PCA-Implementation-from-Scratch-using-Coloredimage

• Compress a colored image using PCA, then visualize the compresses image

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• Decompress the compressed image and visualize it

1- Load the image and convert it to a NumPy array

2- Image Pre-proccessing and Normalization:

     -Normalization
     -Reshape the image
     -calculate mean and standard deviation for image Standardization

3- PCA Impelementation From Scratch:

     * 1- calculate the image mean
     * 2- calculate the coveriance of the image
     * 3- Calculate the standard Deviation
     * 4- Calculate Eigenvalues and EigenVetors then sort them to get the maximum eigenvalue.

4- Project the image array:

    -determine the number of PCA Components
    -subtract the image array from image mean
    -get the dot product of image projected and sorted eigenvectors

5- Compress The Projected image

6- Decompress the compressed image array:

     -Project the decompressed image array back onto the original image space
     -Add the mean back to the decompressed image array
     -Convert the decompressed image array back to a NumPy array

7- Ploting of The Original, Compressed, and Decompressed images.