  Collaborative filtering is a broad and powerful framework for building
recommendation systems that has seen widespread adoption. Over the past decade,
the propensity of such systems for favoring popular products and thus creating
echo chambers have been observed. This has given rise to an active area of
research that seeks to diversify recommendations generated by such algorithms.
  We address the problem of increasing diversity in recommendation systems that
are based on collaborative filtering that use past ratings to predicting a
rating quality for potential recommendations. Following our earlier work, we
formulate recommendation system design as a subgraph selection problem from a
candidate super-graph of potential recommendations where both diversity and
rating quality are explicitly optimized: (1) On the modeling side, we define a
new flexible notion of diversity that allows a system designer to prescribe the
number of recommendations each item should receive, and smoothly penalizes
deviations from this distribution. (2) On the algorithmic side, we show that
minimum-cost network flow methods yield fast algorithms in theory and practice
for designing recommendation subgraphs that optimize this notion of diversity.
(3) On the empirical side, we show the effectiveness of our new model and
method to increase diversity while maintaining high rating quality in standard
rating data sets from Netflix and MovieLens.
