  There are many problems in machine learning and data mining which are
equivalent to selecting a non-redundant, high "quality" set of objects.
Recommender systems, feature selection, and data summarization are among many
applications of this. In this paper, we consider this problem as an
optimization problem that seeks to maximize the sum of a sum-sum diversity
function and a non-negative monotone submodular function. The diversity
function addresses the redundancy, and the submodular function controls the
predictive quality. We consider the problem in big data settings (in other
words, distributed and streaming settings) where the data cannot be stored on a
single machine or the process time is too high for a single machine. We show
that a greedy algorithm achieves a constant factor approximation of the optimal
solution in these settings. Moreover, we formulate the multi-label feature
selection problem as such an optimization problem. This formulation combined
with our algorithm leads to the first distributed multi-label feature selection
method. We compare the performance of this method with centralized multi-label
feature selection methods in the literature, and we show that its performance
is comparable or in some cases is even better than current centralized
multi-label feature selection methods.
