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Why do we subtract the mean in PCA?
Centre the data For PCA to work properly, you have to subtract the mean from each of the data dimensions. The mean subtracted is the average across each dimension. So, all the x values have ˉx (the mean of the x values of all the data points) subtracted, and all the y values have ˉy subtracted from them.
Why divide by the standard deviation of the mean?
as @Silverfish already pointed out in a comment, the standard deviation has the same unit as the measurements. Thus, dividing by standard deviation as opposed to variance, you end up with a plain number that tells you where your case is relative to average and spread as measured by mean and standard deviation.
What does it mean to subtract the mean in PCA?
In mathematical terms, this is known as subtracting the mean and using a Linear Transformation ( covered here ). ˜X X ~ (X tilde) is just the new X, and X is all of our observations, while μ μ (mu) is the mean: The origin of our coordinate system would now have been shifted to the center of our data.
How to apply SVD algorithmically to PCA data?
The way you want to apply the SVD algorithmically, which is the one you normally choose to apply over PCA, is by these steps: 1 Subtract mean, move coordinate system to center of data. 2 Divide by standard deviation (standardizing the data). This step in particular means when we have encoded 1 feature to… 3 Compute SVD 4 Plot PCA More
How does centering make a difference in PCA?
Centered and non-centered data will have identical covariance matrices. So if by PCA we understand the following procedure: Data → Covariance matrix → Eigen-decomposition, then centering does not make any difference.
When to use the correlation matrix in PCA?
Using the correlation matrix is equivalent to standardizing each of the variables (to mean 0 and standard deviation 1). In general, PCA with and without standardizing will give different results. Especially when the scales are different. As an example, take a look at this R heptathlon data set.