‘re-balancing’ or not

[gnlup]

I'm a little confused about whether the dpca.m used 're-balancing' or not. I have thought that the dpca.m didn't use 're-balancing'(the default setting is to accept 'balanced' data), while the input of dpca function is "Xfull" with D+1 dimensions, just as 'firingRatesAverage'. According to the paper on eLife(Kobak, 2016) , if you want to 're-balance' the data, replace X with $\tilde{X}$. The 'Xfull' with D+1 dimensions is just the same as $\tilde{X}$(except that $\tilde{X}$ is flattened). So, the dpca.m used 're-balancing' because it accepts $\tilde{X}$ as input rather than X? Moreover, the default setting is to deal with 'unbalanced' data rather than 'balanced' data?
I'm new to dPCA and MATLAB, and sorry about my poor English. Hope I make my question clear. Thanks a lot!