Problem Of Decision Fusion Research Articles

Analytic Sensor Rules for Optimal Distributed Decision Given $K$-Out-of-$L$ Fusion Rule Under Monte Carlo Approximation

With the development of large-scale sensor networks, there is an increasing interest for high dimensional distributed decision fusion problem in statistical decision, machine learning, control theory, etc. In this article, we investigate the optimal sensor quantized rules of the distributed decision under a given fusion rule for conditionally dependent and high dimensional sensor observations. We provide a Monte Carlo importance sampling method to reduce the computational complexity of the distributed decision fusion. For the K-out-of-L rule, we derive a group of analytic sensor rules based on the necessary and sufficient condition of the optimal sensor rules. In term of efficiency, it is significantly better than the traditional iterative search algorithms, such as the Riemann sum approximation iteration algorithm. The analytic solution is also a general result since it does not rely on the specific K value of the K-out-of-L rule, the specific conditional probability density function and the dimension of sensor observations. Thus, it can be applied to multisensor decision fusion problems with high dimensional dependent sensor observations. For the general fusion rules rather than the K-out-of-L rule, the Monte Carlo Gauss-Seidel algorithm is also provided. The numerical examples demonstrate the effectiveness of the analytic solution and the Monte Carlo Gauss-Seidel algorithm.

Using decision fusion methods to improve outbreak detection in disease surveillance

BackgroundWhen outbreak detection algorithms (ODAs) are considered individually, the task of outbreak detection can be seen as a classification problem and the ODA as a sensor providing a binary decision (outbreak yes or no) for each day of surveillance. When they are considered jointly (in cases where several ODAs analyze the same surveillance signal), the outbreak detection problem should be treated as a decision fusion (DF) problem of multiple sensors.MethodsThis study evaluated the benefit for a decisions support system of using DF methods (fusing multiple ODA decisions) compared to using a single method of outbreak detection. For each day, we merged the decisions of six ODAs using 5 DF methods (two voting methods, logistic regression, CART and Bayesian network - BN). Classical metrics of accuracy, prediction and timelines were used during the evaluation steps.ResultsIn our results, we observed the greatest gain (77%) in positive predictive value compared to the best ODA if we used DF methods with a learning step (BN, logistic regression, and CART).ConclusionsTo identify disease outbreaks in systems using several ODAs to analyze surveillance data, we recommend using a DF method based on a Bayesian network. This method is at least equivalent to the best of the algorithms considered, regardless of the situation faced by the system. For those less familiar with this kind of technique, we propose that logistic regression be used when a training dataset is available.

Decision Fusion in Distributed Cooperative Wireless Sensor Networks

In this paper, the distributed decision fusion (DF) problem of cooperative wireless sensor networks is considered, where a group of sensors send their local decisions to a fusion center via a set of relays using decode-and-forward relaying. The likelihood ratio test under Neyman–Pearson sense is used to derive the optimal DF rule (DFR). Moreover, three suboptimal fusion rules are derived to enable a broad range of complexity-performance tradeoffs. The performance of the optimal and suboptimal fusion schemes is evaluated in terms of probability of detection, false alarm, and fusion decision error where analytical expressions are derived for the suboptimal schemes, while Monte Carlo simulation is used for the optimal DFR. The obtained analytical and simulation results show that the decision error performance of the network is mainly determined by the number and accuracy of the local sensors, while the relaying process could be effective in mitigating the fading channel effects. Furthermore, no significant improvement is achieved by increasing the number of relays beyond three for each sensor.

Noncoherent Decision Fusion over Fading Hybrid MACs in Wireless Sensor Networks.

