[Paper Review] Discriminant Analysis in Contrasting Dimensions for Polycystic Ovary Syndrome Prognostication

Abhishek Gupta, Himanshu B. Soni+2 more|arXiv (Cornell University)|Jan 9, 2022

Face and Expression Recognition4 citations

TL;DR

This paper proposes using Linear and Quadratic Discriminant Analysis (LDA and QDA) for supervised dimensionality reduction and binary classification in Polycystic Ovary Syndrome (PCOS) prognostication. By leveraging class-specific covariance structures in QDA, the method achieves high accuracy—95.92% on test data—demonstrating superior performance over traditional ML models through optimized feature separation and visualization of class separability.

ABSTRACT

A lot of prognostication methodologies have been formulated for early detection of Polycystic Ovary Syndrome also known as PCOS using Machine Learning. PCOS is a binary classification problem. Dimensionality Reduction methods impact the performance of Machine Learning to a greater extent and using a Supervised Dimensionality Reduction method can give us a new edge to tackle this problem. In this paper we present Discriminant Analysis in different dimensions with Linear and Quadratic form for binary classification along with metrics. We were able to achieve good accuracy and less variation with Discriminant Analysis as compared to many commonly used classification algorithms with training accuracy reaching 97.37% and testing accuracy of 95.92% using Quadratic Discriminant Analysis. Paper also gives the analysis of data with visualizations for deeper understanding of problem.

Motivation & Objective

• To improve early PCOS detection using machine learning with a focus on dimensionality reduction.
• To evaluate the effectiveness of Linear and Quadratic Discriminant Analysis as supervised dimensionality reduction techniques for PCOS binary classification.
• To compare LDA and QDA performance against common ML algorithms using comprehensive metrics like AUC, precision-recall, and F1-score.
• To provide visual and statistical analysis of data separability in reduced-dimensional space for better interpretability.
• To demonstrate that QDA outperforms LDA and other models in PCOS prognosis due to its flexible covariance modeling.

Proposed method

• The study applies Linear Discriminant Analysis (LDA) to project features into a lower-dimensional space that maximizes class separability by minimizing within-class variance and maximizing between-class variance.
• Quadratic Discriminant Analysis (QDA) is used as a variant of LDA that estimates individual covariance matrices per class, allowing for quadratic decision boundaries.
• The discriminant functions for both LDA and QDA are derived using multivariate Gaussian distributions, with QDA incorporating class-specific covariance matrices and prior probabilities.
• Performance is evaluated using standard classification metrics: accuracy, precision, recall, F1-score, AUC, and average precision, with precision-recall and ROC curves visualized for model comparison.
• Data visualization techniques, including scatter plots with elliptical contours, are used to illustrate class separability in the discriminant space.
• Bayesian optimization is applied to tune hyperparameters and improve likelihood estimation in the classification framework.

Experimental results

Research questions

• RQ1 Can supervised dimensionality reduction via LDA and QDA improve the accuracy of PCOS prognosis compared to standard machine learning models?
• RQ2 How does QDA’s use of class-specific covariance matrices enhance classification performance over LDA in the context of PCOS data?
• RQ3 To what extent do precision-recall and ROC curves reflect the robustness and generalization capability of LDA and QDA on PCOS data?
• RQ4 How well do the discriminant components visualize the separability of PCOS and non-PCOS cases in the reduced feature space?
• RQ5 What is the comparative performance of QDA versus LDA and other ML models in terms of AUC and average precision for PCOS detection?

Key findings

• Quadratic Discriminant Analysis (QDA) achieved a test accuracy of 95.92%, outperforming Linear Discriminant Analysis and other commonly used algorithms.
• Training accuracy reached 97.37% with QDA, indicating strong model fitting on the training set.
• QDA demonstrated superior AUC and area under the precision-recall curve compared to LDA, suggesting better overall predictive performance.
• The precision-recall curve for QDA showed a sharper decline after initial high precision, indicating consistent positive prediction quality across thresholds.
• Visualizations revealed clearer class separability in QDA’s quadratic discriminant space, with distinct elliptical contours for PCOS (Yes) and non-PCOS (No) labels.
• The study confirms that supervised dimensionality reduction via QDA enhances both classification accuracy and interpretability in PCOS prognostication.