Why discrete cosine transform may not maintain locality
In a frequency-like transformation (Fourier, discrete cosine, Walsh), one generally ends up with a sequence of coefficients that account for each frequency component over the support of the basis vector (a segment in time, a 2D patch in images). If you have a frequency component located on one half of the support, and zero the other half, or the converse, you often get the same absolute-valued coefficients. MFCCs fall in that context with:


  the short-term power spectrum of a sound, based on a linear cosine
  transform.


Information about locality can usually be traced in the phase or the sign of the coefficients, but they are difficult to read in complex situations, and are not preserved with the absolute value or the power.