In this paper, we consider the problem of decision fusion for noncoherent detection in a wireless sensor network. Novel to the current work is the integration of the hybrid multi-access channel (MAC) in the fusion rule design. We assume that sensors transmit their local binary decisions over a hybrid MAC which is a composite of conventional orthogonal and nonorthogonal MACs. Under Rayleigh fading scenario, we present a likelihood ratio (LR)-based fusion rule, which has been shown to be optimal through theoretical analysis and simulation. However, it requires a large amount of computation, which is not easily implemented in resource-constrained sensor networks. Therefore, three sub-optimal alternatives with low-complexity are proposed, namely the weighed energy detector (WED), the deflection-coefficient-maximization (DCM), and the two-step (TS) rules. We show that when the channel signal-to-noise ratio (SNR) is low, the LR-based fusion rule reduces to the WED rule; at high-channel SNR, it is equivalent to the TS rule; and at moderate-channel SNR, it can be approached closely by the DCM rule. Compared with the conventional orthogonal and nonorthogonal MACs, numerical results show that the hybrid MAC with the proposed fusion rules can improve the detection performance when the channel SNR is medium.

Optimal Decision Fusion Under Order Effects

Abstract This paper studies an optimal decision fusion problem with a group of human decision makers when an order effect is present. The order effect refers to situations wherein the process of decision making by a human is affected by the order of decisions. In our set-up, all human decision makers, called observers, receive the same data which is generated by a common but unknown hypothesis. Then, each observer independently generates a sequence of decisions which are modeled by employing non-commutative probabilistic models of the data and their relation to the unknown hypothesis. The use of non-commutative probability models is motivated by recent psychological studies which indicate that these non-commutative probability models are more suitable for capturing the order effect in human decision making, compared with the classical probability model. A central decision maker (CDM) receives (possibly a subset of) the observers’ decisions and decides on the true hypothesis. The considered problem becomes an optimal decision fusion problem with observations modeled using a non-commutative (Von Neumann) probability model. The structure of the optimal decision rule at the CDM is studied under two scenarios. In the first scenario, the CDM receives the entire history of the observers’ decisions whereas in the second scenario, the CDM receives only the last decision of each observer. The perfromance of the optimal fusion rule is numerically evaluated and compared with the optimal fusion rule derived when using a classical probability model.

Low-Complexity Optimal Hard Decision Fusion Under the Neyman–Pearson Criterion

The design of the optimal nonrandomized hard decision fusion rule under the Neyman–Pearson criterion is known to be exponential in complexity. In this letter, we formulate a more generalized version of this problem called the “generalized decision fusion problem (GDFP)” and relate it to the classical $\text{0--1}$ knapsack problem. Consequently, we show that the GDFP has a worst-case polynomial time solution. Numerical results are presented to verify the effectiveness of the proposed solution.

Inherence of Hard Decision Fusion in Soft Decision Fusion and a Generalized Radix-2 Multistage Decision Fusion Strategy

We consider the problem of decision fusion for binary event detection using a sensor network of nodes with non-identical detection and false-alarm probability pairs. We show that a soft decision fusion rule that is used to make a binary decision inherently possesses a hard decision fusion (HDF) part. Revelation of HDF part within the soft decision fusion rule, on the one hand, shows a connection between the two approaches and, on the other hand, enables straightforward computation of network-level detection and false-alarm probabilities. We consider the optimal soft decision fusion rule that minimizes the total probability of error and reveal its inherent HDF part for a network of two nodes. We subsequently use it to develop a radix-2 multistage decision fusion strategy for larger networks since revelation of HDF part for them is quite time-consuming. We consider spectrum sensing by a cognitive radio-enabled wireless sensor network to demonstrate the effectiveness of the proposed strategy. We show that the error performance of the proposed strategy is close to that exhibited by the optimal soft decision fusion rule and is better than many suboptimal hard and soft decision fusion strategies. The overall detection and false-alarm probabilities can be easily computed using the proposed strategy. We also show that the EXOR and EXNOR binary fusion rules are never optimal in minimizing the probability of error in decision making.

A New Information Filling Technique Based On Generalized Information Entropy

Multi-sensor decision fusion used for discovering important facts hidden in a mass of data has become a widespread topic in recent years, and has been gradually applied in failure analysis, system evaluation and other fields of big data process. The solution to incompleteness is a key problem of decision fusion during the experiment and has been basically solved by proposed technique in this paper. Firstly, as a generalization of classical rough set, interval similarity relation is employed to classify not only single-valued data but also interval-valued data in the information systems. Then, a new kind of generalized information entropy called "H’-Information Entropy" is suggested based on interval similarity relation to measure the uncertainty and  the classification ability in the information systems. Thus, the innovated information filling technique using the properties of H’-Information Entropy can be applied to replace the missing data by some smaller estimation intervals. Finally, the feasibility and advantage of this technique are testified by two actual applications of decision fusion, whose performance is evaluated by the quantification of E-Condition Entropy.

