I have computed colour descriptors of a dataset of images and generated a 152×320 matrix (152 samples and 320 features). I would like to use PCA to reduce the dimensionality of my image descriptors space. I know that I could implement this using Matlab PCA built-in function but as I have just started learning about this concept I would like to implement the Matlab code without the built-in function so I can have a clear understanding how the function works. I tried to find how to do that online but all I could find is the either the general concept of PCA or the implementation of it with the built-in functions without explaining clearly how it works. Anyone could help me with a step by step instructions or a link that could explain a simple way on how to implement PCA for dimensionality reduction. The reason why I'm so confused is because there are so many uses for PCA and methods to implement it and the more I read about it the more confused I get.
1 Answers
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PCA is basically taking the dominant eigen vectors of the data (Or better yet their projection of the dominant Eigen Vectors of the covariance matrix).
What you can do is use the SVD (Singular Value Decomposition).
To imitate MATLAB's pca() function here what you should do:
- Center all features (Each column of your data should have zero mean).
- Apply the
svd()function on your data. - Use the V Matrix (Its columns) as your vectors to project your data on. Chose the number of columns to use according to the dimension of the data you'd like to have.
The projected data is now you new dimensionality reduction data.
