Singular Value Decomposition and Dimensionality Reduction, Using R and Cat Image for Illustration Purposes, by Soesilo Wijono,
SVD (singular value decomposition) is an important method used in data science, especially data mining. It can be used, e.g., in dimensionality reduction for recommender system.
Imagine online store, e.g. Amazon, to have million of items, and million of users. In order to perform algorithm for the recommender system, matrix to be used would have million by million dimension. Which is very expensive computation.
Theory for dimensionality reduction is everywhere, so we won’t repeat it again in here. Just remember the basic equation:
X = U A V.T
U matrix has dimension of n x n.
V matrix has dimension of d x d.
A matrix is diagonal matrix with dimension of n x d.
(T represents matrix transpose.)
We want to reduce the dimension of X matrix.
This is an illustration of the method by using a PNG cat image. To help understanding the method visually. In which we’ll use image raw data. In real world, the image data can be replaced by any data, e.g. items x users matrix used in an recommender system, etc.