5D nilsolitons using algebraic Ricci soliton equation.
problem Classifying five-dimensional nilsolitons.
method Using algebraic Ricci soliton equation, derived the structure of 7 out of 10 classes of nilmanifolds.
result 7 out of 10 classes of 5D nilmanifolds admit Ricci soliton structure.
New method classifies patients with kidney transplant based on many features.
problem Classifying patients with many features (ultrahigh-dimensional data).
method Multivariate screening and classification method leveraging feature correlations.
result Achieves optimal misclassification rates and more powerful discovery.
Ray-based framework classifies high-dimensional structures with reduced data.
problem Classifying complex geometrical structures in high dimensions.
method Uses minimal one-dimensional rays to construct structure fingerprints.
result Performance of ray-based classifier matches traditional methods for low-dimensional systems.
Classifies 4D Alexandrov spaces with torus actions.
problem Classifying Alexandrov spaces with torus actions.
method Equivariant classification and homeomorphism analysis.
result Alexandrov spaces are homeomorphic to Riemannian orbifolds.
The classification of 4-dimensional naturally reductive pseudo-Riemannian spaces is given. This classification comprises symmetric spaces, the product of 3-dimensional naturally reductive spaces with the real line and new families of indecomposable manifolds which are studied at the end of the article. The oscillator g…
This paper is concerned with the problems of interaction screening and nonlinear classification in a high-dimensional setting. We propose a two-step procedure, IIS-SQDA, where in the first step an innovated interaction screening (IIS) approach based on transforming the original p-dimensional feature vector is propose…
SqueezeFit reduces high-dimensional data to lower dimensions while preserving label distances.
problem Label-aware dimensionality reduction in high-dimensional spaces.
method Semidefinite programming relaxation of nearest neighbor classification.
result Provable recovery of a planted projection operator from labeled data.
Novel method converts time series data into functional data for high dimensional classification.
problem Small sample size problem in high dimensional time series data.
method Classwise Functional Principal Component Analysis (PCA) followed by Bayesian linear classifier.
result Demonstrated efficacy on synthetic and real data sets.
The paper develops a classification method using penalties on feature selection for high-dimensional data.
problem High-dimensional binary classification with many irrelevant features.
method Empirical risk minimization with l0-penalization for feature selection.
result The method achieves a sparse solution close to true sparsity with high probability and converges to low misclassification risk.
Study classifies 4D Ricci solitons with specific curvature conditions.
problem Classifying 4D gradient steady and expanding Ricci solitons with given curvature properties.
method Asymptotically cylindrical and conical assumptions; half-harmonic and half-nonnegative isotropic curvature conditions.
result Partial classification of 4D gradient expanding Ricci solitons with half-nonnegative isotropic curvature.
I apply the algebraic classification of self-adjoint endomorphisms of R2,2 provided by their Jordan canonical form to the Ricci curvature tensor of four-dimensional neutral manifolds and relate this classification to an algebraic classification of the Ricci curvature spinor. These results parallel similar re…
The article analyzes high-dimensional classification using empirical risk minimization with precise error predictions.
problem Classifying high-dimensional data with Gaussian mixture models.
method Theoretical analysis of ridge-regularized and unregularized empirical risk minimization for high-dimensional Gaussian mixture separation.
result The square loss is optimal for high-dimensional classification in both ridge-regularized and unregularized cases.
Boosting ridge regression for high-dimensional data classification reduces computational cost and improves learning time.
problem High computational demand of inverting regularised covariance matrix in ridge regression for high-dimensional problems.
method Train an ensemble of ridge regressors in randomly projected subspaces, then combine them using adaptive boosting.
result Effective in terms of learning time and improved predictive performance in some cases.
High dimensional data analysis is known to be as a challenging problem. In this article, we give a theoretical analysis of high dimensional classification of Gaussian data which relies on a geometrical analysis of the error measure. It links a problem of classification with a problem of nonparametric regression. We giv…
We obtain a topological and weakly equivariant classification of closed three-dimensional Alexandrov spaces with an effective isometric circle action. As an application of the classification we prove a version of the Borel conjecture for closed three-dimensional Alexandrov spaces with circle symmetry.
The study classifies and normalizes 3D gl-regular Nijenhuis operators.
problem Classifying and normalizing 3D gl-regular Nijenhuis operators.
method Classification and normal form proof.
result Proved A. Bolsinov's conjecture.
Proofs Lie's classification of certain vector field subalgebras.
problem Classifying finite dimensional subalgebras of vector fields on the complex plane.
method Representation theory of sl(2, C) and previous classifications.
result Completes the classification of vector field subalgebras.
Classifies a specific type of Lie groups related to Einstein geometry.
problem Classifying Einstein Lorentzian 3-nilpotent Lie groups with 1-dimensional nondegenerate center.
method Complete classification through mathematical analysis.
result A full classification of the specified Lie groups.
A new algorithm efficiently selects features for functional data classification.
problem Feature selection and classification of functional data in high-dimensional spaces.
method Developed a novel optimization problem integrating logistic loss and functional features. Employed functional principal components and a new adaptive Dual Augmented Lagrangian algorithm for efficient minimization.
result FSFC outperforms other methods in computational time and classification accuracy.
Novel algorithm SAODE improves high-dimensional stream classification in seasonal data.
problem Handling seasonal concept drift in high-dimensional stream classification.
method SAODE classifier that includes time as a super parent to handle seasonal drift.
result SAODE consistently outperforms other methods in stream and concept drift classification.
Paper proposes a novel R-JDRDL method for SPD manifolds.
problem High-dimensional noisy signals analysis.
method Riemannian optimization framework for joint DR and DL.
result R-JDRDL outperforms existing algorithms in image classification.
