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.
New framework improves classification accuracy using Pillai's trace and ULDA.
problem Traditional LDA's limitations in noise sensitivity and non-invertible matrices.
method Integrates Pillai's trace with ULDA for a unified classifier.
result Effective control of Type I error rates and improved classification accuracy.
We introduce a new method of performing high dimensional discriminant analysis, which we call multiDA. We achieve this by constructing a hybrid model that seamlessly integrates a multiclass diagonal discriminant analysis model and feature selection components. Our feature selection component naturally simplifies to wei…
Deep IDA integrates multi-view data to classify COVID-19 severity, identifying molecular signatures.
problem Understanding the complexity of COVID-19 severity from multi-view clinical and molecular data.
method Deep IDA learns nonlinear projections to maximize view associations and class separations, with feature ranking.
result Deep IDA outperforms other methods in classifying COVID-19 severity and identifies interpretable molecular signatures.
Unified framework for multi-view learning with orthogonal projections.
problem Learning individual orthogonal projections for multiple views.
method Successive approximations via eigenvectors, iterative Krylov subspace method.
result Consistently competitive and often better than existing methods.
In this paper, we study the modeling and the classification of functional data presenting regime changes over time. We propose a new model-based functional mixture discriminant analysis approach based on a specific hidden process regression model that governs the regime changes over time. Our approach is particularly a…
Statistical approaches for Functional Data Analysis concern the paradigm for which the individuals are functions or curves rather than finite dimensional vectors. In this paper, we particularly focus on the modeling and the classification of functional data which are temporal curves presenting regime changes over time.…
We consider the problem of discriminative factor analysis for data that are in general non-Gaussian. A Bayesian model based on the ranks of the data is proposed. We first introduce a new {\em max-margin} version of the rank-likelihood. A discriminative factor model is then developed, integrating the max-margin rank-lik…
Similarity-based clustering and semi-supervised learning methods separate the data into clusters or classes according to the pairwise similarity between the data, and the pairwise similarity is crucial for their performance. In this paper, we propose a novel discriminative similarity learning framework which learns dis…
Kernel discriminant analysis uses nonlinear embeddings to improve classification.
problem Limited effectiveness of linear discriminant analysis in capturing nonlinear features.
method Study of nonlinear embeddings in kernel discriminant analysis using polynomial and Gaussian kernels, solving generalized eigenvalue problems.
result Polynomial and Gaussian discriminants capture class differences through population moments and randomized projections.
Interactive DR framework for comparing datasets.
problem Limited flexibility in existing DR methods for comparative analysis.
method Unified linear comparative analysis (ULCA) with interactive optimization and visualization.
result ULCA and optimization algorithm improve comparative analysis efficiency and flexibility.
Paper proposes distributed sparse multicategory discriminant analysis for classification.
problem Sparse multicategory classification with distributed data.
method Convex formulation, distributed setting, invariant discriminant subspace recovery.
result Distributed sparse multicategory linear discriminant analysis performs as good as centralized version after a few rounds of communications.
Smart Bayes integrates generative and discriminative features for improved classification.
problem Improving classification performance by combining generative and discriminative modeling.
method Integrates generative likelihood-ratio features into a logistic-regression-style classifier.
result Often outperforms logistic regression and Naive Bayes in simulations and real data.
Paper proposes faster incremental subclass discriminant analysis.
problem Efficiently classify subclasses in incremental data.
method Exact and approximate linear and kernelized solutions.
result Superior training time and accuracy compared to existing methods.
New method improves self-supervised representation learning using probabilistic modeling and Monte Carlo integration.
problem Improving self-supervised representation learning for multimodal data.
method Discriminative probabilistic modeling with multiple importance sampling (MIS) for robust Monte Carlo integration.
result Proposes a novel non-parametric method for approximating conditional probability densities through convex optimization.
PANDA improves linear discriminant analysis in high dimensions with minimal tuning.
problem Linear discriminant analysis in high-dimensional settings.
method PANDA: a tuning-insensitive method for linear discriminant analysis.
result PANDA achieves optimal convergence rates in estimation error and misclassification rate.
New robust discriminant analysis for non-Gaussian data.
problem Classical discriminant analysis struggles with non-Gaussian distributions and contaminated datasets.
method Each data point follows its own ES distribution with arbitrary scale, leading to robust classification.
result Maximum-likelihood estimation and classification are simple, fast, and robust.
