  Deep neural networks (DNNs) have achieved substantial predictive performance
in various speech processing tasks. Particularly, it has been shown that a
monaural speech separation task can be successfully solved with a DNN-based
method called deep clustering (DC), which uses a DNN to describe the process of
assigning a continuous vector to each time-frequency (TF) bin and measure how
likely each pair of TF bins is to be dominated by the same speaker. In DC, the
DNN is trained so that the embedding vectors for the TF bins dominated by the
same speaker are forced to get close to each other. One concern regarding DC is
that the embedding process described by a DNN has a black-box structure, which
is usually very hard to interpret. The potential weakness owing to the
non-interpretable black-box structure is that it lacks the flexibility of
addressing the mismatch between training and test conditions (caused by
reverberation, for instance). To overcome this limitation, in this paper, we
propose the concept of explainable deep clustering (X-DC), whose network
architecture can be interpreted as a process of fitting learnable spectrogram
templates to an input spectrogram followed by Wiener filtering. During
training, the elements of the spectrogram templates and their activations are
constrained to be non-negative, which facilitates the sparsity of their values
and thus improves interpretability. The main advantage of this framework is
that it naturally allows us to incorporate a model adaptation mechanism into
the network thanks to its physically interpretable structure. We experimentally
show that the proposed X-DC enables us to visualize and understand the clues
for the model to determine the embedding vectors while achieving speech
separation performance comparable to that of the original DC models.
