Principal Component Analysis (PCA) is a technique used to simplify complex data sets by identifying patterns in the data and expressing it in such a way to highlight similarities and differences. It works by subtracting the mean from the data, calculating the covariance matrix, and determining the eigenvectors and eigenvalues to form a feature vector representing the data in a lower dimensional space. PCA can be used to represent image data as a one dimensional vector by stacking the pixel rows of an image and applying this analysis to multiple images.
2. Principal Component Analysis or PCA is a way of identifying patterns in data and expressing data in such a way as to highlight their similarities and differences. PCA is a powerful tool for analyzing data. 2 PCA - Dr. Nidhi Mathur
3. Method Get some data, Subtract the mean, Calculate the covariance matrix, Calculate the eigenvectors and eigenvalues of covariance matrix, Choose components and form a feature vector, Derive the new data set. 3 PCA - Dr. Nidhi Mathur
4. Image Representation Rows of the pixels in an (NxN) image are placed one after the other to form a one dimensional vector. N x N Image 1 x N2 vector 4 PCA - Dr. Nidhi Mathur
5. If there are M images, then Now, this is the starting point of PCA Analysis. 5 PCA - Dr. Nidhi Mathur
6. Let be an 1 x N 2 vector corresponding to an N x N image. Obtain images I1, I2, …..IM. Represent every Ii as vector i. Compute average vector Subtract the mean vector Compute the covariance matrix , where is an N 2 x M matrix Compute the eigenvalues ui of ATA 6 PCA - Dr. Nidhi Mathur
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9. AAT has M eigenvectors/eigenvalues 7 PCA - Dr. Nidhi Mathur
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11. Keep only K eigenvectors.(corresponding to the K largest values.)8 PCA - Dr. Nidhi Mathur