Reducing dimensionality with random projections instead of PCA

Instead of reducing the dimensionality of the appearance patches using PCA, I tried using a random projection matrix instead (similar to the one defined in question 1 here). The matrix was generated once during training and the same one was used again during testing. This approach does not seem to work any better than the previous PCA approach.

Here are the total log probabilities of the same test images that were used previously. Image 1 has taken an undesirable dip and image 4 hasn't been pulled up enough from the other negative test images.

The appearances of the negative test images has gone up relative to the bike images.
Of course, the location probabilities are exactly the same as before because the these are unaffected by the method of dimensionality reduction on appearance patches.
Here are the reconstructed patches obtained by back projecting to 121 dimensions. For this, the reduced dimensionality patches were multiplied by the pseudo-inverse of the random projection matrix that was used.