Active seriation aims at recovering an unknown ordering of $n$ items by adaptively querying pairwise similarities. The observations are noisy measurements of entries of an underlying $n$ x $n$ permuted Robinson matrix, whose permutation encodes the latent ordering. The framework allows the algorithm to start with partial information on the latent ordering, including seriation from scratch as a special case. We propose an active seriation algorithm that provably recovers the latent ordering with high probability. Under a uniform separation condition on the similarity matrix, optimal performance guarantees are established, both in terms of the probability of error and the number of observations required for successful recovery.

翻译：主动序列化旨在通过自适应查询成对相似性来恢复n个项目的未知排序。观测数据是潜在n×n置换罗宾逊矩阵条目的噪声测量，其置换编码了潜在排序。该框架允许算法从潜在排序的部分信息开始，其中从零开始的序列化作为特例。我们提出了一种主动序列化算法，该算法能够以高概率恢复潜在排序。在相似度矩阵满足均匀分离条件下，我们建立了关于错误概率和成功恢复所需观测数量的最优性能保证。