On Computation of Eigenvectors using Principal Component Analysis (PCA)

Abstract

This study focuses on the detailed explanation of principle component analysis that is a key technique used in data science for dimensionality reduction. Principle component analysis greatly helps in handling the curse of dimensionality. This research includes detailed description of computation of eigen vectors that includes eigen vectors decomposition, SVD etc. Some ways to apply the computational techniques in PCA have also been discussed in detail such as the implementation of PCA using Numpy and Scipy. PCA has also been implemented using sklearn. Some key applications of Principal Component Analysis in Machine Learning, Image processing, Finance and Bio informatics has also been discussed. The pipeline starting from standardizing the data, computing the covariance matrix, finding eigen values and extracting Principle Components have also been mentioned. In the last part of thesis, World Happiness data set has been used in which principal component analysis has been done in order to reduce the dimensionality. After that a supervised machine learning algorithm Linear Regression has been used to predict the Ladder score.