**Taught by:** *Alex Williams, Stanford University (September 5, 2017)*

**Videos:**

- Dimensionality Reduction for Matrix- and Tensor-Coded Data [Part 1] (53:36)
- Dimensionality Reduction for Matrix- and Tensor-Coded Data [Part 2] (46:05)

**Description:** In many scientific domains, data is coded in large tables or higher-dimensional arrays. Compressing these data into smaller, more manageable representations is often critical for extracting scientific insights. This tutorial covers matrix and tensor factorizations, a large class of dimensionality-reduction methods that include PCA, non-negative matrix factorization (NMF), independent components analysis (ICA), and others. We pay special attention to canonical polyadic (CP) tensor decomposition, which extends PCA to higher-order data arrays. The first half of the tutorial covers the theoretical concepts and foundations of these methods, many of which are surprisingly recent results. The second half includes hands-on exercises and advice for fitting these models in practice.

**Slides:**

**Additional Resources:**

- GitHub: Code for dimensionality reduction for matrix- and tensor-coded data
- Exercises for dimensionality reduction for matrix- and tensor-coded data
- Data for exercises (MAT) for dimensionality reduction for matrix- and tensor-coded data (.mat file)
- Data for NMF exercises (TXT) (.txt file)