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The Tensor Algebra Compiler (taco)
A fast and versatile library for linear and tensor algebra
math  linearalgebra  tensor 
17 days ago by euler
How Are Principal Component Analysis and Singular Value Decomposition Related?
Principal Component Analysis, or PCA, is a well-known and widely used technique applicable to a wide variety of applications such as dimensionality reduction, data compression, feature extraction, and visualization. The basic idea is to project a dataset from many correlated coordinates onto fewer uncorrelated coordinates called principal components while still retaining most of the variability present in the data.

Singular Value Decomposition, or SVD, is a computational method often employed to calculate principal components for a dataset. Using SVD to perform PCA is efficient and numerically robust. Moreover, the intimate relationship between them can guide our intuition about what PCA actually does and help us gain additional insights into this technique.

In this post, I will explicitly describe the mathematical relationship between SVD and PCA and highlight some benefits of doing so. If you have used these techniques in the past but aren’t sure how they work internally this article is for you. By the end you should have an understanding of the motivation for PCA and SVD, and hopefully a better intuition about how to effectively employ them.
pca  svd  math  linearalgebra 
18 days ago by euler

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