  Based on the rate of resolved stellar origin black hole and neutron star
mergers measured by LIGO and Virgo, it is expected that these detectors will
also observe an unresolved Stochastic Gravitational Wave Background (SGWB) by
the time they reach design sensitivity. Since the same binaries observed by
LIGO and Virgo pass through the LISA mHz frequency band at an earlier stage of
their orbital evolution,it is foreseen that their SGWB will also be observable
by LISA with Signal to Noise Ratio (SNR) $\sim 53$. Unlike the stochastic
signal from Galactic white dwarf binaries, for which a subtraction is expected
to be possible by exploiting its yearly modulation (induced by the motion of
the LISA constellation), the background from unresolved stellar origin black
hole and neutron star binaries acts as a foreground for other stochastic
signals of cosmological or astrophysical origin, which may also be present in
the LISA band. Here, we employ a principal component analysis to model and
extract an additional hypothetical SGWB in the LISA band, without making any a
priori assumptions on its spectral shape. At the same time, we account for the
presence of the foreground from stellar origin black holes and neutron stars,
as well as for possible uncertainties in the LISA noise calibration. We find
that our technique leads to a linear problem and is therefore suitable for fast
and reliable extraction of SGWBs with SNR up to ten times weaker than the
LIGO/Virgo foreground, quite independently of their spectral shape.
