Morteza Mardani

Subspace Learning and Imputation for Streaming Big Data Matrices and Tensors

Extracting latent low-dimensional structure from high-dimensional data is of paramount importance in timely inference tasks encountered with “Big Data” analytics. However, increasingly noisy, heterogeneous, and incomplete datasets, as well as the need for real-time processing of streaming data, pose major challenges to this end. In this context, the present paper permeates benefits from rank minimization to scalable imputation of missing data, via tracking low-dimensional subspaces and unraveling latent (possibly multi-way) structure from incomplete streaming data. For low-rank matrix data, a subspace estimator is proposed based on an exponentially weighted least-squares criterion regularized with the nuclear norm. After recasting the nonseparable nuclear norm into a form amenable to online optimization, real-time algorithms with complementary strengths are developed, and their convergence is established under simplifying technical assumptions. In a stationary setting, the asymptotic estimates obtained offer the well-documented performance guarantees of the batch nuclear-norm regularized estimator. Under the same unifying framework, a novel online (adaptive) algorithm is developed to obtain multi-way decompositions of low-rank tensors with missing entries and perform imputation as a byproduct. Simulated tests with both synthetic as well as real Internet and cardiac magnetic resonance imagery (MRI) data confirm the efficacy of the proposed algorithms, and their superior performance relative to state-of-the-art alternatives.

Recovery of Low-Rank Plus Compressed Sparse Matrices With Application to Unveiling Traffic Anomalies

Given the noiseless superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, the goal of this paper is to establish deterministic conditions under which exact recovery of the low-rank and sparse components becomes possible. This fundamental identifiability issue arises with traffic anomaly detection in backbone networks, and subsumes compressed sensing as well as the timely low-rank plus sparse matrix recovery tasks encountered in matrix decomposition problems. Leveraging the ability of l1 and nuclear norms to recover sparse and low-rank matrices, a convex program is formulated to estimate the unknowns. Analysis and simulations confirm that the said convex program can recover the unknowns for sufficiently low-rank and sparse enough components, along with a compression matrix possessing an isometry property when restricted to operate on sparse vectors. When the low-rank, sparse, and compression matrices are drawn from certain random ensembles, it is established that exact recovery is possible with high probability. First-order algorithms are developed to solve the nonsmooth convex optimization problem with provable iteration complexity guarantees. Insightful tests with synthetic and real network data corroborate the effectiveness of the novel approach in unveiling traffic anomalies across flows and time, and its ability to outperform existing alternatives.

Decentralized Sparsity-Regularized Rank Minimization: Algorithms and Applications

Given a limited number of entries from the superposition of a low-rank matrix plus the product of a known compression matrix times a sparse matrix, recovery of the low-rank and sparse components is a fundamental task subsuming compressed sensing, matrix completion, and principal components pursuit. This paper develops algorithms for decentralized sparsity-regularized rank minimization over networks, when the nuclear- and ℓ1-norm are used as surrogates to the rank and nonzero entry counts of the sought matrices, respectively. While nuclear-norm minimization has well-documented merits when centralized processing is viable, non-separability of the singular-value sum challenges its decentralized minimization. To overcome this limitation, leveraging an alternative characterization of the nuclear norm yields a separable, yet non-convex cost minimized via the alternating-direction method of multipliers. Interestingly, if the decentralized (non-convex) estimator converges, under certain conditions it provably attains the global optimum of its centralized counterpart. As a result, this paper bridges the performance gap between centralized and in-network decentralized, sparsity-regularized rank minimization. This, in turn, facilitates (stable) recovery of the low rank and sparse model matrices through reduced-complexity per-node computations, and affordable message passing among single-hop neighbors. Several application domains are outlined to highlight the generality and impact of the proposed framework. These include unveiling traffic anomalies in backbone networks, and predicting networkwide path latencies. Simulations with synthetic and real network data confirm the convergence of the novel decentralized algorithm, and its centralized performance guarantees.

Joint adaptive modulation-coding and cooperative ARQ for wireless relay networks

This paper presents a cross-layer approach to jointly design adaptive modulation and coding (AMC) at the physical layer and cooperative truncated automatic repeat request (ARQ) protocol at the data link layer. We first derive an exact closed form expression for the spectral efficiency of the proposed joint AMC - cooperative ARQ scheme. Aiming at maximizing this system performance measure, we then optimize an AMC scheme which directly satisfies a prescribed packet loss rate constraint at the data-link layer. The results indicate that utilizing cooperative ARQ as a retransmission strategy, noticeably enhances the spectral efficiency compared with the system that employs AMC alone at the physical layer. Moreover, the proposed adaptive rate cooperative ARQ scheme outperforms the fixed rate counterpart when the transmission modes at the source and relay are chosen based on the channel statistics. This in turn quantifies the possible gain achieved by joint design of AMC and ARQ in wireless relay networks.

Robust network traffic estimation via sparsity and low rank

Accurate estimation of origin-to-destination (OD) traffic flows provides valuable input for network management tasks. However, lack of flow-level observations as well as intentional and unintentional anomalies pose major challenges toward achieving this goal. Leveraging the low intrinsic-dimensionality of OD flows and the sparse nature of anomalies, this paper proposes a convex program with nuclear-norm and ℓ1-norm regularization terms to estimate the nominal and anomalous traffic components, using a small subset of (possibly anomalous) flow counts in addition to link counts. Analysis and simulations confirm that the said estimator can exactly recover sufficiently low-dimensional nominal traffic and sparse enough anomalies when the routing matrix is column-incoherent, and an adequate amount of flow counts are randomly sampled. The results offer valuable insights about the measurement types and network scenaria giving rise to accurate traffic estimation. Tests with real Internet data corroborate the effectiveness of the novel estimator.

