  Recently, network lasso has drawn many attentions due to its remarkable
performance on simultaneous clustering and optimization. However, it usually
suffers from the imperfect data (noise, missing values etc), and yields
sub-optimal solutions. The reason is that it finds the similar instances
according to their features directly, which is usually impacted by the
imperfect data, and thus returns sub-optimal results. In this paper, we propose
triangle lasso to avoid its disadvantage. Triangle lasso finds the similar
instances according to their neighbours. If two instances have many common
neighbours, they tend to become similar. Although some instances are profiled
by the imperfect data, it is still able to find the similar counterparts.
Furthermore, we develop an efficient algorithm based on Alternating Direction
Method of Multipliers (ADMM) to obtain a moderately accurate solution. In
addition, we present a dual method to obtain the accurate solution with the low
additional time consumption. We demonstrate through extensive numerical
experiments that triangle lasso is robust to the imperfect data. It usually
yields a better performance than the state-of-the-art method when performing
data analysis tasks in practical scenarios.
