Houman Zarrabi

Mohammadreza Doostmohammadian, Wei Jiang, Muwahida Liaquat et al.

We consider a discrete-time model of continuous-time distributed optimization over dynamic directed-graphs (digraphs) with applications to distributed learning. Our optimization algorithm works over general strongly connected dynamic networks under switching topologies, e.g., in mobile multi-agent systems and volatile networks due to link failures. Compared to many existing lines of work, there is no need for bi-stochastic weight designs on the links. The existing literature mostly needs the link weights to be stochastic using specific weight-design algorithms needed both at the initialization and at all times when the topology of the network changes. This paper eliminates the need for such algorithms and paves the way for distributed optimization over time-varying digraphs. We derive the bound on the gradient-tracking step-size and discrete time-step for convergence and prove dynamic stability using arguments from consensus algorithms, matrix perturbation theory, and Lyapunov theory. This work, particularly, is an improvement over existing stochastic-weight undirected networks in case of link removal or packet drops. This is because the existing literature may need to rerun time-consuming and computationally complex algorithms for stochastic design, while the proposed strategy works as long as the underlying network is weight-symmetric and balanced. The proposed optimization framework finds applications to distributed classification and learning.

Mohammadreza Doostmohammadian, Alireza Aghasi, Houman Zarrabi

This paper considers distributed optimization algorithms, with application in binary classification via distributed support-vector-machines (D-SVM) over multi-agent networks subject to some link nonlinearities. The agents solve a consensus-constraint distributed optimization cooperatively via continuous-time dynamics, while the links are subject to strongly sign-preserving odd nonlinear conditions. Logarithmic quantization and clipping (saturation) are two examples of such nonlinearities. In contrast to existing literature that mostly considers ideal links and perfect information exchange over linear channels, we show how general sector-bounded models affect the convergence to the optimizer (i.e., the SVM classifier) over dynamic balanced directed networks. In general, any odd sector-bounded nonlinear mapping can be applied to our dynamics. The main challenge is to show that the proposed system dynamics always have one zero eigenvalue (associated with the consensus) and the other eigenvalues all have negative real parts. This is done by recalling arguments from matrix perturbation theory. Then, the solution is shown to converge to the agreement state under certain conditions. For example, the gradient tracking (GT) step size is tighter than the linear case by factors related to the upper/lower sector bounds. To the best of our knowledge, no existing work in distributed optimization and learning literature considers non-ideal link conditions.

Hadi Zanddizari, Sreeraman Rajan, Hassan Rabah et al.

Cloud computing for storing data and running complex algorithms have been steadily increasing. As connected IoT devices such as wearable ECG recorders generally have less storage and computational capacity, acquired signals get sent to a remote center for storage and possible analysis on demand. Recently, compressive sensing (CS) has been used as secure, energy-efficient method of signal sampling in such recorders. In this paper, we propose a secure procedure to outsource the total recovery of CS measurement to the cloud and introduce a privacy-assured signal recovery technique in the cloud. We present a fast, and lightweight encryption for secure CS recovery outsourcing that can be used in wearable devices, such as ECG Holter monitors. In the proposed technique, instead of full recovery of CS-compressed ECG signal in the cloud, to preserve privacy, an encrypted version of ECG signal is recovered by using a randomly bipolar permuted measurement matrix. The user with a key, decrypts the encrypted ECG from the cloud to obtain the original ECG signal. We demonstrate our proposed method using the ECG signals available in the MITBIH Arrhythmia Database. We also demonstrate the strength of the proposed method against partial exposure of the key.

Mohammadreza Doostmohammadian, Hamid R. Rabiee, Houman Zarrabi et al.

Observability of complex systems/networks is the focus of this paper, which is shown to be closely related to the concept of contraction. Indeed, for observable network tracking it is necessary/sufficient to have one node in each contraction measured. Therefore, nodes in a contraction are equivalent to recover for loss of observability, implying that contraction size is a key factor for observability recovery. Here, using a polynomial order contraction detection algorithm, we analyze the distribution of contractions, studying its relation with key network properties. Our results show that contraction size is related to network clustering coefficient and degree heterogeneity. Particularly, in networks with power-law degree distribution, if the clustering coefficient is high there are less contractions with smaller size on average. The implication is that estimation/tracking of such systems requires less number of measurements, while their observational recovery is more restrictive in case of sensor failure. Further, in Small-World networks higher degree heterogeneity implies that there are more contractions with smaller size on average. Therefore, the estimation of representing system requires more measurements, and also the recovery of measurement failure is more limited. These results imply that one can tune the properties of synthetic networks to alleviate their estimation/observability recovery.

Mohammadreza Doostmohammadian, Hamid R. Rabiee, Houman Zarrabi et al.

Single time-scale distributed estimation of dynamic systems via a network of sensors/estimators is addressed in this letter. In single time-scale distributed estimation, the two fusion steps, consensus and measurement exchange, are implemented only once, in contrast to, e.g., a large number of consensus iterations at every step of the system dynamics. We particularly discuss the problem of failure in the sensor/estimator network and how to recover for distributed estimation by adding new sensor measurements from equivalent states. We separately discuss the recovery for two types of sensors, namely αand βsensors. We propose polynomial order algorithms to find equivalent state nodes in graph representation of system to recover for distributed observability. The polynomial order solution is particularly significant for large-scale systems.

Mohammadreza Doostmohammadian, Houman Zarrabi, Hamid R. Rabiee

Measurements and sensing implementations impose certain cost in sensor networks. The sensor selection cost optimization is the problem of minimizing the sensing cost of monitoring a physical (or cyber- physical) system. Consider a given set of sensors tracking states of a dynamical system for estimation purposes. For each sensor assume different costs to measure different (realizable) states. The idea is to assign sensors to measure states such that the global cost is minimized. The number and selection of sensor measurements need to ensure the observability to track the dynamic state of the system with bounded estimation error. The main question we address is how to select the state measurements to minimize the cost while satisfying the observability conditions. Relaxing the observability condition for structurally cyclic systems, the main contribution is to propose a graph theoretic approach to solve the problem in polynomial time. Note that, polynomial time algorithms are suitable for large-scale systems as their running time is upper-bounded by a polynomial expression in the size of input for the algorithm. We frame the problem as a linear sum assignment with solution complexity of O(m3).