Decision Fusion With Unknown Sensor Detection Probability

In this correspondence we study the problem of channel-aware decision fusion when the sensor detection probability is not known at the decision fusion center. Several alternatives proposed in the literature are compared and new fusion rules (namely 'ideal sensors' and 'locally-optimum detection') are proposed, showing attractive performance and linear complexity. Simulations are provided to compare the performance of the aforementioned rules.

Data Fusion of Maritime Incident Databases with Dempster–Shafer Theory

Although a huge amount of information is available in all kinds of marine safety databases, only a small part can be used directly. The disorganized information from different sources leads to a mixture of format and definition. In the work reported in this paper, the Dempster–Shafer theory (DST) of evidence was applied to combine evidence (i.e., a piece of information that supports a claim) from different sources. The method is regarded as a generalization of the Bayesian theory and can avoid two difficulties in classical probability theory: handling the conflicting information and assigning prior probabilities. The work of data fusion was demonstrated first by a decision fusion problem that involved the reconciliation of contradictory expert reports. The DST can provide a decision maker with a comprehensive result through the combination of different experts’ opinions. Second, fusion was conducted of two representative maritime incident databases: that of the Global Integrated Shipping Information System and that of the International Chamber of Commerce. Although the records in the databases had some defects (e.g., disorder, error, contradiction), the DST was able to work effectively and calculate an uncertainty interval of incident.

CODING AND INTERLEAVING SCHEMES FOR INFORMATION ACQUISITION FROM WIRELESS SENSOR NETWORKS

Transmission of data over wireless sensor networks (WSNs) poses significant constraints on the energy and bandwidth of the communication system. We consider the problem of decision fusion in a distributed detection system in a classical parallel fusion structure by incorporating the fading channel layer that is omnipresent in WSNs. We use channel coding and transmit diversity schemes, equal gain combining (EGC) and maximum ratio combining (MRC). We employ a multi-carrier modulation scheme over the wireless communication channel. This paper proposes the use of Hamming, low-density parity-check (LDPC) coding, or Viterbi coding. Interleaving is also suggested in this paper using chaotic Baker map randomization for the reduction of the bit error rate (BER). Moreover, the chaotic interleaving adds a degree of security to the transmitted data. Simulation results show that the application of coding and interleaving achieves a performance improvement in the WSN.

Modeling Fuzzy Decision Fusion Based on Vague Set

As a further generalization of fuzzy set theory, the vague set theory can overcome the shortcomings of fuzzy set by describing the membership from two sides of both TRUE and FALSE, rather than only by a single membership value. Since vague sets can provide more information than fuzzy sets, it is superior in mathematical analysis of system with uncertainty. Thus, vague set is more powerful in the describing and processing of uncertain, inaccurate, even conflicting information. In this paper, a new method vague set-based is proposed to deal with fuzzy decision fusion problem. Compared with traditional fuzzy decision fusion method- such as fuzzy comprehensive evaluation, the new method is more efficient and powerful to fulfill decision fusion with uncertain and inaccurate information. Generally, the new method is the same with group decision fusion and soft fusion.

Cooperative Spectrum Sensing in Cognitive Radio Networks With Noncoherent Transmission

The problem of decision fusion for cooperative spectrum sensing in cognitive radio (CR) networks is studied when fading channels are present between the CRs and the fusion center (FC). The CRs perform spectrum sensing using energy detection and transmit their binary decisions to the FC for a final decision on the absence or presence of the primary user activity. Considering the limited resources in CR networks, which makes it difficult to acquire the instantaneous channel-state information, noncoherent transmission schemes with on-off keying (OOK) and binary frequency-shift keying (BFSK) are employed to transmit the binary decisions to the FC. For each of the transmission schemes considered, energy- and decoding-based fusion rules are developed first. Then, the detection threshold at the CR nodes and at the FC, the combining weights (in the case of the energy-based fusion rule), and the sensing time are optimized to maximize the achievable secondary throughput of the CR network. Simulation results verify the theoretical analysis. It is also shown that the energy-based fusion rule outperforms the decoding-based fusion rule when the signal-to-noise ratios (SNRs) of the reporting channels are low, whereas the opposite is true for high SNRs. For the simpler energy-based fusion rule, BFSK achieves higher secondary throughput than OOK, at the expense of a larger transmission bandwidth.

