  Nonnegative matrix factorization (NMF) factorizes a non-negative matrix into
product of two non-negative matrices, namely a signal matrix and a mixing
matrix. NMF suffers from the scale and ordering ambiguities. Often, the source
signals can be monotonous in nature. For example, in source separation problem,
the source signals can be monotonously increasing or decreasing while the
mixing matrix can have nonnegative entries. NMF methods may not be effective
for such cases as it suffers from the ordering ambiguity. This paper proposes
an approach to incorporate notion of monotonicity in NMF, labeled as monotonous
NMF. An algorithm based on alternating least-squares is proposed for recovering
monotonous signals from a data matrix. Further, the assumption on mixing matrix
is relaxed to extend monotonous NMF for data matrix with real numbers as
entries. The approach is illustrated using synthetic noisy data. The results
obtained by monotonous NMF are compared with standard NMF algorithms in the
literature, and it is shown that monotonous NMF estimates source signals well
in comparison to standard NMF algorithms when the underlying sources signals
are monotonous.
