Temporal graph signals are multivariate time series with individual
components associated with nodes of a fixed graph structure. Data of this kind
arises in many domains including activity of social network users, sensor
network readings over time, and time course gene expression within the
interaction network of a model organism. Traditional matrix decomposition
methods applied to such data fall short of exploiting structural regularities
encoded in the underlying graph and also in the temporal patterns of the
signal. How can we take into account such structure to obtain a succinct and
interpretable representation of temporal graph signals?
We propose a general, dictionary-based framework for temporal graph signal
decomposition (TGSD). The key idea is to learn a low-rank, joint encoding of
the data via a combination of graph and time dictionaries. We propose a highly
scalable decomposition algorithm for both complete and incomplete data, and
demonstrate its advantage for matrix decomposition, imputation of missing
values, temporal interpolation, clustering, period estimation, and rank
estimation in synthetic and real-world data ranging from traffic patterns to
social media activity. Our framework achieves 28% reduction in RMSE compared to
baselines for temporal interpolation when as many as 75% of the observations
are missing. It scales best among baselines taking under 20 seconds on 3.5
million data points and produces the most parsimonious models. To the best of
our knowledge, TGSD is the first framework to jointly model graph signals by
temporal and graph dictionaries.

提出了一种基于字典的时间图信号分解框架（TGSD），可以处理来自真实世界中的多个不同领域的时间序列数据， 并且通过结合时间和图形字典来学习数据的联合编码，实现了丢失数据的处理和提高时间插值性能.