CUR decomposition for compression and compressed sensing of large-scale traffic data

Abstract

Abstract-Intelligent Transportation Systems (ITS) often operate on large road networks, and typically collect traffic data with high temporal resolution. Consequently, ITS need to handle massive volumes of data, and methods to represent that data in more compact representations are sorely needed. Subspace methods such as Principal Component Analysis (PCA) can create accurate low-dimensional models. However, such models are not readily interpretable, as the principal components usually involve a large number of links in the traffic network. In contrast, the CUR matrix decomposition leads to low-dimensional models where the components correspond to individual links in the network; the resulting models can be easily interpreted, and can also be used for compressed sensing of the traffic network. In this paper, the CUR matrix decomposition is applied for two purposes: (1) compression of traffic data; (2) compressed sensing of traffic data. In the former, only data from a "random" subset of links and time instances is stored. In the latter, data for the entire traffic network is inferred from measurements at a "random" subset of links. Numerical results for a large traffic network in Singapore demonstrate the feasibility of the proposed approach.

Low-Dimensional Models for Compressed Sensing and Prediction of Large-Scale Traffic Data

“…To alleviate this problem, several randomized algorithms have been proposed [17], [18]. In our numerical experiments, the SVD sampling method yields the best reconstruction accuracy [16]. The SVD sampling algorithm assigns higher selection probability to the road segments with larger traffic speed variations [16].…”

“…COLUMN BASED (CX) DECOMPOSITION The column based (CX) method has recently found applications in many fields such as text processing, finance and biology [13]- [15]; it uses only a subset of the columns to reconstruct the entire data matrix. In our previous study, we applied the column and row (CUR) based method to impute a matrix of traffic data from a few columns (links) and few rows (time instances) of that matrix [16]. Since the CUR method occasionally requires traffic data for the entire network, it cannot be applied for compressed prediction.…”

“…In our numerical experiments, the SVD sampling method yields the best reconstruction accuracy [16]. The SVD sampling algorithm assigns higher selection probability to the road segments with larger traffic speed variations [16]. This algorithm calculates the Euclidean norm of top k right singular vectors of matrix A ∈ R m×n to assign a score E a i to each column [17].…”

A parametric and non-intrusive reduced order model of car crash simulation

“…Each coefficient in is associated with one vector of the time basis and one vector of the space basis. Hence, the value of this coefficient will give the importance of this combination and then it will supply a skeleton of the crash scenario [35]. It is said by Wang and Zhang [31] that another advantage of CUR compared to SVD concerns the preservation of the structural properties of the original data matrices such that sparsity or non-negativity.…”

“…Traditionally in the CUR decomposition, rows and columns are selected randomly according to the distribution of a leverage scores. This scores may be based on energetic or correlation considerations for instance [35]. Enrichment may be performed using iterative greedy or Tabu algorithms.…”