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In the spin Hall effect (SHE), the vector cross-product relations among charge current, spin current, and spin polarization are strictly followed, so that only the in-plane spin accumulation can be induced at the film surface. But, recently this restriction has been lifted by the symmetry breaking of a magnet, where spin polarization can be additionally manipulated by the magnetization directions. In this work, we demonstrated the magnetization-dependent spin-to-charge signals in yttrium iron garnet/Pt/Co/Pt heterostructure. Without the complications in all-metallic structures, we explicitly identified the magnetization-dependent spin Hall effect. We compared its size with the SHE, and further estimated the magnetization-dependent spin Hall angle. Our approach provides an explicit route in exploring the spin-to-charge conversion with arbitrary and controllable orientations of spin polarization, which offers significant advantages in developing electrically controlled energy-efficient spintronic devices.