Comparative Analysis of Classification Models: Logistic Regression, Naive Bayes, LDA, and QDA

 

Criteria	Logistic Regression	Naive Bayes Classifier	Linear Discriminant Analysis (LDA)	Quadratic Discriminant Analysis (QDA)
Model Type	Parametric	Parametric	Parametric	Parametric
Assumption about Data Distribution	None on distribution, assumes a linear relationship between log odds and features	Assumes independence between features, with specific distribution per class	Assumes Gaussian distribution with same covariance matrix for each class	Assumes Gaussian distribution with different covariance matrices for each class
Decision Boundary	Linear	Linear or Non-linear	Linear	Quadratic (Non-linear)
Computation Complexity	Moderate	Low	Low to Moderate	Moderate
Robustness to Outliers	Moderate	Low	Low	Low
Scalability	Good	Very Good	Moderate	Limited
Use Case	Binary classification, where interpretability is important	Baseline for text classification, when features are independent	When the Gaussian assumption holds, and a linear classifier is preferred	When the Gaussian assumption holds but classes have different covariances, allowing for non-linear decision boundaries
Considers Covariance	No	No	Yes	Yes
Assumes Same Variance (Covariance)	Not Applicable	Yes, implicitly due to feature independence	Yes	No
Limitations	Assumes linear relationship, which may not fit all datasets	Simplistic feature independence assumption can be unrealistic for complex datasets	Sensitive to outliers due to reliance on covariance; performs poorly if assumptions about Gaussian distribution and equal covariances are violated	Computationally intensive with high-dimensional data; sensitive to outliers; requires sufficient data to estimate covariances accurately for each class