Copula-based Multimodal Data Fusion for Inference with Dependent Observations

Fusing heterogeneous data from multiple modalities for inference problems has been an attractive and important topic in recent years. There are several challenges in multi-modal fusion, such as data heterogeneity and data correlation. In this dissertation, we investigate inference problems with heterogeneous modalities by taking into account nonlinear cross-modal dependence. We apply copula based methodology to characterize this dependence. In distributed detection, the goal often is to minimize the probability of detection error at the fusion center (FC) based on a fixed number of observations collected by the sensors. We design optimal detection algorithms at the FC using a regular vine copula based fusion rule. Regular vine copula is an extremely flexible and powerful graphical model used to characterize complex dependence among multiple modalities. The proposed approaches are theoretically justified and are computationally efficient for sensor networks with a large number of sensors. With heterogeneous streaming data, the fusion methods applied for processing data streams should be fast enough to keep up with the high arrival rates of incoming data, and meanwhile provide solutions for inference problems (detection, classification, or estimation) with high accuracy. We propose a novel parallel platform, C-Storm (Copula-based Storm), by marrying copula-based dependence modeling for highly accurate inference and a highly-regarded parallel computing platform Storm for fast stream data processing. The efficacy of C-Storm is demonstrated. In this thesis, we consider not only decision level fusion but also fusion with heterogeneous high-level features. We investigate a supervised classification problem by fusing dependent high-level features extracted from multiple deep neural network (DNN) classifiers. We employ regular vine copula to fuse these high-level features. The efficacy of the combination of model-based method and deep learning is demonstrated. Besides fixed-sample-size (FSS) based inference problems, we study a distributed sequential detection problem with random-sample-size. The aim of the distributed sequential detection problem in a non-Bayesian framework is to minimize the average detection time while satisfying the pre-specified constraints on probabilities of false alarm and miss detection. We design local memory-less truncated sequential tests and propose a copula based sequential test at the FC. We show that by suitably designing the local thresholds and the truncation window, the local probabilities of false alarm and miss detection of the proposed local decision rules satisfy the pre-specified error probabilities. Also, we show the asymptotic optimality and time efficiency of the proposed distributed sequential scheme. In large scale sensors networks, we consider a collaborative distributed estimation problem with statistically dependent sensor observations, where there is no FC. To achieve greater sensor transmission and estimation efficiencies, we propose a two-step cluster-based collaborative distributed estimation scheme. In the first step, sensors form dependence driven clusters such that sensors in the same cluster are dependent while sensors from different clusters are independent, and perform copula-based maximum a posteriori probability (MAP) estimation via intra-cluster collaboration. In the second step, the estimates generated in the first step are shared via inter-cluster collaboration to reach an average consensus. The efficacy of the proposed scheme is justified

Heterogeneous Sensor Signal Processing for Inference with Nonlinear Dependence

Inferring events of interest by fusing data from multiple heterogeneous sources has been an interesting and important topic in recent years. Several issues related to inference using heterogeneous data with complex and nonlinear dependence are investigated in this dissertation. We apply copula theory to characterize the dependence among heterogeneous data. In centralized detection, where sensor observations are available at the fusion center (FC), we study copula-based fusion. We design detection algorithms based on sample-wise copula selection and mixture of copulas model in different scenarios of the true dependence. The proposed approaches are theoretically justified and perform well when applied to fuse acoustic and seismic sensor data for personnel detection. Besides traditional sensors, the access to the massive amount of social media data provides a unique opportunity for extracting information about unfolding events. We further study how sensor networks and social media complement each other in facilitating the data-to-decision making process. We propose a copula-based joint characterization of multiple dependent time series from sensors and social media. As a proof-of-concept, this model is applied to the fusion of Google Trends (GT) data and stock/flu data for prediction, where the stock/flu data serves as a surrogate for sensor data. In energy constrained networks, local observations are compressed before they are transmitted to the FC. In these cases, conditional dependence and heterogeneity complicate the system design particularly. We consider the classification of discrete random signals in Wireless Sensor Networks (WSNs), where, for communication efficiency, only local decisions are transmitted. We derive the necessary conditions for the optimal decision rules at the sensors and the FC by introducing a hidden random variable. An iterative algorithm is designed to search for the optimal decision rules. Its convergence and asymptotical optimality are also proved. The performance of the proposed scheme is illustrated for the distributed Automatic Modulation Classification (AMC) problem. Censoring is another communication efficient strategy, in which sensors transmit only informative observations to the FC, and censor those deemed uninformative . We design the detectors that take into account the spatial dependence among observations. Fusion rules for censored data are proposed with continuous and discrete local messages, respectively. Their computationally efficient counterparts based on the key idea of injecting controlled noise at the FC before fusion are also investigated. In this thesis, with heterogeneous and dependent sensor observations, we consider not only inference in parallel frameworks but also the problem of collaborative inference where collaboration exists among local sensors. Each sensor forms coalition with other sensors and shares information within the coalition, to maximize its inference performance. The collaboration strategy is investigated under a communication constraint. To characterize the influence of inter-sensor dependence on inference performance and thus collaboration strategy, we quantify the gain and loss in forming a coalition by introducing the copula-based definitions of diversity gain and redundancy loss for both estimation and detection problems. A coalition formation game is proposed for the distributed inference problem, through which the information contained in the inter-sensor dependence is fully explored and utilized for improved inference performance

