Yudong Chen

User Association for Load Balancing in Heterogeneous Cellular Networks

For small cell technology to significantly increase the capacity of tower-based cellular networks, mobile users will need to be actively pushed onto the more lightly loaded tiers (corresponding to, e.g., pico and femtocells), even if they offer a lower instantaneous SINR than the macrocell base station (BS). Optimizing a function of the long-term rate for each user requires (in general) a massive utility maximization problem over all the SINRs and BS loads. On the other hand, an actual implementation will likely resort to a simple biasing approach where a BS in tier j is treated as having its SINR multiplied by a factor Aj ≥ 1, which makes it appear more attractive than the heavily-loaded macrocell. This paper bridges the gap between these approaches through several physical relaxations of the network-wide association problem, whose solution is NP hard. We provide a low-complexity distributed algorithm that converges to a near-optimal solution with a theoretical performance guarantee, and we observe that simple per-tier biasing loses surprisingly little, if the bias values Aj are chosen carefully. Numerical results show a large (3.5x) throughput gain for cell-edge users and a 2x rate gain for median users relative to a maximizing received power association.

Low-Rank Matrix Recovery From Errors and Erasures

This paper considers the recovery of a low-rank matrix from an observed version that simultaneously contains both 1) erasures, most entries are not observed, and 2) errors, values at a constant fraction of (unknown) locations are arbitrarily corrupted. We provide a new unified performance guarantee on when minimizing nuclear norm plus l1 norm succeeds in exact recovery. Our result allows for the simultaneous presence of random and deterministic components in both the error and erasure patterns. By specializing this one single result in different ways, we recover (up to poly-log factors) as corollaries all the existing results in exact matrix completion, and exact sparse and low-rank matrix decomposition. Our unified result also provides the first guarantees for 1) recovery when we observe a vanishing fraction of entries of a corrupted matrix, and 2) deterministic matrix completion.

Incoherence-Optimal Matrix Completion

This paper considers the matrix completion problem. We show that it is not necessary to assume joint incoherence, which is a standard but unintuitive and restrictive condition that is imposed by previous studies. This leads to a sample complexity bound that is orderwise optimal with respect to the incoherence parameter (as well as to the rank r and the matrix dimension n up to a log factor). As a consequence, we improve the sample complexity of recovering a semidefinite matrix from O(nr2 log2 n) to O(nr log2 n), and the highest allowable rank from Θ(√n/ log n) to Θ(n/ log2 n). The key step in proof is to obtain new bounds in terms of the ℓ∞,2-norm, defined as the maximum of the row and column norms of a matrix. To illustrate the applicability of our techniques, we discuss extensions to singular value decomposition projection, structured matrix completion and semisupervised clustering, for which we provide orderwise improvements over existing results. Finally, we turn to the closely related problem of low-rank-plus-sparse matrix decomposition. We show that the joint incoherence condition is unavoidable here for polynomialtime algorithms conditioned on the planted clique conjecture. This means it is intractable in general to separate a rank-ω(√n) positive semidefinite matrix and a sparse matrix. Interestingly, our results show that the standard and joint incoherence conditions are associated, respectively, with the information (statistical) and computational aspects of the matrix decomposition problem.

Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization

This paper studies the Tensor Robust Principal Component (TRPCA) problem which extends the known Robust PCA [4] to the tensor case. Our model is based on a new tensor Singular Value Decomposition (t-SVD) [14] and its induced tensor tubal rank and tensor nuclear norm. Consider that we have a 3-way tensor X ε R^n1×n2×n3 such that X = L₀ + S₀, where L₀ has low tubal rank and _{S0 is} sparse. Is that possible to recover both components? In this work, we prove that under certain suitable assumptions, we can recover both the low-rank and the sparse components exactly by simply solving a convex program whose objective is a weighted combination of the tensor nuclear norm and the l1-norm, i.e., min L, E ||L||* + λ||ε||1, s.t. X = L + ε, where λ = 1/√max(n₁, n₂)n₃. Interestingly, TRPCA involves RPCA as a special case when n₃ = 1 and thus it is a simple and elegant tensor extension of RPCA. Also numerical experiments verify our theory and the application for the image denoising demonstrates the effectiveness of our method.

