While putting together the finishing touches on our paper for CMMR 2012 about music genre classification with sparse representation classification,
we noticed something funny going on with the classifier.
In our experiments, we are measuring classifier performance using features that have undergone some dimensionality reduction.
Standard ways to do this are projecting the dataset onto its significant principal directions,
thereby forming linear combinations of the original features and maintaining variability in the data in a lower dimensional space. Another way is to project the dataset onto the span of a set of positive features found through non-negative matrix factorization.
A non-adaptive approach is just randomly projecting the dataset onto a subspace.
We can also downsample the features by lowpass filtering and decimation.
So we coded these up, and after much debugging, are quite sure things are working as expected. I made a mistake though when specifying the downsample factors,
and ended up running lots of experiments with features that were ideally interpolated higher-dimensional versions of their original low dimensional selves.
This interpolation appears to provide somewhat of a boost to the accuracy.
In the figure below, we compare the classification accuracy
for four reduction methods and several reduction factors.
(You can see my mistake has shifted the “Downsample” line a bit.)
At a factor of 4, the feature dimension is 1/4 that of the original.
At 1, we are just using the original feature.
And at a factor of 0.5, the dimension is twice that of the original,
created by putting a zero between each feature element and then
low pass filtering to remove the alias.
I expect there to be a dimensionality that is just right for maximizing the accuracy,
and for there to be some benefit in reducing the dimensionality given that the amount of training data we have does not change.
So the dip at no reduction (1) makes sense.
But why the boost of nearly 8% in mean accuracy
with an ideal interpolation of the features?
(We have seen this happen repeatedly with other features as well.)
PS: Sorry for the long delay in posts! Happy new year too!
Much more will come in a few weeks after submission, exams, and semester start.