Spectrum sensing, spectrum monitoring, and security in cognitive radios

Spectrum sensing is a key function of cognitive radios and is used to determine whether a primary user is present in the channel or not. In this dissertation, we formulate and solve the generalized likelihood ratio test (GLRT) for spectrum sensing when both primary user transmitter and the secondary user receiver are equipped with multiple antennas. We do not assume any prior information about the channel statistics or the primary user’s signal structure. Two cases are considered when the secondary user is aware of the energy of the noise and when it is not. The final test statistics derived from GLRT are based on the eigenvalues of the sample covariance matrix. In-band spectrum sensing in overlay cognitive radio networks requires that the secondary users (SU) periodically suspend their communication in order to determine whether the primary user (PU) has started to utilize the channel. In contrast, in spectrum monitoring the SU can detect the emergence of the PU from its own receiver statistics such as receiver error count (REC). We investigate the problem of spectrum monitoring in the presence of fading where the SU employs diversity combining to mitigate the channel fading effects. We show that a decision statistic based on the REC alone does not provide a good performance. Next we introduce new decision statistics based on the REC and the combiner coefficients. It is shown that the new decision statistic achieves significant improvement in the case of maximal ratio combining (MRC). Next we consider the problem of cooperative spectrum sensing in cognitive radio networks (CRN) in the presence of misbehaving radios. We propose a novel approach based on the iterative expectation maximization (EM) algorithm to detect the presence of the primary users, to classify the cognitive radios, and to compute their detection and false alarm probabilities. We also consider the problem of centralized binary hypothesis testing in a cognitive radio network (CRN) consisting of multiple classes of cognitive radios, where the cognitive radios are classified according to the probability density function (PDF) of their received data (at the FC) under each hypotheses

Hypothesis Testing Using Spatially Dependent Heavy-Tailed Multisensor Data

The detection of spatially dependent heavy-tailed signals is considered in this dissertation. While the central limit theorem, and its implication of asymptotic normality of interacting random processes, is generally useful for the theoretical characterization of a wide variety of natural and man-made signals, sensor data from many different applications, in fact, are characterized by non-Gaussian distributions. A common characteristic observed in non-Gaussian data is the presence of heavy-tails or fat tails. For such data, the probability density function (p.d.f.) of extreme values decay at a slower-than-exponential rate, implying that extreme events occur with greater probability. When these events are observed simultaneously by several sensors, their observations are also spatially dependent. In this dissertation, we develop the theory of detection for such data, obtained through heterogeneous sensors. In order to validate our theoretical results and proposed algorithms, we collect and analyze the behavior of indoor footstep data using a linear array of seismic sensors. We characterize the inter-sensor dependence using copula theory. Copulas are parametric functions which bind univariate p.d.f. s, to generate a valid joint p.d.f. We model the heavy-tailed data using the class of alpha-stable distributions. We consider a two-sided test in the Neyman-Pearson framework and present an asymptotic analysis of the generalized likelihood test (GLRT). Both, nested and non-nested models are considered in the analysis. We also use a likelihood maximization-based copula selection scheme as an integral part of the detection process. Since many types of copula functions are available in the literature, selecting the appropriate copula becomes an important component of the detection problem. The performance of the proposed scheme is evaluated numerically on simulated data, as well as using indoor seismic data. With appropriately selected models, our results demonstrate that a high probability of detection can be achieved for false alarm probabilities of the order of 10^-4. These results, using dependent alpha-stable signals, are presented for a two-sensor case. We identify the computational challenges associated with dependent alpha-stable modeling and propose alternative schemes to extend the detector design to a multisensor (multivariate) setting. We use a hierarchical tree based approach, called vines, to model the multivariate copulas, i.e., model the spatial dependence between multiple sensors. The performance of the proposed detectors under the vine-based scheme are evaluated on the indoor footstep data, and significant improvement is observed when compared against the case when only two sensors are deployed. Some open research issues are identified and discussed

Hypothesis Testing and Model Estimation with Dependent Observations in Heterogeneous Sensor Networks

Advances in microelectronics, communication and signal processing have enabled the development of inexpensive sensors that can be networked to collect vital information from their environment to be used in decision-making and inference. The sensors transmit their data to a central processor which integrates the information from the sensors using a so-called fusion algorithm. Many applications of sensor networks (SNs) involve hypothesis testing or the detection of a phenomenon. Many approaches to data fusion for hypothesis testing assume that, given each hypothesis, the sensors\u27 measurements are conditionally independent. However, since the sensors are densely deployed in practice, their field of views overlap and consequently their measurements are dependent. Moreover, a sensor\u27s measurement samples may be correlated over time. Another assumption often used in data fusion algorithms is that the underlying statistical model of sensors\u27 observations is completely known. However, in practice these statistics may not be available prior to deployment and may change over the lifetime of the network due to hardware changes, aging, and environmental conditions. In this dissertation, we consider the problem of data fusion in heterogeneous SNs (SNs in which the sensors are not identical) collecting dependent data. We develop the expectation maximization algorithm for hypothesis testing and model estimation. Copula distributions are used to model the correlation in the data. Moreover, it is assumed that the distribution of the sensors\u27 measurements is not completely known. we consider both parametric and non-parametric model estimation. The proposed approach is developed for both batch and online processing. In batch processing, fusion can only be performed after a block of data samples is received from each sensor, while in online processing, fusion is performed upon arrival of each data sample. Online processing is of great interest since for many applications, the long delay required for the accumulation of data in batch processing is not acceptable. To evaluate the proposed algorithms, both simulation data and real-world datasets are used. Detection performances of the proposed algorithms are compared with well-known supervised and unsupervised learning methods as well as with similar EM-based methods, which either partially or entirely ignore the dependence in the data