Classifies SL(n) covariant matrix-valued valuations on Lp-spaces.
problem Classifying SL(n) covariant matrix-valued valuations on Lp-spaces.
method Established a complete classification for continuous and SL(n) covariant matrix-valued valuations on Lp(Rn,|x|2dx), eliminating matrix symmetry assumption.
result Unique characterization of such valuations by the moment matrix in n>2, rotation matrix in 2D.
Matrix-variate distributions can intuitively model the dependence structure of matrix-valued observations that arise in applications with multivariate time series, spatio-temporal or repeated measures. This paper develops an Expectation-Maximization algorithm for discriminant analysis and classification with matrix-var…
Classifies contravariant matrix-valued valuations on polytopes without continuity assumptions.
problem Classifying contravariant matrix-valued valuations on polytopes without continuity assumptions.
method Complete classification of contravariant matrix-valued valuations on polytopes in Rn without continuity assumptions. result The only such valuation is the general Lutwak-Yang-Zhang matrix in dimension n≥4, and a new function in dimension 3. Paper proposes GSSNMF for legal document classification and topic modeling.
problem Lack of methods that can both classify and model topics with guidance.
method Guided Semi-Supervised Non-negative Matrix Factorization (GSSNMF).
result Improves both classification accuracy and topic coherence.
A new method classifies color images using quaternion algebra.
problem Classifying color images with preserved intrinsic relationships.
method LSQMM model with quaternion nuclear norm regularization and ADMM algorithm.
result LSQMM outperforms state-of-the-art methods in classification accuracy and efficiency.
SMM preserves matrix data structure for SVM classification.
problem Preserving spatial correlations in matrix data for SVM.
method SMM uses spectral elastic net combining nuclear and Frobenius norms.
result SMM improves SVM performance on matrix data.
Paper improves matrix-valued data classification using nonparametric LDA.
problem Classification of matrix-valued data in neuroimaging and signal processing.
method Nonparametric LDA based on NPMLE for vectorized and scaled matrices.
result Improves classification performance across various data structures.
We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the means and the precision matrix, which we assume has a Kronecker product decomposition. Our penalties encourage pairs of response category mean matrices to have equal…
Matrix sketching is a recently developed data compression technique. An input matrix A is efficiently approximated with a smaller matrix B, so that B preserves most of the properties of A up to some guaranteed approximation ratio. In so doing numerical operations on big data sets become faster. Sketching algorithms gen…
Classification of SL(n) covariant valuations on Orlicz spaces.
problem Classifying continuous SL(n) covariant valuations on Orlicz spaces.
method Complete classification without symmetric assumptions, focusing on moment matrix and a new functional in dimension two.
result The moment matrix is the only SL(n) covariant valuation for n≥3, and a new functional appears in dimension two.
Matrix SMD converges to unique solution minimizing Bregman divergence.
problem High-dimensional multi-output classification and matrix completion problems.
method Stochastic Mirror Descent with matrix parameters and matrix mirror functions.
result Matrix SMD converges exponentially to the unique solution minimizing Bregman divergence.
Machine learning techniques for Recommendation System (RS) and Classification has become a prime focus of research to tackle the problem of information overload. RS are software tools that aim at making informed decisions about the services that a user may like. On the other hand, classification technique deals with th…
Optimizes classification algorithms with bounds on error rates.
problem Bounding uncertainties in classifier outputs for diagnostic testing.
method Set-theoretic and probabilistic arguments to derive uniform error bounds.
result Optimal partition minimizes the largest Gershgorin radius of the confusion matrix.
Exponentially fast SMF algorithm for multi-class classification.
problem Learning interpretable features from high-dimensional data.
method Novel framework that 'lifts' SMF as a low-rank matrix estimation problem.
result Provable exponential convergence to global minimizer under mild assumptions.
Unified framework for comparing classification metrics across different imbalance rates.
problem Differences in scale and sensitivity to class imbalance rates in classification metrics.
method Introduces outperformance standardization (OPS) function to map metrics to a common scale.
result Unified o-value metric provides clear comparison across different imbalance rates.
