Carl G. Looney

Fuzzy Petri nets for rule-based decisionmaking

The technique of fuzzy reasoning by transformations of fuzzy truth state vectors by fuzzy matrices is extended to Petri nets. The result is a novel type of neural network in which the transition bars serve as the neutrons, and the nodes are conditions. Conditions may be conjuncted and disjuncted in a natural way to allow the firing of the neurons. The neuron fires to feed the implication truths into one or more consequent conditions when the MIN of the truth values of the antecedent conditions is greater than the neuron threshold. Disjunctions are also modeled in a natural way. Modifications are made to the usual Petri model to allow fuzzy rule-based reasoning by propositional logic. First, fuzzy values are allowed for rules and truths of conditions that appear in rules. Next, multiple copies, rather than the original, of the fuzzy truth tokens are passed along all arrows that depart a node or transition bar where the truth resides. An algorithm is presented for reasoning using these networks, as well as a simple example for exercising the algorithm. Abduction may be done analogously be reversing all arrows and propagating truth tokens backwards. >

A probabilistic framework for modeling and real-time monitoring human fatigue

A probabilistic framework based on the Bayesian networks for modeling and real-time inferring human fatigue by integrating information from various sensory data and certain relevant contextual information is introduced. A static fatigue model that captures the static relationships between fatigue, significant factors that cause fatigue, and various sensory observations that typically result from fatigue is first presented. Such a model provides mathematically coherent and sound basis for systematically aggregating uncertain evidences from different sources, augmented with relevant contextual information. The static model, however, fails to capture the dynamic aspect of fatigue. Fatigue is a cognitive state that is developed over time. To account for the temporal aspect of human fatigue, the static fatigue model is extended based on dynamic Bayesian networks. The dynamic fatigue model allows to integrate fatigue evidences not only spatially but also temporally, therefore, leading to a more robust and accurate fatigue modeling and inference. A real-time nonintrusive fatigue monitor was built based on integrating the proposed fatigue model with a computer vision system developed for extracting various visual cues typically related to fatigue. Performance evaluation of the fatigue monitor using both synthetic and real data demonstrates the validity of the proposed fatigue model in both modeling and real-time inference of fatigue

Competitive fuzzy edge detection

Abstract Our fuzzy classifier detects classes of image pixels corresponding to gray level variation in the various directions. It uses an extended Epanechnikov function as a fuzzy set membership function (FSMF) for each class where the class assigned to each pixel is the one with the greatest fuzzy truth of membership. This classification is done first, after which a competition is run as a second step to thin the edges. Like the Canny edge detector, the edge sensitivity of our competitive fuzzy edge detector (CFED) can be set from low to high by the user. The performance of our algorithm is somewhat similar to that of the Canny algorithm but ours is significantly faster. For both, the proper level of sensitivity must be chosen by the user for the best results because the tradeoff is more edges with more noise versus fewer edges and less noise. However, the settings are less sensitive and more intuitive for our algorithm. We make comparisons on good and degraded images.

Advances in feedforward neural networks: demystifying knowledge acquiring black boxes

We survey research of recent years on the supervised training of feedforward neural networks. The goal is to expose how the networks work, how to engineer them so they can learn data with less extraneous noise, how to train them efficiently, and how to assure that the training is valid. The scope covers gradient descent and polynomial line search, from backpropagation through conjugate gradients and quasi Newton methods. There is a consensus among researchers that adaptive step gains (learning rates) can stabilize and accelerate convergence and that a good starting weight set improves both the training speed and the learning quality. The training problem includes both the design of a network function and the fitting of the function to a set of input and output data points by computing a set of coefficient weights. The form of the function can be adjusted by adjoining new neurons and pruning existing ones and setting other parameters such as biases and exponential rates. Our exposition reveals several useful results that are readily implementable.

Radial basis functional link nets and fuzzy reasoning

Abstract We modify the architecture of radial basis function neural networks so as to also model linear as well as the usual nonlinear input–output relationships. The resulting network learns with fewer iterations and is more accurate than radial basis function neural networks or multiple layered perceptrons. Two training algorithms are presented for the new network: quick training and full training. The full training algorithm adjusts more parameters and requires more computation, but quick training is simpler and faster while also being very accurate. These networks, like radial basis function networks, are at least as powerful as the Takagi–Sugeno type of fuzzy rule-based systems. We compare their training results with those of multiple layered perceptrons and radial basis function neural networks on three data sets to show the advantage of our architecture and algorithm.

