  The stochasticity in galaxy clustering, the mismatch between galaxy and
underlying matter distribution, suppresses the matter clustering amplitude
reconstructed by the combination of galaxy auto-correlation and galaxy-galaxy
lensing cross-correlation. In this work, we solve the stochasticity systematics
by parameterizing the cross correlation coefficient $r(k)$ between galaxy and
matter. We investigate the performance of 12 kinds of parameterization schemes,
against the cosmoDC2 $\&$ TNG300-1 galaxy samples over a wide range of redshift
and flux cut. The 2-parameter fits are found to describe the stochasticity up
to $k_{\rm max}=0.9\,{\rm Mpc^{-1}}h$, while the best performing quadratic
scheme $r^2_s(k) = 1+c_1 k+c_2 k^2$ reaches better than $1\%$ accuracy for both
the direct ${r}^2_s(k)$ fit and reconstructing matter clustering. Then, we
apply the accurate quadratic scheme to forecast the tomographic matter
clustering reconstruction by the combination DESI-like LRG $\times$ CSST-like
cosmic shear. Depending on assumption of stochasticity, we find that the
neglect of a serious stochasticity would result in significant systematic bias
in both the reconstruction and the inferred cosmological parameters, even if we
adopt scale cut $k_{\rm max}=0.1\,{\rm Mpc^{-1}}h$. We demonstrate the
necessity of including stochasticity in reconstruction, and forecast that the
reconstruction alone enables a $S_8$ constraint at about $1.5\%$ precision,
free from galaxy bias and stochasticity. We will validate our method for DESI
spectroscopic survey, and the analysis is expected to be complementary to DESI
cosmological constraint by BAO and RSD.
