  In topic modeling, many algorithms that guarantee identifiability of the
topics have been developed under the premise that there exist anchor words --
i.e., words that only appear (with positive probability) in one topic.
Follow-up work has resorted to three or higher-order statistics of the data
corpus to relax the anchor word assumption. Reliable estimates of higher-order
statistics are hard to obtain, however, and the identification of topics under
those models hinges on uncorrelatedness of the topics, which can be
unrealistic. This paper revisits topic modeling based on second-order moments,
and proposes an anchor-free topic mining framework. The proposed approach
guarantees the identification of the topics under a much milder condition
compared to the anchor-word assumption, thereby exhibiting much better
robustness in practice. The associated algorithm only involves one
eigen-decomposition and a few small linear programs. This makes it easy to
implement and scale up to very large problem instances. Experiments using the
TDT2 and Reuters-21578 corpus demonstrate that the proposed anchor-free
approach exhibits very favorable performance (measured using coherence,
similarity count, and clustering accuracy metrics) compared to the prior art.
