  Ongoing and upcoming galaxy surveys are providing precision measurements of
galaxy clustering. However a major obstacle in its cosmological application is
the stochasticity in the galaxy bias. We explore whether the principal
component analysis (PCA) of galaxy correlation matrix in hyperspace of galaxy
properties (e.g. magnitude and color) can reveal further information on
mitigating this issue. Based on the hydrodynamic simulation TNG300-1, we
analyze the cross power spectrum matrix of galaxies in the magnitude and color
space of multiple photometric bands. (1) We find that the first principal
component $E_i^{(1)}$ is an excellent proxy of the galaxy deterministic bias
$b_{D}$, in that $E_i^{(1)}=\sqrt{P_{mm}/\lambda(1)}b_{D,i}$. Here $i$ denotes
the $i$-th galaxy sub-sample. $\lambda^{(1)}$ is the largest eigenvalue and
$P_{mm}$ is the matter power spectrum. We verify that this relation holds for
all the galaxy samples investigated, down to $k\sim 2h/$Mpc. Since $E_i^{(1)}$
is a direct observable, we can utilize it to design a linear weighting scheme
to suppress the stochasticity in the galaxy-matter relation. For an LSST-like
magnitude limit galaxy sample, the stochasticity $\mathcal{S}\equiv 1-r^2$ can
be suppressed by a factor of $\ga 2$ at $k=1h/$Mpc. This reduces the
stochasticity-induced systematic error in the matter power spectrum
reconstruction combining galaxy clustering and galaxy-galaxy lensing from $\sim
12\%$ to $\sim 5\%$ at $k=1h/$Mpc. (2) We also find that $\mathcal{S}$
increases monotonically with $f_\lambda$ and $f_{\lambda^2}$.
$f_{\lambda,\lambda^2}$ quantify the fractional contribution of other
eigenmodes to the galaxy clustering and are direct observables. Therefore the
two provide extra information on mitigating galaxy stochasticity.
