Algebraic and Geometric Basis of Principal Components: An Overview

  • Pramit Pandit Department of Agricultural Statistics, Applied Mathematics and Computer Science, University of Agricultural Sciences, Bengaluru, Karnataka, India
  • K. N. Krishnamurthy Department of Agricultural Statistics, Applied Mathematics and Computer Science, University of Agricultural Sciences, Bengaluru, Karnataka, India
  • K. B. Murthy Department of Agricultural Statistics, Applied Mathematics and Computer Science, University of Agricultural Sciences, Bengaluru, Karnataka, India
Keywords: Algebraic basis, basis of principal components, geometric basis, principal components, properties of principal components

Abstract

Principal Component Analysis is considered as a dimension-reduction tool which may be used to reduce a large set of possibly correlated variables to hopefully a smaller set of uncorrelated variables that still accounts for most of the variation of the original large set. To understand the inner constructs of principal components, concepts of algebraic as well as geometric basis of principal components are prerequisites. Hence, in the current study, an attempt has been made to provide a step by step and vivid discussion of the basis of principle components and its various important properties.

Author Biographies

Pramit Pandit, Department of Agricultural Statistics, Applied Mathematics and Computer Science, University of Agricultural Sciences, Bengaluru, Karnataka, India

Pramit Pandit obtained his Bachelor’s degree (Hons.) in Agriculture from Uttar Banga Krishi Viswavidyalaya and Master’s (Ag.) majoring in Agricultural Statistics from University of Agricultural Sciences, Bengaluru. He was the recipient of ICAR-Junior Research Fellowship during his Master’s degree programme for securing All India basis 2nd rank in AIEEA-UG-2016 examination in Statistical Sciences. He also secured All India basis 1st rank in AICE-JRF/SRF(PGS)-2018 in Agricultural Statistics and qualified ICAR-NET-2018. He was awarded with the prestigious UAS Gold Medal 2019 along with the Professor G. Gurumurthy Memorial Gold Medal, Sri Godabanahal Thuppamma Basappa Mallikarjuna Gold Medal and Sri Nijalingappa’s 77th Birthday Commemoration Gold Medal for his exemplary academic excellence. He was also the recipient of best ‘Best M.Sc. Thesis Award’ for his research work on, ‘Statistical Models for Insect Count Data On Rice’, conducted under the supervision of Prof. K. N. Krishnamurthy.

K. N. Krishnamurthy, Department of Agricultural Statistics, Applied Mathematics and Computer Science, University of Agricultural Sciences, Bengaluru, Karnataka, India

K. N. Krishnamurthy received his B.Sc., M.Sc. and M.Phil. degrees in Statistics from Bangalore University and Ph.D. degree in Statistics from Himalayan University. Prof. Krishnamurthy is a recipient of the Best Teacher award from the National Institute for Education & Research, New Delhi during 2017. He is currently working as Head of the department as well as University Head of the Department of Agricultural Statistics, Applied Mathematics & Computer Science, University of Agricultural Sciences, GKVK, Bengaluru. He has 38 years of experience in teaching at the University.

K. B. Murthy, Department of Agricultural Statistics, Applied Mathematics and Computer Science, University of Agricultural Sciences, Bengaluru, Karnataka, India

K. B. Murthy received his B.Sc. and M.Sc. degrees in Mathematics from Mysore University and Ph.D. degree in Mathematics from Himalayan University. He has specialised in graph theory and applied sciences and has a teaching experience of over 25 years. He has published many papers in National and International Journals and also participated in many International conferences. He is a member of Board of Studies of University of Agricultural Sciences, GKVK, Bengaluru. Dr. K. B. Murthy is the recipient of the GAURAVACHARYA-2017 award for the significant contribution in the field of graph theory and education from National Institute for Education and Research, New Delhi.

Published
2020-10-14
Section
Articles