Tensor Completion for Weakly-dependent Data on Graph for Metro Passenger Flow Prediction
This work addresses a specific challenge in spatiotemporal data analysis for applications like urban transportation, though it is incremental in nature.
The paper tackles the problem of low-rank tensor completion for weakly-dependent spatiotemporal data, such as metro passenger flow, by proposing a novel CP decomposition framework with L1-norm and Graph Laplacian penalties, resulting in improved performance demonstrated in a case study on Hong Kong metro data.
Low-rank tensor decomposition and completion have attracted significant interest from academia given the ubiquity of tensor data. However, the low-rank structure is a global property, which will not be fulfilled when the data presents complex and weak dependencies given specific graph structures. One particular application that motivates this study is the spatiotemporal data analysis. As shown in the preliminary study, weakly dependencies can worsen the low-rank tensor completion performance. In this paper, we propose a novel low-rank CANDECOMP / PARAFAC (CP) tensor decomposition and completion framework by introducing the $L_{1}$-norm penalty and Graph Laplacian penalty to model the weakly dependency on graph. We further propose an efficient optimization algorithm based on the Block Coordinate Descent for efficient estimation. A case study based on the metro passenger flow data in Hong Kong is conducted to demonstrate improved performance over the regular tensor completion methods.