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Ensemble correlation-based low-rank matrix completion with applications to traffic data imputation

机译：集成基于相关性的低秩矩阵完成及其在交通数据估算中的应用

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摘要

Low-rank matrix completion (LRMC) is a recently emerging technique which has achieved promising performance in many real-world applications, such as traffic data imputation. In order to estimate missing values, the current LRMC based methods optimize the rank of the matrix comprising the whole traffic data, potentially assuming that all traffic data is equally important. As a result, it puts more emphasis on the commonality of traffic data while ignoring its subtle but crucial difference due to different locations of loop detectors as well as dates of sampling. To handle this problem and further improve imputation performance, a novel correlation-based LRMC method is proposed in this paper. Firstly, LRMC is applied to get initial estimations of missing values. Then, a distance matrix containing pairwise distance between samples is built based on a weighted Pearson's correlation which strikes a balance between observed values and imputed values. For a specific sample, its most similar samples based on the distance matrix constructed are chosen by using an adaptive K-nearest neighboring (KNN) search. LRMC is then applied on these samples with much stronger correlation to obtain refined estimations of missing values. Finally, we also propose a simple but effective ensemble learning strategy to integrate multiple imputed values for a specific sample for further improving imputation performance. Extensive numerical experiments are performed on both traffic flow volume data as well as standard benchmark datasets. The results confirm that the proposed correlation-based LRMC and its ensemble learning version achieve better imputation performance than competing methods. (C) 2017 Elsevier B.V. All rights reserved.
机译：低秩矩阵完成（LRMC）是最近出现的一项技术，在许多实际应用中（例如交通数据插补）已实现了令人鼓舞的性能。为了估计缺失值，当前基于LRMC的方法优化了包括整个交通数据的矩阵的等级，并可能假设所有交通数据同等重要。结果，它更加强调流量数据的通用性，而忽略了由于环路检测器位置不同以及采样日期不同而引起的细微但至关重要的差异。为了解决这个问题并进一步提高插补性能，本文提出了一种新的基于相关的LRMC方法。首先，应用LRMC来获得缺失值的初始估计。然后，基于加权的皮尔森相关性建立包含样本之间成对距离的距离矩阵，该相关性在观察值和推定值之间取得平衡。对于特定样本，通过使用自适应K最近邻（KNN）搜索选择基于构建的距离矩阵的最相似样本。然后，将LRMC与这些样本具有更强的相关性，以获取缺失值的精确估计。最后，我们还提出了一种简单而有效的整体学习策略，以整合特定样本的多个估算值，以进一步提高估算性能。对交通流量数据以及标准基准数据集都进行了广泛的数值实验。结果证实，所提出的基于相关的LRMC及其整体学习版本比竞争方法具有更好的归因性能。 （C）2017 Elsevier B.V.保留所有权利。

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