Adaptive Machine Learning Algorithms with Python: Solve Data Analytics and Machine Learning Problems on Edge Devices

© The Author(s), under exclusive license to APress Media, LLC, part of Springer Nature 2022

C. ChatterjeeAdaptive Machine Learning Algorithms with Pythonhttps://doi.org/10.1007/978-1-4842-8017-1_4

4. First Principal Eigenvector

Chanchal Chatterjee¹  

(1)

San Jose, CA, USA

 

4.1 Introduction and Use Cases

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 ϕ₁ corresponding to the largest eigenvalue λ₁ of A. Here Aϕ_i= λ_iϕ_i for i=1,…,