Diversity maximization under matroid constraints
Abstract
Aggregator websites typically present documents in the form of
representative clusters. In order for users to get a broader perspective, it is important to deliver a diversified set of representative documents in those clusters. One approach to diversification is to maximize the average dissimilarity among documents. Another way to
capture diversity is to avoid showing several documents from the
same category (e.g. from the same news channel). We combine
the above two diversification concepts by modeling the latter approach as a (partition) matroid constraint, and study diversity maximization problems under matroid constraints. We present the first
constant-factor approximation algorithm for this problem, using a
new technique. Our local search 0:5-approximation algorithm is
also the first constant-factor approximation for the max-dispersion
problem under matroid constraints. Our combinatorial proof technique for maximizing diversity under matroid constraints uses the
existence of a family of Latin squares which may also be of independent interest.
In order to apply these diversity maximization algorithms in the
context of aggregator websites and as a preprocessing step for our
diversity maximization tool, we develop greedy clustering algorithms that maximize weighted coverage of a predefined set of topics. Our algorithms are based on computing a set of cluster centers,
where clusters are formed around them. We show the better performance of our algorithms for diversity and coverage maximization
by running experiments on real (Twitter) and synthetic data in the
context of real-time search over micro-posts. Finally we perform a
user study validating our algorithms and diversity metrics.