A machine learning engineer at a credit union is developing a model to classify loan applicants into three risk categories: low, medium, and high. The dataset contains several continuous predictor variables, such as income, credit score, and debt-to-income ratio. The engineer performs an exploratory data analysis and observes that the predictor variables are approximately normally distributed for each risk category and that the covariance matrices across the three categories are very similar.
Given this analysis, which classification model is most justified, and why?
Principal Component Analysis (PCA) followed by a k-nearest neighbors (KNN) classifier, to reduce dimensionality while capturing maximum variance.
Linear Discriminant Analysis (LDA), because the assumption of equal covariance matrices among the classes is met.
Logistic Regression, because it does not make any assumptions about the distribution of the predictor variables.
Quadratic Discriminant Analysis (QDA), because it provides a more flexible, non-linear decision boundary.
The correct answer is Linear Discriminant Analysis (LDA). LDA is a generative classifier that assumes predictors are normally distributed within each class and that all classes share the same covariance matrix (homoscedasticity). The scenario explicitly states that both of these assumptions are met.
Quadratic Discriminant Analysis (QDA) is similar to LDA but does not assume the covariance matrices are equal. Using QDA when the covariances are equal introduces unnecessary complexity and a higher risk of overfitting without providing a better fit, making LDA the more parsimonious and appropriate choice.
While Logistic Regression is a robust classifier that does not assume normality of the predictors, LDA can be more powerful and stable when its assumptions are actually met, as they are in this scenario.
Principal Component Analysis (PCA) is an unsupervised dimensionality reduction technique that finds directions of maximum variance, ignoring class labels. Since the goal is to separate known classes, the supervised nature of LDA, which maximizes class separability, is far more suitable.
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Why wouldn’t PCA combined with KNN be suitable in this problem?