First Principal Eigenvector
Chanchal Chatterjee · Apress eBooks · 2022
In this chapter, I present a unified framework to derive and discuss ten adaptive algorithms (some well-known) for principal eigenvector computation, which is also known as principal component analysis (PCA) or the Karhunen-Loeve [Karhunen–Loève theorem, Wikipedia] transform. The first principal eigenvector of a symmetric positive definite matrix A ∈ℜ nXn is the eigenvector ϕ 1 corresponding to the largest eigenvalue λ 1 of A . Here A ϕ i = λ i ϕ i for i =1,…, n , where λ 1 >λ 2 ≥...≥λ n >0 are the n largest eigenvalues of A corresponding to eigenvectors ϕ 1 ,…, ϕ n .