  Learning new representations of input observations in machine learning is
often tackled using a factorization of the data. For many such problems,
including sparse coding and matrix completion, learning these factorizations
can be difficult, in terms of efficiency and to guarantee that the solution is
a global minimum. Recently, a general class of objectives have been
introduced-which we term induced dictionary learning models (DLMs)-that have an
induced convex form that enables global optimization. Though attractive
theoretically, this induced form is impractical, particularly for large or
growing datasets. In this work, we investigate the use of practical alternating
minimization algorithms for induced DLMs, that ensure convergence to global
optima. We characterize the stationary points of these models, and, using these
insights, highlight practical choices for the objectives. We then provide
theoretical and empirical evidence that alternating minimization, from a random
initialization, converges to global minima for a large subclass of induced
DLMs. In particular, we take advantage of the existence of the (potentially
unknown) convex induced form, to identify when stationary points are global
minima for the dictionary learning objective. We then provide an empirical
investigation into practical optimization choices for using alternating
minimization for induced DLMs, for both batch and stochastic gradient descent.
