**linearalgebra**

The Tensor Algebra Compiler (taco)

17 days ago by euler

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?

18 days ago by euler

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
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.

18 days ago by euler

linear algebra - Second derivative of $detsqrt{F^TF}$ with respect to $F$ - Mathematics Stack Exchange

21 days ago by yig

list of useful tensors and identities

matrix
calculus
reference
linearalgebra
math
mathematics
21 days ago by yig