  Linear mixture models have proven very useful in a plethora of applications,
e.g., topic modeling, clustering, and source separation. As a critical aspect
of the linear mixture models, identifiability of the model parameters is
well-studied, under frameworks such as independent component analysis and
constrained matrix factorization. Nevertheless, when the linear mixtures are
distorted by an unknown nonlinear functions -- which is well-motivated and more
realistic in many cases -- the identifiability issues are much less studied.
This work proposes an identification criterion for a nonlinear mixture model
that is well grounded in many real-world applications, and offers
identifiability guarantees. A practical implementation based on a judiciously
designed neural network is proposed to realize the criterion, and an effective
learning algorithm is proposed. Numerical results on synthetic and real-data
corroborate effectiveness of the proposed method.