Interactive clustering and merging with a new fuzzy expected value

Abstract Major problems exist in both crisp and fuzzy clustering algorithms. The fuzzy c-means type of algorithms use weights determined by a power m of inverse distances that remains fixed over all iterations and over all clusters, even though smaller clusters should have a larger m. Our method uses a different “distance” for each cluster that changes over the early iterations to fit the clusters. Comparisons show improved results. We also address other perplexing problems in clustering: (i) find the optimal number K of clusters; (ii) assess the validity of a given clustering; (iii) prevent the selection of seed vectors as initial prototypes from affecting the clustering; (iv) prevent the order of merging from affecting the clustering; and (v) permit the clusters to form more natural shapes rather than forcing them into normed balls of the distance function. We employ a relatively large number K of uniformly randomly distributed seeds and then thin them to leave fewer uniformly distributed seeds. Next, the main loop iterates by assigning the feature vectors and computing new fuzzy prototypes. Our fuzzy merging then merges any clusters that are too close to each other. We use a modified Xie-Bene validity measure as the goodness of clustering measure for multiple values of K in a user-interaction approach where the user selects two parameters (for eliminating clusters and merging clusters after viewing the results thus far). The algorithm is compared with the fuzzy c-means on the iris data and on the Wisconsin breast cancer data.

Logical controls via Boolean rule matrix transformations

A model is described that uses Boolean rule matrices that are equivalent to implication digraphs to transform truth states associated with rule conditions into deduced or abduced truth states. Such transformations realize propositional logic to deduce controls for complex real-time noninteractive systems. The algorithm runs in deterministically polynomial time and is easy to implement. The rule matrix is decomposable into subsystems with rule submatrices for distributed processing in multiple microprocessors. A single transformation of a truth state fires every entire implication path for which the initial, i.e. root, condition is true, whereas a user-interactive production system fires a single rule at a time and uses the output in the firing of other rules. The method can be used to perform stimulus-response-type control such as humans use to perform such feats as flying airplanes, riding bicycles, or controlling nuclear reactors.

Cognitive situation and threat assessments of ground battlespaces

Abstract We develop an integrated multi-phase approach to middle and high level data fusion with an application to situation and threat assessments. The method first builds a feature vector for each detected ground target that includes time, position and target class in a particular rectangular geographical area of the battlespace. It then clusters the feature vectors by position using a new robust clustering algorithm and makes an inventory of each cluster as to target classes, counts and posture parameters. Situation assessment is done next via a three-tiered cascaded process of case-based reasoning on cluster attribute records to infer the unit types, sizes, and purposes. These are then fed into our fuzzy belief network that performs inferencing via heuristic belief propagation for threat assessment, that is, it infers the actions and intentions of the enemy. A simple synthetic example demonstrates the process.

Active information fusion for decision making under uncertainty

Many information fusion applications especially in military domains are often characterized as a high degree of complexity due to three challenges: 1) data are often acquired from sensors of different modalities and with different degrees of uncertainty; 2) decision must be made quickly; and 3) the world situation as well as sensory observations evolve over time. In this paper, we propose a dynamic active information fusion framework that can simultaneously address the three challenges. The proposed framework is based on Dynamic Bayesian Networks (DBNs) with an embedded active sensor controller. The DBNs provide a coherent and unified hierarchical probabilistic framework to represent, integrate and infer corrupted dynamic sensory information of different modalities. The sensor controller allows it to actively select and invoke a subset of sensors to produce the sensory information that is most relevant to the current task with reasonable time and limited resources. The proposed framework can therefore provide dynamic, purposive and sufficing information fusion particularly well suited to applications where the decision must be made from dynamically available information of diverse and disparate sources. To verify the proposed framework, we use target recognition problem as a proof-of-concept. The experimental results demonstrate the utility of the proposed framework in efficiently modeling and inferring dynamic events.

Stabilization and speedup of convergence in training feedforward neural networks

Abstract We review the training problem for feedforward neural networks and discuss various techniques for accelerating and stabilizing the convergence during training. Among other techniques, these include a self-adjusting step gain, bipolar sigmoid activation functions, training on all classes in parallel, adjusting the exponential rates in the sigmoids, bounding the sigmoid derivatives away from zero, training on exemplars to which noise has been added, adjusting the initial weight set to a subdomain of low values of the sum-squared error, and adjusting the momentum coefficient over the iterations. We also examine methods to assure the generalization of the learning, which include the pruning of unimportant weights and adding noise to exemplars for training.