PCA is preferable to Random Projection, as hence the name, Random Projection is just that, where PCA finds components in such a way that maximizes the variability within the data. While it is possible Random Projection will produce a mapping nearly as good as PCA, the latter is guaranteed to produce a projection that is optimal for maximizing the information retained.
When to use PCA vs Random Projection?
PCA is preferable to Random Projection, as hence the name, Random Projection is just that, where PCA finds components in such a way that maximizes the variability within the data. While it is possible Random Projection will produce a mapping nearly as good as PCA, the latter is guaranteed to produce a projection that is optimal for maximizing the information retained.
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