PRINCIPAL COMPONENT ANALYSIS AS AN APPLICATION OF SINGULAR VALUE DECOMPOSITION - Nabilah Shabrina, Tasya
Principal Component Analysis is a descriptive statistical technique that is typically applied for the dimensional reduction of multivariate data. Principal Component Analysis will project high-dimensional data on new variables that are orthogonal and capable of capturing maximum data variance, which are referred to as principal components. In this final assignment, we will explore the relationship between Principal Component Analysis and Singular Value Decomposition, by reviewing how Singular Value Decomposition is able to provide solutions to Principal Component Analysis. Singular Value Decomposition itself is usually used as an approximation methods that offers a matrix approximation with a lower rank. This decomposition will result in the factorization of a matrix into three other matrices: the orthogonal matrices U and V, and also ? the matrix whose main diagonal contains singular values. These three matrices help us to obtain the principal components of the original matrix directly. So by using Singular Value Decomposition, Principal Component Analysis can be performed efficiently and effectively. In this final project, an analysis of the Principal Component Analysis algorithm based on Singular Value Decomposition will be presented, including an explanation of the principal components from Singular Value Decomposition and the relationship between singular values as the variance explained by each main component. In addition, we will look at the practical application and implications of Singular Value Decomposition in Principal Component Analysis in performing dimensional reduction and visualization.