Now that you understand the basics of Principal Component Analysis, this module focuses on how to apply it thoughtfully. You will learn how to decide how many components to retain by examining the proportion of variance explained and interpreting scree plots. You will also explore how to interpret principal component loadings to understand what each component reveals about the original features. Through hands-on practice, you will see how PCA can be used not only for visualization but also as a powerful pre-processing step before supervised learning. By the end of this module, you will be able to reduce dimensionality with purpose and insight.

This module introduces you to the world of clustering, where the goal is to uncover natural groupings in data without any labels. You will learn how the k-means algorithm partitions observations into clusters based on similarity, and how it iteratively refines those groupings by updating centroids. Along the way, you will grapple with the challenge of choosing the right number of clusters and explore heuristic tools like the elbow method. Through hands-on work, you will evaluate clustering results and interpret what each group represents in context. Clustering is as much an art as it is a science, and this module will help you build intuition for both.

In this module, you will explore hierarchical clustering—a method that builds nested groupings without requiring you to choose the number of clusters in advance. You will learn how the agglomerative approach works step by step and how to interpret dendrograms to uncover meaningful structure in your data. Unlike K-means, hierarchical clustering offers a full picture of how observations relate to one another at different levels of similarity. You will also examine how scaling and distance metrics can influence clustering results, and why evaluating clusters is often more subjective than definitive. This module encourages you to think critically about what makes a clustering solution useful, not just mathematically valid.

This module introduces low-rank matrix completion as a principled approach to handling missing data and powering recommender systems. You will learn how PCA can be used as a matrix approximation tool to reconstruct missing entries, implement an iterative completion algorithm, and validate model choices via masking. A compact case study demonstrates practical trade-offs with small p, and the module concludes by mapping the same ideas to user–item recommendation with attention to preprocessing, evaluation, scale, and ethics.