Explain KNN and PCA and key tradeoffs

A Data Scientist internship interview includes questions on core machine learning concepts:

1. K-Nearest Neighbors (KNN)

• Describe how KNN performs both classification and regression.
• How would you select k? What occurs if k is set too low or too high?
• How do you decide on a distance metric such as Euclidean or cosine?
• Which preprocessing steps matter most, including feature scaling and encoding categorical variables?
• Talk about its computational cost and how you would scale KNN to large datasets.
• What problems appear in high-dimensional feature spaces, often called the curse of dimensionality?

2. Principal Component Analysis (PCA)

• Which optimization objective does PCA target? Explain the geometric meaning behind it.
• How is PCA actually calculated: through eigendecomposition of the covariance matrix or via SVD?
• How do you pick the number of components, using explained variance or cross-validation?
• In what situations can PCA reduce performance, such as loss of interpretability, non-linear structure, or data leakage?
• If PCA is applied before KNN, when could it improve results and when could it make them worse?

Give clear, interview-ready responses that include practical tradeoffs.

Overview: It tests knowledge of K-Nearest Neighbors, an instance-based method for classification and regression, and Principal Component Analysis, a linear dimensionality reduction technique, with attention to tradeoffs around distance metrics, preprocessing choices, computational cost, high-dimensional limits, PCA’s optimization and computation strategies, and how reducing dimensions affects downstream nonparametric methods. This type of question is typical for Data Scientist internship interviews in machine learning at a fundamentals-to-intermediate level because it checks both the theory and the practical concerns involved in using non-parametric algorithms and linear feature extraction on real data.

This question is drawn from a Data Scientist interview experience.