Proposes KMvDA for object recognition from multi-view data.
problem Recognizing objects from different views, even when views are heterogeneous.
method Introduces kernel multi-view discriminant analysis (KMvDA) and uses random Fourier features (RFF) for large-scale learning.
result KMvDA and RFF approximation improve object recognition from multi-view data.
Dimensionality reduction is an important operation in information visualization, feature extraction, clustering, regression, and classification, especially for processing noisy high dimensional data. However, most existing approaches preserve either the global or the local structure of the data, but not both. Approache…
This tutorial explains Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA) as two fundamental classification methods in statistical and probabilistic learning. We start with the optimization of decision boundary on which the posteriors are equal. Then, LDA and QDA are derived for binary and mul…
This paper analyzes implicit bias in Deep Linear Discriminant Analysis.
problem The implicit bias of Deep Linear Discriminant Analysis.
method Analyzing gradient flow on a L-layer diagonal linear network.
result Under balanced initialization, the network transforms additive updates into multiplicative updates, conserving the (2/L) quasi-norm.
The paper integrates statistical significance and discriminative power in pattern discovery.
problem Discovering actionable patterns that meet rigorous statistical significance and discriminative power criteria.
method Integrates statistical significance and discriminative power criteria into state-of-the-art algorithms.
result Improves discriminative power and statistical significance of discovered patterns without quality deterioration.
DFSOS improves sparse discriminant analysis for high-dimensional data.
problem Sparse discriminant analysis in high-dimensional settings with feature selection.
method Deflation-Free Sparse Optimal Scoring (DFSOS) using Bregman iteration and orthogonality-constrained optimization.
result DFSOS achieves comparable or better classification accuracy than deflation-based methods.
Discriminative Dictionary Learning (DL) methods have been widely advocated for image classification problems. To further sharpen their discriminative capabilities, most state-of-the-art DL methods have additional constraints included in the learning stages. These various constraints, however, lead to additional computa…
Develops methods for integrating multivariate normals and computing classification measures.
problem Computing performance of multivariate normal models is challenging due to lack of general analytical expressions.
method Mathematical results and open-source software for integrating and analyzing multivariate normal distributions.
result Provides tools for calculating classification errors, discriminability, and reliability.
Proposes improved classification via transfer learning with regularized linear discriminant analysis.
problem High dimensionality and small sample sizes lead to poor classification performance.
method Regularized random-effects linear discriminant analysis, combining ridge estimates from target and source models.
result Explicit derivation of asymptotic weights and classification error rates in high-dimensional settings.
New method for tensor classification with missing data.
problem Handling incomplete tensor data in high-dimensional classification.
method High-dimensional tensor linear discriminant analysis with TGMM and Tensor LDA-MD.
result Established convergence rates and minimax optimal bounds for misclassification rate.
New method compresses large sample data for faster discriminant analysis.
problem Large sample sizes in discriminant analysis increase computational burden.
method Proposes a new compression approach for reducing training samples.
result Significant computational gains and superior predictive ability compared to random sub-sampling.
This paper proposes a new subspace learning method, named Quantized Fisher Discriminant Analysis (QFDA), which makes use of both machine learning and information theory. There is a lack of literature for combination of machine learning and information theory and this paper tries to tackle this gap. QFDA finds a subspac…
We introduce a new discriminant analysis method (Empirical Discriminant Analysis or EDA) for binary classification in machine learning. Given a dataset of feature vectors, this method defines an empirical feature map transforming the training and test data into new data with components having Gaussian empirical distrib…
A brain computer interface (BCI) is a system which provides direct communication between the mind of a person and the outside world by using only brain activity (EEG). The event-related potential (ERP)-based BCI problem consists of a binary pattern recognition. Linear discriminant analysis (LDA) is widely used to solve…
New method improves OOD detection by integrating diffusion models into discriminator models.
problem Overconfidence in discriminator models leads to poor OOD detection.
method Integrates diffusion models into discriminator and generation models to mitigate overconfidence.
result Demonstrates significant improvement in AUROC scores for challenging datasets.
The paper addresses evaluating survival predictions using discrimination measures, finding a robust method to convert distributions to risks.
problem Evaluating survival distribution predictions with discrimination measures is challenging and often leads to unfair comparisons.
method The paper surveys existing methods and recommends summing over the predicted cumulative hazard as the most robust method to convert distributions to risks.
result Summing over the predicted cumulative hazard is the most robust method to convert distribution predictions to risk predictions.
