Compressive Sensing of Internet Traffic Matrices using CUR Decomposition
Missing values in traffic matrix (TM) is a well known fact which needs to be interpolated with least error as TM is a key input to various network operations and management tasks. Compressive sensing deals with the reconstruction of missing observations by taking advantage of the presence of low-rank structure in TMs. Matrix decomposition techniques, more specifically singular value decomposition (SVD) and its variants such as sparsity regularized matrix factorization (SRMF) and sparsity regularized SVD (SRSVD), has attracted considerable attention in the field of compressive sensing of traffic matrices. However, SVD suffers from two limitations stemmed in its assumptions, which involves an assumption of continuous random variables and lack of interpretability of decomposed matrices.
 In the present work, in order to address the above-identified limitations we develop a simple yet powerful compressive sensing framework with two key components: i) Temporally Local Interpolation (TLI) and ii) CUR decomposition. We utilize a publicly available real traffic matrix obtained from Abilene network. Results show that i) our preprocessing technique, TLI, outperforms existing baseline approximation in terms of exhibiting least error in reconstruction of missing values with loss rates ranging from 1% to 98%. ii) The proposed framework can reconstruct up to 98% of the pure random missing data with an error of 29.8%, which is found to be comparatively better than SVD-based approaches. iii) When augmented with k-Nearest Neighbors (KNN), the proposed framework can reconstruct up to 98% of the pure random missing data with an error of 28.9%, which is comparatively better than (SRMF + KNN) and (SRSVDB + KNN). iv) The proposed framework is also found to be computationally efficient in terms of low computational time as it takes less than 0.7 seconds (using Matlab on a 3.20 GHz Windows machine), which is the least computational time taken as compared to SRMF (3.02 seconds), NMF (1.01 seconds), SRSVD (1.00 second) and SRSVD base (0.83 seconds).