Estimating traffic and anomaly maps via network tomography

Mapping origin-destination (OD) network traffic is pivotal for network management and proactive security tasks. However, lack of sufficient flow-level measurements as well as potential anomalies pose major challenges towards this goal. Leveraging the spatiotemporal correlation of nominal traffic, and the sparse nature of anomalies, this paper brings forth a novel framework to map out nominal and anomalous traffic, which treats jointly important network monitoring tasks including traffic estimation, anomaly detection, and traffic interpolation. To this end, a convex program is first formulated with nuclear and l1-norm regularization to effect sparsity and low rank for the nominal and anomalous traffic with only the link counts and a small subset of OD-flow counts. Analysis and simulations confirm that the proposed estimator can exactly recover sufficiently low-dimensional nominal traffic and sporadic anomalies so long as the routing paths are sufficiently “spread-out” across the network, and an adequate amount of flow counts are randomly sampled. The results offer valuable insights about data acquisition strategies and network scenaria giving rise to accurate traffic estimation. For practical networks where the aforementioned conditions are possibly violated, the inherent spatiotemporal traffic patterns are taken into account by adopting a Bayesian approach along with a bilinear characterization of the nuclear and l1 norms. The resultant nonconvex program involves quadratic regularizers with correlation matrices, learned systematically from (cyclo)stationary historical data. Alternating-minimization based algorithms with provable convergence are also developed to procure the estimates. Insightful tests with synthetic and real Internet data corroborate the effectiveness of the novel schemes.

Link-Adaptive and QoS-Provisioning Cooperative ARQ—Applications to Relay-Assisted Land Mobile Satellite Communications

In a cooperative relay network, a relay (R) node may facilitate data transmission to the destination (D) node when the latter node cannot correctly decode the source (S) node data. This paper considers such a system model and presents a cross-layer approach to jointly design adaptive modulation and coding (AMC) at the physical layer and the truncated cooperative automatic repeat request (C-ARQ) protocol at the data-link layer for quality-of-service (QoS)-constrained applications. The average spectral efficiency and packet loss rate of the joint C-ARQ and AMC scheme are first derived in closed form. Aiming to maximize the system spectral efficiency, AMC schemes for the S-D and R-D links are optimized, whereas a prescribed packet-loss-rate constraint is satisfied. As an interesting application, joint link adaptation and blockage mitigation in land mobile satellite communications (LMSC) with temporally correlated channels is then investigated. In LMSC, the S node data can be delivered to the D node when the S-D is in the outage, therefore provisioning the QoS requirements. For applications without instantaneous feedback, an optimized rate selection scheme based on the channel statistics is also devised. Detailed and insightful numerical results are presented, which indicate the superior performance of the proposed joint AMC and C-ARQ schemes over their optimized joint AMC and traditional ARQ counterparts.

Cross-Layer Design of Wireless Multihop Random Access Networks

Joint design of flow control, multipath routing, and random access control is considered for wireless multihop networks. Based on a network utility maximization formulation, Aloha persistence probabilities are optimized together with multicommodity end-to-end rates and per-link flow rates. Although the joint optimization of Aloha and flow control was previously tackled using a convex reformulation, adding the routing component renders the problem inherently nonconvex. To cope with this challenge, a successive convex approximation approach is taken to obtain a locally optimal solution efficiently. A parallelized distributed algorithm is developed, which scales well in the network size and exhibits low computational complexity. An online implementation is also proposed and tested. Numerical examples verify the novel design and highlight the performance advantage over state-of-the-art alternatives.

Unveiling anomalies in large-scale networks via sparsity and low rank

In the backbone of large-scale networks, traffic flows experience abrupt unusual changes which can result in congestion, and limit the extent to which end-user quality of service requirements are met. Diagnosing such traffic volume anomalies is a crucial task towards engineering the traffic in the network. This is challenging however, since the available data are the superposition of unobservable origin-to-destination (OD) flows per link. Leveraging the low intrinsic-dimensionality of OD flows and the sparse nature of anomalies, a convex program is formulated to unveil anomalies across flows and time. A centralized solver is developed using the proximal gradient algorithm, which offers provable iteration complexity guarantees. An equivalent nonconvex but separable criterion enables in-network processing of link-load measurements, when optimized via the alternating-direction method of multipliers. The novel distributed iterations entail reduced-complexity local tasks, and affordable message passing between neighboring nodes. Interestingly, under mild conditions the distributed algorithm approaches its centralized counterpart. Numerical tests with synthetic and real network data corroborate the effectiveness of the novel scheme.

Cross-layer link adaptation design for relay channels with cooperative ARQ protocol

The cooperative automatic repeat request (C-ARQ) is a link layer relaying protocol which exploits the spatial diversity and allows the relay node to retransmit the source data packet to the destination, when the latter is unable to decode the source data correctly. This paper presents a cross-layer link adaptation design for C-ARQ based relay channels in which both source and relay nodes employ adaptive modulation coding and power adaptation at the physical layer. For this scenario, we first derive closed-form expressions for the system spectral efficiency and average power consumption. We then present a low complexity iterative algorithm to find the optimized adaptation solution by maximizing the spectral efficiency subject to a packet loss rate (PLR) and an average power consumption constraint. The results indicate that the proposed adaptation scheme enhances the spectral efficiency noticeably when compared to other adaptive schemes, while guaranteeing the required PLR performance.