Spatio-Temporal Urban Knowledge Graph Enabled Mobility Prediction

With the rapid development of the mobile communication technology, mobile trajectories of humans are massively collected by Internet service providers (ISPs) and application service providers (ASPs). On the other hand, the rising paradigm of knowledge graph (KG) provides us a promising solution to extract structured "knowledge" from massive trajectory data. In this paper, we focus on modeling users' spatio-temporal mobility patterns based on knowledge graph techniques, and predicting users' future movement based on the "knowledge" extracted from multiple sources in a cohesive manner. Specifically, we propose a new type of knowledge graph, i.e., spatio-temporal urban knowledge graph (STKG), where mobility trajectories, category information of venues, and temporal information are jointly modeled by the facts with different relation types in STKG. The mobility prediction problem is converted to the knowledge graph completion problem in STKG. Further, a complex embedding model with elaborately designed scoring functions is proposed to measure the plausibility of facts in STKG to solve the knowledge graph completion problem, which considers temporal dynamics of the mobility patterns and utilizes PoI categories as the auxiliary information and background knowledge. Extensive evaluations confirm the high accuracy of our model in predicting users' mobility, i.e., improving the accuracy by 5.04% compared with the state-of-the-art algorithms. In addition, PoI categories as the background knowledge and auxiliary information are confirmed to be helpful by improving the performance by 3.85% in terms of accuracy. Additionally, experiments show that our proposed method is time-efficient by reducing the computational time by over 43.12% compared with existing methods.

Nonlinear Traffic Prediction as a Matrix Completion Problem with Ensemble Learning

This paper addresses the problem of short-term traffic prediction for signalized traffic operations management. Specifically, we focus on predicting sensor states in high-resolution (second-by-second). This contrasts with traditional traffic forecasting problems, which have focused on predicting aggregated traffic variables, typically over intervals that are no shorter than five minutes. Our contributions can be summarized as offering three insights: first, we show how the prediction problem can be modeled as a matrix completion problem. Second, we use a block-coordinate descent algorithm and demonstrate that the algorithm converges in sublinear time to a block coordinate-wise optimizer. This allows us to capitalize on the “bigness” of high-resolution data in a computationally feasible way. Third, we develop an ensemble learning (or adaptive boosting) approach to reduce the training error to within any arbitrary error threshold. The latter uses past days so that the boosting can be interpreted as capturing periodic patterns in the data. The performance of the proposed method is analyzed theoretically and tested empirically using both simulated data and a real-world high-resolution traffic data set from Abu Dhabi, United Arab Emirates. Our experimental results show that the proposed method outperforms other state-of-the-art algorithms.

A Riemannian rank-adaptive method for low-rank matrix completion

The low-rank matrix completion problem can be solved by Riemannian optimization on a fixed-rank manifold. However, a drawback of the known approaches is that the rank parameter has to be fixed a priori. In this paper, we consider the optimization problem on the set of bounded-rank matrices. We propose a Riemannian rank-adaptive method, which consists of fixed-rank optimization, rank increase step and rank reduction step. We explore its performance applied to the low-rank matrix completion problem. Numerical experiments on synthetic and real-world datasets illustrate that the proposed rank-adaptive method compares favorably with state-of-the-art algorithms. In addition, it shows that one can incorporate each aspect of this rank-adaptive framework separately into existing algorithms for the purpose of improving performance.

Predicting affinity ties in a surname network

From administrative registers of last names in Santiago, Chile, we create a surname affinity network that encodes socioeconomic data. This network is a multi-relational graph with nodes representing surnames and edges representing the prevalence of interactions between surnames by socioeconomic decile. We model the prediction of links as a knowledge base completion problem, and find that sharing neighbors is highly predictive of the formation of new links. Importantly, We distinguish between grounded neighbors and neighbors in the embedding space, and find that the latter is more predictive of tie formation. The paper discusses the implications of this finding in explaining the high levels of elite endogamy in Santiago.

