LH - -Computational Tutorial: Dimensionality Reduction for Matrix- and Tensor-Coded Data (I & II)

Dimensionality Reduction for Matrix- and Tensor-Coded Data (I & II)
Dimensionality Reduction for Matrix- and Tensor -Coded Data (I & II)
MIT, Stanford

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 includes 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 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.

Taught by: Alex Williams, Stanford University

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