  Similarity is a fundamental measure in network analyses and machine learning
algorithms, with wide applications ranging from personalized recommendation to
socio-economic dynamics. We argue that an effective similarity measurement
should guarantee the stability even under some information loss. With six
bipartite networks, we investigate the stabilities of fifteen similarity
measurements by comparing the similarity matrixes of two data samples which are
randomly divided from original data sets. Results show that, the fifteen
measurements can be well classified into three clusters according to their
stabilities, and measurements in the same cluster have similar mathematical
definitions. In addition, we develop a top-$n$-stability method for
personalized recommendation, and find that the unstable similarities would
recommend false information to users, and the performance of recommendation
would be largely improved by using stable similarity measurements. This work
provides a novel dimension to analyze and evaluate similarity measurements,
which can further find applications in link prediction, personalized
recommendation, clustering algorithms, community detection and so on.
