A method for constructing deep neural networks (DNNs) for accurate supervised source enhancement is proposed. Attempts were made in previous studies to estimate the power spectral densities (PSDs) of sound sources, which are used to estimate Wiener filters for source enhancement, from the output of multiple beamformings using DNNs. Although performance improved, it was not possible to guarantee accurate PSD estimation since the trained DNNs were treated as black boxes. The proposed DNN construction method uses non-negative auto-encoders and complementarity subtraction. This study also reveals that auto-encoders whose weights are non-negative correspond to non-negative matrix factorization (NMF), which decomposes source PSDs into non-negative spectral bases and their activations. It further introduces a complementarity subtraction method for estimating PSDs accurately. Through several experiments, it was confirmed that the signal-to-interference plus noise ratio improved by approximately 12 dB for datasets captured in various noisy/reverberant rooms.