Towards an optimal user association in heterogeneous cellular networks

We investigate how a heterogeneous cellular network should self-organize by proposing a load-aware user association scheme. This is an important consideration, in order to move traffic off congested cells and onto more lightly loaded cells. Although the network-wide optimal association problem is NP hard, a closely related utility maximization problem can be made convex by applying relaxations on the association metric. We then address a low-complexity distributed algorithm that converges to a near-optimal solution with theoretical guarantee on its performance, requiring limited information and no coordination. This is directly related to range extension and small-cell biasing, which is how cell associations are likely to work in practice. Our load-aware association scheme provides theoretical guidance on the best “biasing factor” for different tiers of base stations. Numerical results show a 3.5x throughput gain for cell-edge users and a 2x gain for median users relative to the standard max-SINR association where a mobile connects to the strongest base station.

Low-rank matrix recovery from errors and erasures

This paper considers the recovery of a low-rank matrix from an observed version that simultaneously contains both (a) erasures: most entries are not observed, and (b) errors: values at a constant fraction of (unknown) locations are arbitrarily corrupted. We provide a new unified performance guarantee on when a (natural) recently proposed method, based on convex optimization, succeeds in exact recovery. Our result allows for the simultaneous presence of random and deterministic components in both the error and erasure patterns. On the one hand, corollaries obtained by specializing this one single result in different ways recovers (upto poly-log factors) all the existing works in matrix completion, and sparse and low-rank matrix recovery. On the other hand, our results also provide the first guarantees for (a) deterministic matrix completion, and (b) recovery when we observe a vanishing fraction of entries of a corrupted matrix.

Multi-Dimensional traffic flow time series analysis with self-organizing maps

The two important features of self-organizing maps (SOM), topological preservation and easy visualization, give it great potential for analyzing multi-dimensional time series, specifically traffic flow time series in an urban traffic network. This paper investigates the application of SOM in the representation and prediction of multi-dimensional traffic time series. First, SOMs are applied to cluster the time series and to project each multi-dimensional vector onto a two-dimensional SOM plane while preserving the topological relationships of the original data. Then, the easy visualization of the SOMs is utilized and several exploratory methods are used to investigate the physical meaning of the clusters as well as how the traffic flow vectors evolve with time. Finally, the k-nearest neighbor (kNN) algorithm is applied to the clustering result to perform short-term predictions of the traffic flow vectors. Analysis of real world traffic data shows the effectiveness of these methods for traffic flow predictions, for they can capture the nonlinear information of traffic flows data and predict traffic flows on multiple links simultaneously.

Pattern Discovering of Regional Traffic Status with Self-Organizing Maps

It is believed that the evolution of traffic status follows certain temporal-spatial rules and patterns, and the challenge is to extract such patterns from mass traffic data. In this paper, the traffic status of multiple links in a certain region is considered. Self-organizing maps (SOMs) are applied to organize flow data of links into physically relevant clusters, with each cluster representing one pattern. The clustering results are then interpreted using several exploratory methods which utilize the SOMs advantages of topological preservation and easy visualization. Case studies on real-world data reveal some meaningful phenomena and rules of regional traffic status, which prove the effectiveness of our approaches

Traffic Data Analysis Using Kernel PCA and Self-Organizing Map

In intelligent transportation system, one of the most difficult tasks is to manage the mass amount of data and discover useful information from them, so data mining plays an important role in extracting temporal and spatial relations in a networked system. In this paper, we propose a novel method for traffic data analysis. Kernel principal component analysis (KPCA) is used to reduce data dimensionality and extract features from them, then self-organizing map (SOM) is applied in the unsupervised clustering of links. Subject interpretation and regression equations are used to analyze the clustering result. Case studies on real data from UTC-SCOOT System in Beijing prove that the proposed method is effective in extracting non-linear relations between different links and revealing hidden patterns in traffic flow data. The result yielded can support further analysis, like traffic parameter forecasting and traffic flow control

PCA Based Hurst Exponent Estimator for fBm Signals Under Disturbances

In this paper, the validity of PCA eigenspectrum based Hurst exponent estimator proposed in[J. B. Gao, Y. Cao, and J.-M. Lee, ldquoPrincipal Component Analysis of 1/f alpha noise,rdquo Phys. Lett. A, vol. 314, no. 5-6, pp. 392-400, 2003] for single fBm signal is proved. Moreover, how to apply this estimator for fBm signals corrupted with some other signals are discussed. Theoretical analysis and experiments show that it can also be used for 1) mixed fBm signals with different Hurst exponents, 2) fBm signals corrupted with additive Gaussian white noise when the signal-to-noise ratio (SNR) is not too small, and 3) fBm signals corrupted with additive deterministic sine/cosine signals. However, the estimation accuracy depends on the SNR value for the first two situations.