CDF uses centroids to split features for high-dimensional classification.
problem High-dimensional classification problems with complex class structures.
method CDF introduces a centroid-driven splitting strategy in decision trees.
result CDF outperforms conventional methods in high-dimensional classification.
A hierarchical approach improves classification accuracy in large datasets.
problem Improving classification accuracy in large datasets with high dimensionality.
method Hierarchical subspace learning to scale manifold learning methods.
result Average 5% increase in classification accuracy.
Paper proposes sparse classification method for high-dimensional data.
problem Sparse classification in high-dimensional data with positive-confidence samples.
method Developed a novel sparse-penalization framework using L1, SCAD, and MCP penalties for convex and non-convex shrinkage.
result Proved near minimax-optimal sparse recovery rates under Restricted Strong Convexity condition.
Random Projection (RP) technique has been widely applied in many scenarios because it can reduce high-dimensional features into low-dimensional space within short time and meet the need of real-time analysis of massive data. There is an urgent need of dimensionality reduction with fast increase of big genomics data. Ho…
The paper classifies orbit closures of symplectic Lie algebras.
problem Classifying orbit closures of symplectic Lie algebras under the action of Sp(4,R). method Analyzing the natural action of Sp(4,R) on the set of 4-dimensional Lie algebras with symplectic structures. result A complete classification of orbit closures of 4-dimensional symplectic Lie algebras.
The paper classifies special geometric shapes in 2D and 3D.
problem Classifying complete gradient Yamabe solitons in low dimensions.
method Completely classified nontrivial non-flat 2D and 3D complete gradient Yamabe solitons.
result Nontrivial non-flat 2D and 3D complete gradient Yamabe solitons have been completely classified.
Improved LDA method for better classification and dimensionality reduction.
problem Improving linear discriminant analysis for better classification performance.
method Integrates spectrally-corrected covariance matrix and regularized discriminant analysis.
result SRLDA has a linear classification global optimal solution under spiked model assumption.
Classifies homogeneous Riemannian structures on 3D Lie groups.
problem Classifying homogeneous Riemannian structures on 3D Lie groups.
method Classification based on left invariant metrics and previous classifications.
result Complete classification of homogeneous Riemannian structures on 3D Lie groups.
Simple heuristics can outperform sophisticated methods in high-dimensional pattern recognition.
problem Quantifying the difficulty of high-dimensional pattern recognition problems.
method Classification benchmarks based on simple random projection heuristics.
result Optimal classification curves asymptotes indicate no structural advantage over simple heuristics.
In this paper we consider three deeply connected classificational problems on four-dimensional manifolds. First we consider and describe locally regular distributions. Second we give a classification of almost complex structures of general position in terms of distributions. Finally we classify nondegenerate Monge-Ampe…
GDMaps reduces high-dimensional data to lower dimensions for better classification.
problem High-dimensional data classification and representation.
method Grassmannian Diffusion Maps technique for nonlinear dimensionality reduction.
result GDMaps effectively identifies intrinsic subspace structures in high-dimensional data.
Classifies and computes cohomologies of complex structures on Lie groups.
problem Classifying and computing cohomologies of complex structures on Lie groups.
method Complete classification and computation of invariant cohomologies for left invariant structures.
result Computed invariant cohomologies for various generalized complex and Kähler structures.
Develops a new tensor classification method for high-dimensional data.
problem Efficient learning algorithms exploiting tensorial structure in high-dimensional multi-way arrays.
method Tensor Train Multi-way Multi-level Kernel (TT-MMK) combining Canonical Polyadic decomposition, Dual Structure-preserving Support Vector Machine, and Tensor Train approximation.
result The TT-MMK method provides higher prediction accuracy and is more reliable computationally compared to other techniques.
New methods implement manifold scattering transform for high-dimensional point cloud data.
problem Classifying data on complex, non-linear manifolds.
method Adapting diffusion maps theory for numerical implementation.
result Effective for signal and manifold classification tasks.
L. Paoluzzi constructed a family of compact orientable three-dimensional hyperbolic manifolds with totally geodesic boundary, which were, by construction, closely related to the three-dimensional torus. This paper gives their complete classification up to isometry, and also their isometry groups. The key tool is the so…
New result on finite gerbes simplifies classification of certain bundles.
problem Classifying finite-dimensional gerbes with torsion DD-class. method Proves torsion for a wide class of finite gerbes built from principal bundles.
result Finite gerbes built from finite-dimensional fibre bundles have torsion DD-class. This paper converts NACE classification into embeddings to preserve hierarchical structure.
problem Preserving hierarchical structure in NACE classification while reducing dimensions.
method Custom metrics for hierarchical structure retention; state-of-the-art models and dimensionality reduction.
result The proposed approach effectively preserves hierarchical structures in NACE classification.
We use Bott-Chern cohomology to measure the non-Kählerianity of 6-dimensional nilmanifolds endowed with the invariant complex structures in M. Ceballos, A. Otal, L. Ugarte, and R. Villacampa's classification, [Invariant Complex Structures on 6-Nilmanifolds: Classification, Frölicher Spectral Sequence and Special Hermit…
The paper classifies 4D gradient Ricci solitons under specific curvature conditions.
problem Classifying four-dimensional gradient Ricci solitons under various conditions.
method Analyzing specific curvature conditions to classify solitons.
result Classification results for 4D gradient Ricci solitons under certain conditions.
A classification and examples of four-dimensional isoclinic three-webs of codimension two are given. The examples considered prove the existence theorem for many classes of webs for which the general existence theorems are not proved yet.