The non-negative constraint is so that components will only add together. One can never subtract a feature, or add a negative feature. For instance complex sou

The non-negative constraint is so that components will only add together. One can never subtract a feature, or add a negative feature. For instance complex sounds can be decomposed into many smaller sound "atoms". Usually this is done in usually spectrogram representation split in small sections of time. With NMF, the weight matrix becomes how much each of the atoms is added to form the sound mixture. The weights can then be used for classification, similarity or synthesis. Allowing to add a negative amount of a sound atom would make interpretation harder. What does it mean for an anti-sound to be present? Destructive interference of waveforms is possible, but quite rare to encompass a whole "atom" in a realistic acoustic scenario. And when not combined with its inverse it just sounds like a sound to the human ear. So its contribution is not always negative either. NMF interpretation is straightforward in comparison.