Contents
How does SVD save storage space?
Smaller the image, less is the cost associated with transmission and storage. SVD refactors the given digital image into three matrices. Singular values are used to refactor the image and at the end of this process, image is represented with smaller set of values, hence reducing the storage space required by the image.
What is PCA and SVD?
Principal component analysis (PCA) is usually explained via an eigen-decomposition of the covariance matrix. However, it can also be performed via singular value decomposition (SVD) of the data matrix X.
How does image compression help with SVD decomposition?
Image compression helps deal with that headache. It minimizes the size of an image in bytes to an acceptable level of quality. This means that you are able to store more images in the same disk space as compared to before. Image compression takes advantage of the fact that only a few of the singular values obtained after SVD are large.
Why is SVD so important in data science?
It has some interesting algebraic properties and conveys important geometrical and theoretical insights about linear transformations. It also has some important applications in data science. In this article, I will try to explain the mathematical intuition behind SVD and its geometrical meaning.
Why is SVD called a dimensionality reduction technique?
Diagonal matrix D causes scaling. So basically it allows us to express our original matrix as a linear combination of low-rank matrices. Only the first few, singular values are large. The terms other than the first few can be ignored without losing much information and this is why SVD is referred to as a dimensionality reduction technique.
Is the SVD a decomposition of a complex transformation?
The SVD can also be seen as the decomposition of one complex transformation in 3 simpler transformations (rotation, scaling, and rotation). Diagonal matrix D causes scaling. So basically it allows us to express our original matrix as a linear combination of low-rank matrices. Only the first few, singular values are large.