You are a Lead Data Scientist working on a churn prediction model for a subscription service with high-dimensional sparse data. Propose a feature engineering pipeline that includes: 1) Techniques for handling temporal cyclical features (e.g., time of day), 2) Dimensionality reduction methods specifically for categorical variables, and 3) Interaction term creation to capture user behavior patterns. Explain the mathematical intuition behind each choice and how it mitigates the curse of dimensionality.