Lossy compression involves throwing out redundant data; if you look at the data as a vector, you are effectively reducing the number of dimensions in the vector. Speech recognition involves rearranging the data to find its primary components (e.g. pitch, timbre, etc.). Most voice / audio compression schemes perform a similar rearrangement, as this is a convenient way to find (and eliminate) redundant data.

In particular, Fourier transforms, wavelet transforms, cepstrum transforms, subband filtering, and principal component analysis are techniques common to both audio compression and speech recognition.