The recently established RPCA method provides us a convenient way to restore low-rank matrices from grossly corrupted observations. While elegant in theory and powerful in reality, RPCA may be not an ultimate solution to the low-rank matrix recovery problem. Indeed, its performance may not be perfect even when data are strictly low-rank. This is because conventional RPCA ignores the clustering structures of the data which are ubiquitous in modern applications. As the number of cluster grows, the coherence of data keeps increasing, and accordingly, the recovery performance of RPCA degrades. We show that the challenges raised by coherent data (i.e., the data with high coherence) could be alleviated by Low-Rank Representation (LRR), provided that the dictionary in LRR is configured appropriately. More precisely, we mathematically prove that if the dictionary itself is low-rank then LRR is immune to the coherence parameter which increases with the underlying cluster number. This provides an elementary principle for dealing with coherent data. Subsequently, we devise a practical algorithm to obtain proper dictionaries in unsupervised environments. Our extensive experiments on randomly generated matrices verify our claims.

研究表明，当数据具有高相干性时，常规的RPCA方法表现不佳。使用低秩表示（LRR）能够缓解这一问题，并且当字典本身是低秩的时，LRR更能有效地处理相干数据。作者设计了一种无监督环境下获取适当字典的实用算法，并在随机生成的矩阵上进行广泛实验以验证其结果。

使用低秩字典追踪技术恢复连贯数据