Multidimensional data have become ubiquitous and are frequently encountered in situations where the information is aggregated over multiple data atoms. The aggregation can be over time or other features, such as geographical location. We often have access to multiple aggregated views of the same data, each aggregated in one or more dimensions, especially when data are collected or measured by different agencies. For instance, item sales can be aggregated temporally, and over groups of stores based on their location or affiliation. However, data mining and machine learning models benefit from detailed data for personalized analysis and prediction. Thus, data disaggregation algorithms are becoming increasingly important in various domains. The goal of this paper is to reconstruct finer-scale data from multiple coarse views, aggregated over different (subsets of) dimensions. The proposed method, called Prema , leverages low-rank tensor factorization tools to fuse the multiple views and provide recovery guarantees under certain conditions. Prema can tackle challenging scenarios, such as missing or partially observed data, double aggregation, and even blind disaggregation (without knowledge of the aggregation patterns) using a variant of Prema called B-Prema . To showcase the effectiveness of Prema , the paper includes extensive experiments using real data from different domains: retail sales, crime counts, and weather observations.

中文翻译：

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Prema：从多个聚合视图进行有原则的张量数据恢复

多维数据已经无处不在，并且在信息跨多个数据原子聚合的情况下经常遇到。聚合可以随着时间的推移或其他功能（例如地理位置）而进行。我们经常可以访问同一数据的多个聚合视图，每个视图都在一个或多个维度上聚合，尤其是当数据是由不同机构收集或衡量时。例如，商品销售可以根据其位置或从属关系在时间上和在商店组中进行汇总。但是，数据挖掘和机器学习模型受益于详细的数据用于个性化分析和预测。因此，数据分解算法在各个领域中变得越来越重要。本文的目的是从多个粗略视图中重建更精细的数据，汇总在不同的（子集）维度上。所提出的方法称为Prema ，利用低秩张量因子分解工具融合多个视图，并在特定条件下提供恢复保证。 Prema 可以使用以下方法解决具有挑战性的场景，例如丢失或部分观察到的数据，双重聚合甚至盲目分解（不了解聚合模式） Prema 叫 B-Prema 。展示效果Prema ，本文包括使用来自不同领域的真实数据进行的广泛实验：零售，犯罪计数和天气观测。