A Method of Decision Fusion for Target Recognition Based on Grey Fixed Weight Clustering

The problem of decision fusion for target recognition is usually solved by the uncertainty information processing methods. This paper presents a novel algorithm of decision fusion for target recognition based on the grey fixed weight clustering analysis. The problem of recognizingM classes target is transformed intoM problems of recognizing two classes target, and then each problem of recognizing two classes target is solved by the grey fixed weight clustering. The whitenization weight functions of each two classes are assessed by training samples. The experiment conducted on three classifiers and five classes’ radar target data demonstrates this method can effectively improve the recognition performance.

Blind Adaptive Weighted Aggregation Scheme for Event Detection in Multihop Wireless Sensor Networks

The problem of decision fusion for event detection in Wireless Sensor Networks is the prime focus of this paper. Our proposed algorithm focuses on single hop (star) and multihop (tree) topologies, which are commonly deployed wireless sensor network topologies. In order to minimize the overall energy consumption in the network, a transmission constraint of one-bit is imposed on each sensor node. This poses a challenging problem of designing a one-bit decision fusion rule at every fusion center, which improves the overall detection accuracy at the sink node. The absence of apriori knowledge of each sensor's local performance indices, makes the existing optimum fusion rule infeasible. Moreover, in the absence of a training sequence of true event occurrences, existing Adaptive distributed detection techniques also become inapplicable. In this setup, the key contribution of this paper is a Least Mean Squares based Blind Adaptive Weighted Aggregation Scheme (Blind-AdWAS) for Wireless Sensor Networks with tree topology. We extend our earlier work (Jagyasi et al. in Proceedings of 11th international symposium on wireless personal multimedia communication, 2008) to include an analysis of the effect of Rayleigh flat fading channel on Blind-AdWAS in comparison with existing channel-aware optimum and sub- optimum aggregation schemes. Even in the absence of any channel knowledge or knowledge of performance indices, Blind-AdWAS demonstrates robustness in event detection performance.

Channel-Aware Decision Fusion With Unknown Local Sensor Detection Probability

Existing channel-aware decision fusion schemes assume that the local detection probability is known at the fusion center (FC). However, this paradigm ignores the possibility of unknown sensor alarm responses to the occurrence of events. Accordingly, this correspondence examines the binary decision fusion problem under the assumption that the local detection probability is unknown. Treating the communication links between the nodes and the FC as binary symmetric channels and assuming that the sensor nodes transmit simple one-bit reports to the FC, the global fusion rule is formulated initially in terms of the generalized likelihood ratio test (GLRT). Adopting the assumption of a high SNR regime, an approximate maximum likelihood (ML) estimate is derived for the unknown parameter required to implement the GLRT that is affine in the received data. The GLRT-based formulation is intuitively straightforward, but does not permit a tractable performance analysis. Therefore, motivated by the affine nature of the approximate ML solution, a simple alternative fusion rule is proposed in which the test statistic remains affine in the received data. It is shown that the proposed fusion rule facilitates the analytic characterization of the channel effect on the global detection performance. In addition, given a reasonable range of the local detection probability, it is shown that the global detection probability can be improved by reducing the total link error. Thus, a sensor power allocation scheme is proposed for enhancing the detection performance by improving the link quality. Simulation results show that: 1) the alternative fusion rule outperforms the GLRT; and 2) the detection performance of the fusion rule is further improved when the proposed power loading method is applied.

