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∑MathAdvanced

Marchenko-Pastur Distribution

The Marchenko–Pastur (MP) distribution describes the limiting eigenvalue distribution of sample covariance matrices S = (1/n) XX^{\top} when both the dimension p and the sample size n grow with p/n \to \gamma.

#marchenko-pastur#random matrix theory#sample covariance+10
∑MathAdvanced

Manifolds & Manifold Hypothesis

A manifold is a space that locally looks like Euclidean space, stitched together by coordinate charts and smooth transition maps.

#manifold
Advanced
Filtering by:
#pca
#topological manifold
#smooth manifold
+12
∑MathIntermediate

Low-Rank Approximation

Low-rank approximation replaces a big matrix with one that has far fewer degrees of freedom while preserving most of its action.

#low-rank approximation#eckart-young theorem#svd+12
∑MathIntermediate

Eigendecomposition

Eigendecomposition expresses a matrix as a change of basis times a diagonal scaling, revealing its natural stretching directions.

#eigendecomposition#eigenvalue#eigenvector+11