Machine Learning, Dimensionality Reduction, Eigenvectors, Algorithms, Mathematics.
∇ var(vᵗ) = (some constant λ) ∇ vᵗv ∇ vᵗ*Cov(c(x))*v = λ ∇ vᵗv ∴ 2*M*v = 2*λ*v … Cov(c(x)) = M ∴ Mv = λ v Woahhhh, did you catch that?? This is what PCA tells us! We just showed that the vectors along which the variance of our data is maximum are nothing but the eigenvectors of the covariance