In quantum information processing, unitary transformations are oftentimes used to implement computing tasks. However, unitary transformations are not enough to all situations. Therefore, it is important to explore non-unitary transformations in quantum computing and simulation. Here, we introduce non-unitary transformations by performing singular value decomposition (SVD) into two-photon interference. Through simulation, we show losses modeled by non-unitary transformation can be perceived as variable to continuously control two-photon interference, and the coincidence statistics can be changed by an appropriate choice of observation basis. The results are promising in the design of integrated optical circuits, providing a way towards large-scale programmable circuits.