PSMM method optimizes matrix sufficient dimension reduction.
problem Feature matrices with row- and column-wise interpretations require efficient dimension reduction.
method PSMM method converts matrix problem into classification problems using rank-1 normal matrix.
result PSMM outperforms existing methods and provides strong interpretability.
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 …
Over the years data has become increasingly higher dimensional, which has prompted an increased need for dimension reduction techniques. This is perhaps especially true for clustering (unsupervised classification) as well as semi-supervised and supervised classification. Although dimension reduction in the area of clus…
The classification of multivariate functional data is an important task in scientific research. Unlike point-wise data, functional data are usually classified by their shapes rather than by their scales. We define an outlyingness matrix by extending directional outlyingness, an effective measure of the shape variation …
Method estimates noise transition matrix from noisy labels without relying on unreliable class-posterior estimation.
problem Estimating noise transition matrix from noisy data.
method Total variation regularization to encourage distinguishable predicted probabilities.
result Consistent estimator of the noise transition matrix under mild assumptions.
Enhanced EEG classification using augmented covariance matrix.
problem Improving motor imagery classification from EEG signals.
method Proposes a new framework based on the augmented covariance matrix derived from an autoregressive model.
result The augmented covariance matrix outperformed state-of-the-art methods.
DACE estimates covariance from compressed data, improving accuracy.
problem Estimating covariance from large, distributed data.
method Data-aware weighted sampling for unbiased estimation.
result DACE provides more accurate covariance estimation under compression.
Proposes a framework to balance supervised and unsupervised learning using random matrix theory.
problem Balancing supervised and unsupervised learning in high-dimensional data.
method QLDS model with quadratic margin maximization under low density separation assumption.
result Establishes a smooth bridge between supervised and unsupervised learning methods.
Dual-T method improves transition matrix estimation in noisy label learning.
problem Large estimation error in noisy class posterior leads to poor transition matrix estimation.
method Introducing an intermediate class to avoid direct estimation of noisy class posterior, factorizing the transition matrix into two easier-to-estimate matrices.
result The dual-T estimator leads to better classification performances.
Paper recovers multi-subspace matrices from permuted data.
problem Recovering a multi-subspace matrix from permuted data with corrupted columns.
method Four-stage algorithm pipeline: outlier identification, subspace reconstruction, outlier classification, unsupervised sensing.
result The pipeline provides theoretical guarantees for reliable multi-subspace matrix recovery.
MGMC method handles missing data in medical datasets for accurate disease classification.
problem Handling missing data in incomplete medical datasets for accurate disease classification.
method Multigraph Geometric Matrix Completion (MGMC) using multiple graph convolutional networks.
result MGMC achieves superior classification and imputation performance compared to state-of-the-art approaches.
In recent years, a number of artificial intelligent services have been developed such as defect detection system or diagnosis system for customer services. Unfortunately, the core in these services is a black-box in which human cannot understand the underlying decision making logic, even though the inspection of the lo…
As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is mainly exploited for the task of classification, this paper is developed to study th…
Paper proposes C-STM for multimodal neuroimaging data classification.
problem Multimodal neuroimaging data fusion for better classification.
method Coupled Support Tensor Machine (C-STM) using latent factors from ACMTF.
result C-STM achieves better classification performance than single-mode classifiers.
The aim of this paper was to compare soft confusion matrix approach and Bayes metaclassifier under the multi-label classification framework. Although the methods were successfully applied under the multi-label classification framework, they have not been compared directly thus far. Such comparison is of vital importanc…
Paper tackles noisy similarity labels for multi-class classification.
problem Learning multi-class classifiers from noisy similarity-labeled data.
method Proposes a method using a noise transition matrix to learn from noisy data.
result Demonstrates superior performance compared to state-of-the-art methods.
