  A wavelet space-scale decomposition (SSD) analysis of large scale structures
in the universe has been developed. The SSD method of identifying and measuring
structures in the spatial distribution of objects has been demonstrated. The
position and strength (richness) of the identified clusters can be described by
the corresponding coefficient of the wavelet transform. Using this technique,
we systematically detected the clustering and its evolution of QSO's Ly$\alpha$
forest lines in real data and simulated samples. We showed that the clusters of
Ly$\alpha$ absorbers do exist on scales as large as at least 20 h$^{-1}$ Mpc at
significance levels of 2-4 $\sigma$. Independent data sets show about the same
strength distribution of the decomposed clusters. The number densities of the
clusters on scales of 10 - 20 h$^{-1}$ Mpc are found to evolve in an opposite
sense as that of the lines themselves, i.e. they decrease with redshift. We
also showed that the number density and the strength distribution of clusters
can play an important role in testing or discriminating models, i.e. it can
distinguish real data and simulated samples, which cannot be discriminated by
traditional ways. We used Daubechies 4 and Mallat wavelets as the bases of the
SSD. All above-mentioned conclusions do not depend on either wavelet basis.
