Singular Value Decomposition (SVD)
It is a data reduction tool.
Let's say you have big data with a lot of dimensions then SVD can be used to reduce the dimensions into key features.
SVD is the first step in most dimension reduction techniques.
It is a data driven generalization of Fourier Transform (FFT).
FFT is one of the most useful transformation in most of the mathematics based on sine and cosine expansions to approximate functions. There is also Bessel's function, Aries' functions and Spherical harmonics.
And this was the technique of last generation of computation science.
SVD is used to map a system of interest in a system that is system.
But in many systems of interest today. Like turbulent flow over the Boeing wing.
There is not an easy tranformation function available to help in this complex problem.
SVD is going to allow us to do tailor the coordinate system based on the problem that we have.
What SVD can do for you?
1. Solve Ax = B (linear system of equations) for non-square A matrices.
We are going to use it particularly for Linear Regression models.
This has been useful in detection of disease medical science usecase.
2. It is also the basis of PCA (Principal Composition Analysis).
3. SVD helps in building and understanding correlation matrices.
It is used by Google in PageRank algorithm.
It is the basis of many facial recognition algorithms of Facebook.
It is also used in the recommendation systems of Amazon and Netflix.
Reasons for using it:
1.
It is based on simple and interpretable linear algebra. Anytime you have a data matrix you can apply SVD to it.
2.
It is scalable.
Tags: Technology,Mathematical Foundations for Data Science,Machine Learning,
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