We consider a challenging multi-label classification problem where both feature matrix $\X$ and label matrix $\Y$ have missing entries. An existing method concatenated $\X$ and $\Y$ as $[\X; \Y]$ and applied a matrix completion (MC) method to fill the missing entries, under the assumption that $[\X; \Y]$ is of low-rank…
Study connects Lie groups to specific Riemannian manifolds.
problem Understanding Lie groups through Riemannian manifold properties.
method Investigates Lie groups as 3D almost paracontact almost paracomplex Riemannian manifolds.
result Established correspondence between Lie algebra and matrix representation.
New algorithms estimate matrix norms without matrix multiplication.
problem Estimating matrix norms efficiently in a matrix-free setting.
method Randomized algorithms based on Hutchinson's estimator modifications.
result Oracle complexity bounds for two-to-infinity and one-to-two norms.
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.
Method reduces categorical data to lower dimensions using density matrices.
problem Dimensionality reduction for categorical data.
method Density-matrix construction from class-conditional frequencies; spectral embedding.
result Low-dimensional spectral embeddings with controlled rank.
Classifies matrices in the quaternionic hyperbolic unitary group.
problem Understanding the structure of matrices in the quaternionic hyperbolic unitary group.
method Used complex representation and characteristic polynomial to study matrices.
result Computed the characteristic polynomial and studied its sign.
We investigate task clustering for deep-learning based multi-task and few-shot learning in a many-task setting. We propose a new method to measure task similarities with cross-task transfer performance matrix for the deep learning scenario. Although this matrix provides us critical information regarding similarity betw…
Two algorithms estimate Wasserstein distance matrices from few entries for manifold learning.
problem Estimating Wasserstein distance matrices from limited data for manifold learning.
method Proposes two algorithms: matrix completion and Nyström completion for square Wasserstein matrices.
result Nyström completion can outperform matrix completion with a fixed sample budget and improve classification stability.
Unified framework detects overfitting in crash classification models.
problem Evaluation metrics fail to detect overfitting in crash classification models.
method Random Matrix Theory and Heavy-Tailed Self-Regularization framework applied to various model types.
result Power-law exponent α reliably distinguishes well-regularized from overfit models.
There is growing interest in multi-label image classification due to its critical role in web-based image analytics-based applications, such as large-scale image retrieval and browsing. Matrix completion has recently been introduced as a method for transductive (semi-supervised) multi-label classification, and has seve…
Finding a new mathematical representations for graph, which allows direct comparison between different graph structures, is an open-ended research direction. Having such a representation is the first prerequisite for a variety of machine learning algorithms like classification, clustering, etc., over graph datasets. In…
Study uses machine learning to detect early COVID-19 from CT images.
problem Early detection of COVID-19 from CT images.
method Machine learning methods applied to patches of CT images, feature extraction (GLCM, LDP, GLRLM, GLSZM, DWT), SVM classification.
result Best classification accuracy of 99.68% with 10-fold cross-validation and GLSZM feature extraction.
The lack of proper class discrimination among the Hyperspectral (HS) data points poses a potential challenge in HS classification. To address this issue, this paper proposes an optimal geometry-aware transformation for enhancing the classification accuracy. The underlying idea of this method is to obtain a linear proje…
Machine learning classifies polymer links with high accuracy.
problem Classifying knots and links in polymer melts and biological systems.
method Feedforward neural network trained on writhe density matrix.
result 97% accuracy in classifying six prime links across temperatures and lengths.
ExMatrix visualizes RF models, aiding in decision understanding.
problem Lack of interpretability in complex models like RF.
method ExMatrix, a novel visualization method for RF interpretability.
result ExMatrix handles large, complex RF models and promotes interpretability.
BeMF improves recommendation reliability in recommender systems.
problem Improving reliability in recommender systems beyond accuracy.
method Bernoulli Matrix Factorization (BeMF) for model-based collaborative filtering.
result BeMF selects more reliable predictions, improving recommendation quality.
Data-dependent hashing has recently attracted attention due to being able to support efficient retrieval and storage of high-dimensional data such as documents, images, and videos. In this paper, we propose a novel learning-based hashing method called "Supervised Discrete Hashing with Relaxation" (SDHR) based on "Super…