High-Dimensional Quadratic Discriminant Analysis under Spiked Covariance Model

• URL: http://arxiv.org/abs/2006.14325v1
• Date: Thu, 25 Jun 2020 12:00:26 GMT
• Title: High-Dimensional Quadratic Discriminant Analysis under Spiked Covariance Model
• Authors: Houssem Sifaou, Abla Kammoun, Mohamed-Slim Alouini
• Abstract summary: We propose a novel quadratic classification technique, the parameters of which are chosen such that the fisher-discriminant ratio is maximized. Numerical simulations show that the proposed classifier not only outperforms the classical R-QDA for both synthetic and real data but also requires lower computational complexity.
• Score: 101.74172837046382
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quadratic discriminant analysis (QDA) is a widely used classification technique that generalizes the linear discriminant analysis (LDA) classifier to the case of distinct covariance matrices among classes. For the QDA classifier to yield high classification performance, an accurate estimation of the covariance matrices is required. Such a task becomes all the more challenging in high dimensional settings, wherein the number of observations is comparable with the feature dimension. A popular way to enhance the performance of QDA classifier under these circumstances is to regularize the covariance matrix, giving the name regularized QDA (R-QDA) to the corresponding classifier. In this work, we consider the case in which the population covariance matrix has a spiked covariance structure, a model that is often assumed in several applications. Building on the classical QDA, we propose a novel quadratic classification technique, the parameters of which are chosen such that the fisher-discriminant ratio is maximized. Numerical simulations show that the proposed classifier not only outperforms the classical R-QDA for both synthetic and real data but also requires lower computational complexity, making it suitable to high dimensional settings.

Related papers

• Synergistic eigenanalysis of covariance and Hessian matrices for enhanced binary classification [72.77513633290056]
  We present a novel approach that combines the eigenanalysis of a covariance matrix evaluated on a training set with a Hessian matrix evaluated on a deep learning model. Our method captures intricate patterns and relationships, enhancing classification performance.
  arXiv  Detail & Related papers  (2024-02-14T16:10:42Z)
• Regularized Linear Discriminant Analysis Using a Nonlinear Covariance Matrix Estimator [11.887333567383239]
  Linear discriminant analysis (LDA) is a widely used technique for data classification. LDA becomes inefficient when the data covariance matrix is ill-conditioned. Regularized LDA methods have been proposed to cope with such a situation.
  arXiv  Detail & Related papers  (2024-01-31T11:37:14Z)
• Parametric Classification for Generalized Category Discovery: A Baseline Study [70.73212959385387]
  Generalized Category Discovery (GCD) aims to discover novel categories in unlabelled datasets using knowledge learned from labelled samples. We investigate the failure of parametric classifiers, verify the effectiveness of previous design choices when high-quality supervision is available, and identify unreliable pseudo-labels as a key problem. We propose a simple yet effective parametric classification method that benefits from entropy regularisation, achieves state-of-the-art performance on multiple GCD benchmarks and shows strong robustness to unknown class numbers.
  arXiv  Detail & Related papers  (2022-11-21T18:47:11Z)
• Theoretical Insights Into Multiclass Classification: A High-dimensional Asymptotic View [82.80085730891126]
  We provide the first modernally precise analysis of linear multiclass classification. Our analysis reveals that the classification accuracy is highly distribution-dependent. The insights gained may pave the way for a precise understanding of other classification algorithms.
  arXiv  Detail & Related papers  (2020-11-16T05:17:29Z)
• Self-Weighted Robust LDA for Multiclass Classification with Edge Classes [111.5515086563592]
  A novel self-weighted robust LDA with l21-norm based between-class distance criterion, called SWRLDA, is proposed for multi-class classification. The proposed SWRLDA is easy to implement, and converges fast in practice.
  arXiv  Detail & Related papers  (2020-09-24T12:32:55Z)
• Population structure-learned classifier for high-dimension low-sample-size class-imbalanced problem [3.411873646414169]
  Population Structure-learned classifier (PSC) is proposed. PSC can obtain better generalization performance on IHDLSS. PSC is superior to the state-of-art methods in IHDLSS.
  arXiv  Detail & Related papers  (2020-09-10T08:33:39Z)
• Improved Design of Quadratic Discriminant Analysis Classifier in Unbalanced Settings [19.763768111774134]
  quadratic discriminant analysis (QDA) or its regularized version (R-QDA) for classification is often not recommended. We propose an improved R-QDA that is based on the use of two regularization parameters and a modified bias.
  arXiv  Detail & Related papers  (2020-06-11T12:17:05Z)
• Robust Generalised Quadratic Discriminant Analysis [6.308539010172309]
  The classification rule in GQDA is based on the sample mean vector and the sample dispersion matrix of a training sample, which are extremely non-robust under data contamination. The present paper investigates the performance of the GQDA classifier when the classical estimators of the mean vector and the dispersion matrix used therein are replaced by various robust counterparts.
  arXiv  Detail & Related papers  (2020-04-11T18:21:06Z)
• Saliency-based Weighted Multi-label Linear Discriminant Analysis [101.12909759844946]
  We propose a new variant of Linear Discriminant Analysis (LDA) to solve multi-label classification tasks. The proposed method is based on a probabilistic model for defining the weights of individual samples. The Saliency-based weighted Multi-label LDA approach is shown to lead to performance improvements in various multi-label classification problems.
  arXiv  Detail & Related papers  (2020-04-08T19:40:53Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.