What is the role of eigen vectors in PCA?
The eigenvectors and eigenvalues of a covariance (or correlation) matrix represent the “core” of a PCA: The eigenvectors (principal components) determine the directions of the new feature space, and the eigenvalues determine their magnitude.
Can we apply PCA on images?
One of the use cases of PCA is that it can be used for image compression — a technique that minimizes the size in bytes of an image while keeping as much of the quality of the image as possible. In this post, we will discuss that technique by using the MNIST dataset of handwritten digits.
How do you take PCA images?
Hands-on implementation of image compression using PCA Reshaping the image to 2-dimensional so we are multiplying columns with depth so 225 X 3 = 675. Applying PCA so that it will compress the image, the reduced dimension is shown in the output. As you can see in the output, we compressed the image using PCA.
How are the smallest eigenvectors used in PCA?
The smallest eigenvectors will often simply represent noise components, whereas the largest eigenvectors often correspond to the principal components that define the data. Dimensionality reduction by means of PCA is then accomplished simply by projecting the data onto the largest eigenvectors of its covariance matrix.
How are eigenvectors used in feature extraction?
Instead, rotating the data by the eigenvectors of its covariance matrix, allowed us to directly recover the independent components and (up to a scaling factor). This can be seen as follows: The eigenvectors of the covariance matrix of the original data are (each column represents an eigenvector):
How are eigen values used in computer vision?
Eigen values and vectors are used extensively in computer vision. For example, to get a first hand exposure you may check the topic of Principal Component Analysis (PCA) in any standard book of Digital Image Processing such as: Digital Image Processing by Rafael C. Gonzalez and Richard E. Woods.
Do you have an intuitive understanding of eigenvectors?
There are many articles out there explaining PCA and its importance, though I found a handful explaining the intuition behind Eigenvectors in the light of PCA. This article aims to give a visual and intuitive understanding of Eigenvectors, such that it makes you better equipped to understand PCA.
https://www.youtube.com/watch?v=ZwiDOse1wQU