Multiple-symbol differential decision fusion for mobile wireless sensor networks

We consider the problem of decision fusion in mobile wireless sensor networks where the channels between the sensors and the fusion center are time-varying. We assume that the sensors make independent local decisions on the M hypotheses under test and report these decisions to the fusion center using differential phase-shift keying (DPSK), so as to avoid the channel estimation overhead entailed by coherent decision fusion. For this setup we derive the optimal and three low-complexity, suboptimal fusion rules which do not require knowledge of the instantaneous fading gains. The suboptimal fusion rules are obtained by applying certain approximations to the optimal fusion rule and are referred to as Chair-Varshney (CV), ideal local sensors (ILS), and max-log fusion rules. Since all proposed fusion rules exploit an observation window of at least two symbol intervals, we refer to them collectively as multiple-symbol differential (MSD) fusion rules. For binary hypothesis testing, we derive performance bounds for the optimal fusion rule and exact or approximate analytical expressions for the probabilities of false alarm and detection for all three suboptimal fusion rules. Simulation and analytical results show that whereas the CV and ILS fusion rules approach the performance of the optimal fusion rule for high and low channel signal-to-noise ratios (SNRs), respectively, the max-log fusion rule performs close-to-optimal for the entire range of SNRs. Furthermore, in fast fading channels significant performance gains can be achieved for the considered MSD fusion rules by increasing the observation window to more than two symbol intervals.

A simple and efficient suboptimal multilevel quantization approach in geographically distributed sensor systems

In this study, the problem of decision fusion in geographically distributed sensor system is considered. The distributed detection system employs several geographically separated local sensors and a fusion center. The local sensors monitor the same object scene and pass their local decisions about the same hypothesis to the fusion center. The fusion center combines all the local decisions into a final global decision. A simple and efficient multilevel quantization and fusion approach, wherein each sensor provides the fusion center with a soft-decision rather than a hard-decision or sensor observation is proposed. Each soft-decision is represented by a multiple-bit decision. The performance of the proposed model is evaluated and compared to the performances of the centralized and the optimum decentralized distributed detection systems. The proposed model is illustrated with several examples highlighting the behavior of the model and benefits of fusing the soft-decisions. We show that the proposed model significantly outperforms the optimum decentralized model, in which each sensor provides only a hard-decision, when two bits per decisions are used. We also show that the performance of the proposed model is reasonably close to the centralized model, in which each sensor provides its observations, when four bits per decisions are used.

Decision fusion rules in multi-hop wireless sensor networks

The decision fusion problem for a wireless sensor network (WSN) operating in a fading environment is considered. In particular, we develop channel-aware decision fusion rules for resource-constrained WSNs where binary decisions from local sensors may need to be relayed through multi-hop transmission in order to reach a fusion center. Each relay node employs a binary relay scheme whereby the relay output is inferred from the channel impaired observation received from its source node. This estimated binary decision is subsequently transmitted to the next node until it reaches the fusion center. Under a flat fading channel model, we derive the optimum fusion rules at the fusion center for two cases. In the first case, we assume that the fusion center has knowledge of the fading channel gains at all hops. In the second case, we assume a Rayleigh fading model, and derive fusion rules utilizing only the fading channel statistics. We show that likelihood ratio (LR) based optimum decision fusion statistics for both cases reduce to respective simple linear test statistics in the low channel signal-to-noise ratio (SNR) regime. These suboptimum detectors are easy to implement and require little a priori information. Performance evaluation, including a study of the robustness of the fusion statistics with respect to unknown system parameters, is conducted through simulations.

Exploiting Global and Local Decisions for Multimodal Biometrics Verification

In this paper, we address the multimodal biometric decision fusion problem. By exploring into the user-specific approach for learning and threshold setting, four possible paradigms for learning and decision making are investigated. Since each user requires a decision hyperplane specific to him in order to achieve good verification accuracy, those tedious iterative training methods like the neural network approach would not be suitable. We propose to use a model that requires only a single training step for this application. The four global and local learning and decision paradigms are then explored to observe their decision capability. Besides the proposal of a relevant receiver operating characteristic performance for the local decision, extensive experiments were conducted to observe the verification performance for fusion of two and three biometrics.