2D-DOA Estimation for EMVS Array with Nonuniform Noise

Electromagnetic vector sensor (EMVS) array is one of the most potential arrays for future wireless communications and radars because it is capable of providing two-dimensional (2D) direction-of-arrival (DOA) estimation as well as polarization angles of the source signal. It is well known that existing subspace algorithm cannot directly be applied to a nonuniform noise scenario. In this paper, we consider the 2D-DOA estimation issue for EMVS array in the presence of nonuniform noise and propose an improved subspace-based algorithm. Firstly, it recasts the nonuniform noise issue as a matrix completion problem. The noiseless array covariance matrix is then recovered via solving a convex optimization problem. Thereafter, the shift invariant principle of the EMVS array is adopted to construct a normalized polarization steering vector, after which 2D-DOA is easily estimated as well as polarization angles by incorporating the vector cross-product technique and the pseudoinverse method. The proposed algorithm is effective to EMVS array with arbitrary sensor geometry. Furthermore, the proposed algorithm is free from the nonuniform noise. Several simulations verify the improvement of the proposed method.

$$\varvec{m}$$–Isometric Composition Operators on Directed Graphs with One Circuit

The aim of this paper is to investigate m–isometric composition operators on directed graphs with one circuit. We establish a characterization of m–isometries and prove that complete hyperexpansivity coincides with 2–isometricity within this class. We discuss the m–isometric completion problem for unilateral weighted shifts and for composition operators on directed graphs with one circuit. The paper is concluded with an affirmative solution of the Cauchy dual subnormality problem in the subclass with circuit containing one element.

HOSVD-Based Algorithm for Weighted Tensor Completion

Matrix completion, the problem of completing missing entries in a data matrix with low-dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is the tensor analog that attempts to impute missing tensor entries from similar low-rank type assumptions. In this paper, we study the tensor completion problem when the sampling pattern is deterministic and possibly non-uniform. We first propose an efficient weighted Higher Order Singular Value Decomposition (HOSVD) algorithm for the recovery of the underlying low-rank tensor from noisy observations and then derive the error bounds under a properly weighted metric. Additionally, the efficiency and accuracy of our algorithm are both tested using synthetic and real datasets in numerical simulations.

Nonconvex Low-Rank Tensor Completion from Noisy Data

This paper investigates a problem of broad practical interest, namely, the reconstruction of a large-dimensional low-rank tensor from highly incomplete and randomly corrupted observations of its entries. Although a number of papers have been dedicated to this tensor completion problem, prior algorithms either are computationally too expensive for large-scale applications or come with suboptimal statistical performance. Motivated by this, we propose a fast two-stage nonconvex algorithm—a gradient method following a rough initialization—that achieves the best of both worlds: optimal statistical accuracy and computational efficiency. Specifically, the proposed algorithm provably completes the tensor and retrieves all low-rank factors within nearly linear time, while at the same time enjoying near-optimal statistical guarantees (i.e., minimal sample complexity and optimal estimation accuracy). The insights conveyed through our analysis of nonconvex optimization might have implications for a broader family of tensor reconstruction problems beyond tensor completion.

Medical Image Denoising Via Matrix Norm Minimization Problems

This paper presents the matrix completion problem for image denoising. Three problems based on matrix norm are performing: Spectral norm minimization problem (SNP), Nuclear norm minimization problem (NNP), and Weighted nuclear norm minimization problem (WNNP). In general, images representing by a matrix this matrix contains the information of the image, some information is irrelevant or unfavorable, so to overcome this unwanted information in the image matrix, information completion is used to comperes the matrix and remove this unwanted information. The unwanted information is handled by defining {0,1}-operator under some threshold. Applying this operator on a given matrix keeps the important information in the image and removing the unwanted information by solving the matrix completion problem that is defined by P. The quadratic programming use to solve the given three norm-based minimization problems. To improve the optimal solution a weighted exponential is used to compute the weighted vector of spectral that use to improve the threshold of optimal low rank that getting from solving the nuclear norm and spectral norm problems. The result of applying the proposed method on different types of images is given by adopting some metrics. The results showed the ability of the given methods.