Trouble understanding an article about MFCC I'm willing to apply the same audio preparation that this article page 3.

However, I don't understand the final part : 

The final 28-D output feature vector consists of the 13-D vector output from the DCT plus
the log mean energy to account for volume, and their first temporal
derivatives


Can someone tell me what's exactly in this final vector and why did the authors chose to use such a method ?
So the output of the Discrete Cosine Transform gives a 13-vector. To this, they append the log mean energy. That gives a 14-vector.

They then subtract from this the previous 14-vector to yield another 14-vector, which they concatenate with the existing 14-vector.

That gives a 28-vector.

I suspect the log mean energy is just:
$$
{\tt LME} = \log\left(\frac{1}{N} \sum_{N} x_n^2 \right)
$$
where $N$ is the length of the frame used.