Principal Component Analysis and Optimization: A Tutorial

This data accompanies Principal Component Analysis and Optimization: A Tutorial by Robert Reris and J. Paul Brooks, presented at the 2015 INFORMS Computing Society Conference, Operations Research and Computing: Algorithms and Software for Analytics, Richmond, Virginia January 11-13, 2015. The data contains R code, output, and comments that follow the examples for principal component analysis in the paper

R Code to Accompany “Principal Component Analysis and Optimization: A Tutorial”

This data accompanies Principal Component Analysis and Optimization: A Tutorial by Robert Reris and J. Paul Brooks, presented at the 2015 INFORMS Computing Society Conference, Operations Research and Computing: Algorithms and Software for Analytics, Richmond, Virginia January 11-13, 2015. The data contains R code, output, and comments that follow the examples for principal component analysis in the paper

R Code to Accompany “Principal Component Analysis and Optimization: A Tutorial”

This data accompanies Principal Component Analysis and Optimization: A Tutorial by Robert Reris and J. Paul Brooks, presented at the 2015 INFORMS Computing Society Conference, Operations Research and Computing: Algorithms and Software for Analytics, Richmond, Virginia January 11-13, 2015. The data contains R code, output, and comments that follow the examples for principal component analysis in the paper

Eigenvalue and Generalized Eigenvalue Problems: Tutorial

This paper is a tutorial for eigenvalue and generalized eigenvalue problems. We first introduce eigenvalue problem, eigen-decomposition (spectral decomposition), and generalized eigenvalue problem. Then, we mention the optimization problems which yield to the eigenvalue and generalized eigenvalue problems. We also provide examples from machine learning, including principal component analysis, kernel supervised principal component analysis, and Fisher discriminant analysis, which result in eigenvalue and generalized eigenvalue problems. Finally, we introduce the solutions to both eigenvalue and generalized eigenvalue problems.Comment: 8 pages, Tutorial pape

An Introduction to Independent Component Analysis: InfoMax and FastICA algorithms

This paper presents an introduction to independent component analysis (ICA). Unlike principal component analysis, which is based on the assumptions of uncorrelatedness and normality, ICA is rooted in the assumption of statistical independence. Foundations and basic knowledge necessary to understand the technique are provided hereafter. Also included is a short tutorial illustrating the implementation of two ICA algorithms (FastICA and InfoMax) with the use of the Mathematica software

PCA and K-Means decipher genome

In this paper, we aim to give a tutorial for undergraduate students studying statistical methods and/or bioinformatics. The students will learn how data visualization can help in genomic sequence analysis. Students start with a fragment of genetic text of a bacterial genome and analyze its structure. By means of principal component analysis they ``discover'' that the information in the genome is encoded by non-overlapping triplets. Next, they learn how to find gene positions. This exercise on PCA and K-Means clustering enables active study of the basic bioinformatics notions. Appendix 1 contains program listings that go along with this exercise. Appendix 2 includes 2D PCA plots of triplet usage in moving frame for a series of bacterial genomes from GC-poor to GC-rich ones. Animated 3D PCA plots are attached as separate gif files. Topology (cluster structure) and geometry (mutual positions of clusters) of these plots depends clearly on GC-content.Comment: 18 pages, with program listings for MatLab, PCA analysis of genomes and additional animated 3D PCA plot