We study sample covariance matrices of the form $W=(1/n)CC^{\intercal}$, where C is a k × n matrix with independent and identically distributed (i.i.d.) mean 0 ...

Ecologists are fascinated by the prevalence of nestedness in biogeographic and community data, where it is thought to promote biodiversity in mutualistic systems. Traditionally, nestedness has been ...

This article presents a from-scratch C# implementation of the second technique: using SVD to compute eigenvalues and eigenvectors from the standardized source data. If you're not familiar with PCA, ...

After breakfast one morning in August, the mathematician Terence Tao opened an email from three physicists he didn’t know. The trio explained that they’d stumbled across a simple formula that, if true ...

Transforming a dataset into one with fewer columns is more complicated than it might seem, explains Dr. James McCaffrey of Microsoft Research in this full-code, step-by-step machine learning tutorial.