Extends knotted defect classification to bounded domains using handlebodies.
problem Classifying knotted defects in bounded domains.
method Using continuous maps and monodromies around meridional loops, global defects are described in terms of planar diagrams.
result Classification scheme for defects in handlebodies.
We show that the local equivalence problem for second-order ordinary differential equations under point transformations is completely characterized by differential invariants of order at most 10 and that this upper bound is sharp. We also show that, modulo Cartan duality and point transformations, the Painlevé-I equati…
Efficient method classifies locally stationary time series based on second-order characteristics.
problem Classifying locally stationary time series for various applications.
method Autoregressive approximation, ensemble aggregation, distance-based threshold.
result Zero misclassification error rate asymptotically for mildly differing second-order characteristics.
A hybrid model reduces graph complexity for improved classification accuracy.
problem High computational complexity and large number of parameters in higher-order graph convolutional networks.
method Weight sharing mechanism and novel fusion pooling layer to reduce parameters and complexity.
result The proposed model achieves highest classification accuracy with fewer trainable parameters.
This is an review on the point classification of second order ODE's by Ruslan Sharipov. His works were published in 1997-1998 at the Electronic Archive at LANL and undeservedly forgotten. Last chapter is an application of this classification to the investigation of Painleve equations.
In 1896 Tresse gave a complete description of relative differential invariants for the pseudogroup action of point transformations on the 2nd order ODEs. The purpose of this paper is to review, in light of modern geometric approach to PDEs, this classification and also discuss the role of absolute invariants and the eq…
Method extracts features from signals for classification with explainability.
problem Lack of interpretability in signal classification models.
method Combining scattering transform and multiclass logistic regression with zeroth-order optimization.
result Uncovered the meaning of scattering transform coefficients.
A novel transformer model improves classification of partially ordered sequences.
problem Classification of partially ordered sequences with uncertainty in timestamps.
method Developed a transformer-based model for partially ordered sequences, benchmarked against set models.
result Transformer-based model outperforms set models on three datasets.
Classifies defects in ordered media using homotopy theory.
problem Classifying defects in ordered media like liquid crystals.
method Using homotopy theory and continuous maps from ordered media to quotient spaces.
result Equivalence classes of defects are enumerated by subgroups of the quaternion group.
Neural networks classify examples in a consistent order across datasets.
problem Consistent classification order of neural networks across different datasets.
method Empirical observations on various benchmarks.
result Neural networks classify examples in a similar order across training and test sets.
Study natural operators transforming tensor fields, proving all bilinear ones are of order one.
problem Understanding natural differential operators on tensor fields.
method Proved all bilinear operators are of order one, then classified operators in specific cases.
result Full classification of natural differential operators on tensor fields.
New classification of nonorientable 4-manifolds with specific fundamental groups.
problem Classifying nonorientable 4-manifolds with cyclic fundamental groups.
method Simple cut-and-paste construction, using results from Hambleton-Kreck-Teichner and Khan.
result Plausible classification of a large set of nonorientable 4-manifolds with cyclic fundamental groups of order 2p.
Self-directed learners can minimize mistakes in online classification.
problem Minimizing mistakes in online classification with adaptive prediction order.
method Designing efficient self-directed learners for linear classification.
result Strong separation between worst-order and random-order learning for linear classification.
We study the classification performance of Kronecker-structured models in two asymptotic regimes and developed an algorithm for separable, fast and compact K-S dictionary learning for better classification and representation of multidimensional signals by exploiting the structure in the signal. First, we study the clas…
HyperBERT enhances BERT for node classification on text-attributed hypergraphs.
problem Challenges in capturing hypergraph structure and text attributes in node classification.
method Mixing hypergraph-aware layers with BERT for improved node classification.
result HyperBERT achieves state-of-the-art results on text-attributed hypergraph benchmarks.
