Re: PCA without Mean Centering

Amac Herdagdelen wrote:

If I center the feature vectors around 0 by subtracting the mean values, I get a full matrix (actually I can not even store the resulting matrix in the memory) and I am unable to further process the data. The data values in the matrix are binary. Because the matrix is sparse, most of the variables (i.e. features or columns) have a mean close to 0 with a few exceptional cases which could be 1 at the maximum.

Amac, I'll let others comment on whether or not trying to do PCA on a binary adjacency matrix s a sensible thing to do. But your question about mean centering is worth worrying about. I don't have a real answer to your question, just an observation.

In the usual context of PCA, you want to mean center your data, because otherwise the first component does not really describe the largest direction of variation in the data, but rather it tends to describe the mean of the data, or at least some combination of the mean and the direction of largest variation. That may be what's desired in some cases, but it's not the usual thing to do with PCA. Usually in PCA, one is interested in the directions of variation _about the mean_.

Imagine a cloud of points in 3-space, and imagine a vector pointing from the origin to the center of the cloud. Is the cloud's center near to the origin, with respect to the size of the cloud? Or far away? That sort of thing is what will determine how not mean centering will affect the results of the PCA.

Hope this helps.
.

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