Multi-Matrices Factorization with Application to Missing Sensor Data Imputation

We formulate a multi-matrices factorization model (MMF) for the missing sensor data estimation problem. The estimation problem is adequately transformed into a matrix completion one. With MMF, an n-by-t real matrix, R, is adopted to represent the data collected by mobile sensors from n areas at the time, T(1), T(2), … , T(t), where the entry, R(i,j), is the aggregate value of the data collected in the ith area at T(j). We propose to approximate R by seeking a family of d-by-n probabilistic spatial feature matrices, U((1)), U((2)), … , U(()(t)()), and a probabilistic temporal feature matrix, V ∈ ℝ(d)(×)(t), where [Formula: see text]. We also present a solution algorithm to the proposed model. We evaluate MMF with synthetic data and a real-world sensor dataset extensively. Experimental results demonstrate that our approach outperforms the state-of-the-art comparison algorithms.