In this paper the notion of an M-th order invariant bilinear differential pairing is introduced and a formal definition is given. If the manifold has an AHS structure, then various first order pairings are constructed. This yields a classification of all first order invariant bilinear differential pairings on homogeneo…
This paper introduces matrix product state (MPS) decomposition as a new and systematic method to compress multidimensional data represented by higher-order tensors. It solves two major bottlenecks in tensor compression: computation and compression quality. Regardless of tensor order, MPS compresses tensors to matrices …
This paper improves multi-label classification by leveraging high-order label correlations.
problem Improving accuracy in multi-label classification tasks using label correlations.
method Exploiting high-order label correlations through a supervised learning classifier system (UCS) and label powerset (LP) strategy.
result The proposed method outperforms other LP-based methods on multiple benchmark datasets.
New algebraic-geometric method classifies superintegrable systems in any dimension.
problem Classifying superintegrable systems in arbitrary dimensions is challenging.
method Algebraic-geometric approach based on quasi-projective varieties.
result Established foundations for classification in arbitrary dimensions.
Paper introduces variance-based measures for second-order uncertainty quantification in classification problems.
problem Uncertainty in machine learning predictions and decision-making.
method Second-order uncertainty quantification using variance-based measures.
result Variance-based measures effectively quantify uncertainty on a class-based level and are competitive with entropy-based measures.
Paper proposes a new MLC framework without predefined label order, improving performance and generalization.
problem Exposure bias in multi-label classification due to lack of predefined label order.
method Proposes a new framework that transforms MLC into a sequence prediction problem without predefined label order.
result The proposed method outperforms competitive baselines and has better generalization capability.
A new R package for ordinal classification and preprocessing.
problem Lack of proper methods for ordinal data in machine learning.
method Developed an R package named ocapis in Scala.
result Improves classification and preprocessing of ordinal data.
IsoNN learns graph representations without node order constraints.
problem Lack of interpretability and erratic performance in graph classification due to node-orderless property.
method IsoNN uses graph matching with subgraph templates to learn isomorphic features and break node-order.
result IsoNN achieves superior performance on graph classification tasks compared to existing methods.
Classifies scalar second-order PDEs with low-dimensional symmetry groups.
problem Classifying differential equations with specific symmetry groups.
method Algebraic technique based on covariant form for constructing equations.
result Complete classification of quasi-linear scalar second-order PDEs with free symmetry groups of dimension ≤3.
We present a family of four-dimensional Lorentzian manifolds whose invariant classification requires the seventh covariant derivative of the curvature tensor. The spacetimes in questions are null radiation, type N solutions on an anti-de Sitter background. The large order of the bound is due to the fact that these spac…
We analyze Darboux transformations in very general settings for multidimensional linear partial differential operators. We consider all known types of Darboux transformations, and present a new type. We obtain a full classification of all operators that admit Wronskian type Darboux transformations of first order and a …
A new GCN model learns higher-order neighbors without explicit adjacency matrix computation.
problem GCN's performance drops for deeper structures due to limited neighborhood information.
method Assumes higher-order neighbors are similar to first-order neighbors, learns weights through Lasso to minimize feature loss.
result HWGCN achieves state-of-the-art results on various datasets.
Third-order symmetric Lorentzian manifolds, i.e. Lorentzian manifold with zero third derivative of the curvature tensor, are classified. These manifolds are exhausted by a special type of pp-waves, they generalize Cahen-Wallach spaces and second-order symmetric Lorentzian spaces.
We give a classification of n-component links up to Cn-move. In order to prove this classification, we characterize Brunnian links, and have that a Brunnian link is ambient isotopic to a band sum of trivial link and Milnor's links.
By using a certain second order differential equation, the notion of adapted coordinates on Finsler manifolds is defined and some classifications of complete Finsler manifolds are found. Some examples of Finsler metrics, with positive constant sectional curvature, not necessarily of Randers type nor projectively flat, …
Using the classification of transitive groups we classify indecomposable quandles of size <36. This classification is available in Rig, a GAP package for computations related to racks and quandles. As an application, the list of all indecomposable quandles of size <36 not of type D is computed.
