Title: Watch: PCA and clustering
Course: Advanced Data Science: A Graduate Course > Section: Module 6: Unsupervised learning: clustering and PCA

Watch

▶ Recorded lecture (~20 min) + slides ↓:
- Why unsupervised learning is genuinely harder to evaluate: with no ground-truth label there is no held-out accuracy, so validity comes from stability, internal cohesion, and interpretability instead.
- PCA as a variance-preserving rotation of the feature space: the principal components are the eigenvectors of the covariance matrix, ordered so the first axis captures the most variance, and why you almost always standardize first so units do not decide the answer.
- How to read PCA output: loadings tell you what each component means, the scree plot and cumulative variance tell you how many components to keep, and scores place each observation in the reduced space.
- k-means and Lloyd’s algorithm: alternate between assigning points to the nearest centroid and recomputing centroids as the mean of their members; it minimizes within-cluster sum of squares but only converges to a local optimum, so multiple restarts and k-means++ initialization matter.
- How to argue for a number of clusters rather than eyeball it: bootstrap or subsample the data and measure how often the same points cluster together (stability), read the silhouette width, and consult the gap statistic, then look for agreement across these signals.
- The traps of t-SNE: perplexity changes the picture, distances between clusters are not meaningful, cluster sizes are distorted, and running it twice gives different layouts, so it is a lens for generating hypotheses and never evidence for a count.

“Advanced Data Science by Michelle Blomberg is licensed under CC BY-NC-SA 4.0.”