We propose a novel linear discriminant analysis approach for the classification of high-dimensional matrix-valued data that commonly arises from imaging studies. Motivated by the equivalence of the conventional linear discriminant analysis and the ordinary least squares, we consider an efficient nuclear norm penalized …
Extends Fisher's Discriminant Analysis for interval-valued data.
problem Classifying entities represented by intervals and histograms.
method Adapts Fisher's Discriminant Analysis using Moore's interval arithmetic and Mallows' distance.
result Discriminant directions for interval-valued data are numerically maximized.
A new method for LDA using randomized Kaczmarz improves accuracy for large datasets.
problem Efficiently performing LDA on large datasets.
method Randomized Kaczmarz method applied to linear discriminant analysis.
result The method achieves comparable accuracy to full data LDA.
We consider the task of classification in the high dimensional setting where the number of features of the given data is significantly greater than the number of observations. To accomplish this task, we propose a heuristic, called sparse zero-variance discriminant analysis (SZVD), for simultaneously performing linear …
A new LDA variant improves multi-label classification performance.
problem Improving multi-label classification performance.
method Saliency-based weights redefine between-class and within-class scatter matrices for multi-label classification.
result The proposed method leads to performance improvements in various multi-label classification problems.
We consider the high-dimensional discriminant analysis problem. For this problem, different methods have been proposed and justified by establishing exact convergence rates for the classification risk, as well as the l2 convergence results to the discriminative rule. However, sharp theoretical analysis for the variable…
A new IPM uses ReLU networks to measure probability discrepancies.
problem Measuring the difference between two probability distributions in high dimensions.
method Proposes a new parametric IPM using ReLU neural networks to optimize and distinguish between distributions.
result The proposed IPM has good convergence rates and can be used as a surrogate for other IPMs.
In this paper we formulate a probabilistic model for class-specific discriminant subspace learning. The proposed model can naturally incorporate the multi-modal structure of the negative class, which is neglected by existing class-specific methods. Moreover, it can be directly used to define a class-specific probabilis…
A new classification rule for FDA improves classification performance by accounting for unequal covariance matrices.
problem Unequal covariance matrices in practical situations affect the performance of FDA and its variants.
method Proposes a novel classification rule for FDA that accounts for unequal covariance matrices, applicable to many FDA variants.
result The new classification rule improves classification performance compared to original FDA and variants.
Existing networks directly learn feature representations on 3D point clouds for shape analysis. We argue that 3D point clouds are highly redundant and hold irregular (permutation-invariant) structure, which makes it difficult to achieve inter-class discrimination efficiently. In this paper, we propose a two-faceted sol…
We present a novel approach to the formulation and the resolution of sparse Linear Discriminant Analysis (LDA). Our proposal, is based on penalized Optimal Scoring. It has an exact equivalence with penalized LDA, contrary to the multi-class approaches based on the regression of class indicator that have been proposed s…
New model selects uncorrelated and discriminative features for unsupervised feature selection.
problem Selecting uncorrelated and discriminative features in high-dimensional data.
method Adaptive graph-based generalized regression model with uncorrelated constraint and ℓ2,1-norm regularization. result The model effectively selects uncorrelated and discriminative features, improving clustering performance.
A new QDA classifier for high-dimensional data with spiked covariance.
problem Classifying high-dimensional data with distinct covariance matrices.
method Proposes a novel quadratic classification technique with parameters chosen to maximize the fisher-discriminant ratio.
result The proposed classifier outperforms classical R-QDA and requires lower computational complexity.
New findings show fixed-kernel discriminators are weaker than feature-learning ones.
problem Comparing performance of fixed-kernel and feature-learning discriminators.
method Using function classes F2 and F1, constructing pairs of distributions, and linking IPMs with sliced Wasserstein distances. result Fixed-kernel IPM and SD cannot discriminate certain distributions that feature-learning IPM and SD can.
DNLL loss improves deep LDA accuracy and consistency.
problem Pathological solutions in unconstrained Deep LDA.
method Introducing Discriminative Negative Log-Likelihood (DNLL) loss.
result Deep LDA trained with DNLL produces clean latent spaces and better calibrated probabilities.