We classify the polycyclic totally ordered simple dimension groups, i.e. dimension groups given by a dense embedding of n-dimensional lattice into the real line. Our method is based on the geometry of simple geodesics on the hyperbolic surface of genus greater or equal two. The main theorem says that isomorphism classe…
Recurrent neural networks (RNNs) are types of artificial neural networks (ANNs) that are well suited to forecasting and sequence classification. They have been applied extensively to forecasting univariate financial time series, however their application to high frequency trading has not been previously considered. Thi…
Portable, Wearable and Wireless electrocardiogram (ECG) Systems have the potential to be used as point-of-care for cardiovascular disease diagnostic systems. Such wearable and wireless ECG systems require automatic detection of cardiovascular disease. Even in the primary care, automation of ECG diagnostic systems will …
A new optimizer for deep learning improves accuracy and reduces training time.
problem Training deep neural networks for classification tasks.
method Hybrid Newton/Gradient Descent (NGD) method exploiting convexity of cross-entropy loss.
result Improves validation error and provides qualitative differences in hidden layer basis functions.
Paper introduces r-DEP classifier for binary classification tasks.
problem No natural ordering for feature patterns in practical situations.
method Introduces reduced dilation-erosion (r-DEP) classifier using multi-valued mathematical morphology.
result r-DEP classifiers outperform traditional SVCs in balanced accuracy.
Enhances image classification by integrating semantic hierarchy into CNN models.
problem Limited use of external guidance in image classification.
method Integrates label-hierarchy knowledge into CNN-based classifiers and uses order-preserving embeddings.
result Boosts image classification performance through semantic hierarchy integration.
A model verifies during classification to reduce memorization, matching baseline accuracy with fewer parameters.
problem Classification systems require memorizing all classes, leading to increased memory usage and poor sample efficiency.
method Iterative nondifferentiable queries for verification during classification, balancing recognition and verification.
result The model can match baseline accuracy while using fewer parameters, but requires careful balance between recognition and verification.
HONEM learns embeddings for higher-order networks, improving performance in various tasks.
problem Existing methods fail to capture non-Markovian higher-order dependencies in networks.
method HONEM is a higher-order network embedding method designed for HON, capturing non-Markovian dependencies.
result HONEM outperforms other methods in node classification, network reconstruction, link prediction, and visualization.
New methods for ordinal classification of interval-valued data and functional data.
problem Ordinal classification of interval-valued data and functional data.
method Six ordinal classifiers are proposed, including parametric, binary decomposition, logistic regression, distance-based, k-nearest-neighbor, kernel PCA, and random forest methods.
result Considering ordering and interval-valued information improves the accuracy of ordinal classification.
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…
Novel analysis improves weighted majority vote in multiclass classification.
problem Improving the performance of weighted majority vote in multiclass classification.
method Analyzes expected risk of weighted majority vote, considering prediction correlations and provides a bound for efficient minimization.
result Minimization of the new bound typically does not degrade the test error of the ensemble.
In [Tohoku Math. J. 62 (2010), 45--53] the second author showed that, except for a few cases, the order N of a cyclic group of self-homeomorphisms of a closed orientable topological surface Sg of genus g≥2 determines the group up to a topological conjugation, provided that N≥3g. The first author et al…
Study shows surgeries on certain knots yield left-orderable 3-manifolds.
problem Integral Dehn surgeries on genus one fibered knots in lens spaces.
method Classification of genus one fibered knots by Baker and analysis of surgeries.
result All integral Dehn surgeries on these knots yield left-orderable 3-manifolds.
New radar-based method improves multiclass classification of road users, especially in challenging conditions.
problem Accurate classification of multiple road users in challenging scenarios.
method 50 features extracted from radar data, subset chosen, tested on random forest and LSTM classifiers, addressed data imbalance issues.
result Substantial improvements in multiclass classification compared to ordinary methods.
Paper uses genome Markov structure for outlier detection and read classification.
problem Identifying outliers and classifying reads in genome databases.
method Applying second-order Markov models to triplet base distributions.
result Improved accuracy in outlier identification and read classification.
Study classifies polyharmonic helices in various space forms.
problem Classifying polyharmonic helices in different space forms.
method Derived classification results for polyharmonic helices in space forms.
result Polyharmonic helices of arbitrary order in space forms of negative curvature are geodesics.
C-HMCNN(h) improves HMC classification by leveraging class hierarchy.
problem Hierarchical multi-label classification with class hierarchy constraints.
method Exploits class hierarchy to produce coherent predictions for multi-label classification.
result C-HMCNN(h) outperforms state-of-the-art models in HMC classification.