The integration of different imaging modalities, such as structural, diffusion tensor, and functional magnetic resonance imaging, with deep learning models has yielded promising outcomes in discerning phenotypic characteristics and enhancing disease diagnosis. The development of such a technique hinges on the efficient fusion of heterogeneous multimodal features, which initially reside within distinct representation spaces. Naively fusing the multimodal features does not adequately capture the complementary information and could even produce redundancy. In this work, we present a novel joint self-supervised and supervised contrastive learning method to learn the robust latent feature representation from multimodal MRI data, allowing the projection of heterogeneous features into a shared common space, and thereby amalgamating both complementary and analogous information across various modalities and among similar subjects. We performed a comparative analysis between our proposed method and alternative deep multimodal learning approaches. Through extensive experiments on two independent datasets, the results demonstrated that our method is significantly superior to several other deep multimodal learning methods in predicting abnormal neurodevelopment. Our method has the capability to facilitate computer-aided diagnosis within clinical practice, harnessing the power of multimodal data. The source code of the proposed model is publicly accessible on GitHub: https://github.com/leonzyzy/Contrastive-Network.

Deep metric learning techniques have been used for visual representation in various supervised and unsupervised learning tasks through learning embeddings of samples with deep networks. However, classic approaches, which employ a fixed distance metric as a similarity function between two embeddings, may lead to suboptimal performance for capturing the complex data distribution. The Bregman divergence generalizes measures of various distance metrics and arises throughout many fields of deep metric learning. In this paper, we first show how deep metric learning loss can arise from the Bregman divergence. We then introduce a novel method for learning empirical Bregman divergence directly from data based on parameterizing the convex function underlying the Bregman divergence with a deep learning setting. We further experimentally show that our approach performs effectively on five popular public datasets compared to other SOTA deep metric learning methods, particularly for pattern recognition problems.

This paper investigates evasion attacks on end-to-end deep-learning malware detection over ELF (Executable and Linkable Format) binaries. We show that an attacker can deliberately modify bytes in a malware ELF binary such that a well-trained neural network is misled and predicts it as benign. We examine five methods that can modify ELF binaries without affecting functionalities and leverage them in evasion attacks. We explore two state-of-the-art end-to-end deep learning malware detectors, including MalConv and FireEyeNet, over a real-world dataset with 1,422 ELF binaries. Our experimental results show that evasion attacks with 3 out of the 5 methods are effective and can force the two CNNs to predict incorrectly. For instance, the most effective modification achieves up to 76.6% evasion rate on FireEyeNet and 8.4% evasion rate on MalConv. We also demonstrate that retraining CNNs with deliberately modified binaries can significantly mitigate evasion attacks.

The availability of sophisticated IT tools has provided computer system attackers with the capacity to develop dangerous metamorphic or polymorphic malware . Such malware presents behaviors similar to biological viruses enabling them to evade detection from conventional anti-malware methods. To circumvent this challenge, we carried out this research experiment to build and train machine learning models, and our proposed models achieved 99% & 99.6% accuracy in detecting and classifying PE-oriented malware. This excellent performance of our proposed models is undoubtedly a function of several factors but majorly on the synthesized DNA datasets (from our previous research works), which we used to train our proposed models. The synthesized DNA datasets are composed of salient features (dynamic and static) extracted from behaviors of nonmalicious programs (.exe, .dll, etc.) before and after infection by malware using reverse engineering and tracing tools. Then using a encoding algorithm and bioinformatics tools, we synthesized these features into a DNA-like representation (data sets) akin to the biological Deoxyribonucleic acid(DNA).

Contrastive learning techniques continue to receive a lot of attention in the self-supervised learning area. Specifically, the learned distance features can be further utilized to capture the distance between latent features in the embedding space and improve the performance of both supervised and unsupervised learning tasks. However, most contrastive learning efforts are focused on learning the geometric distance between the latent features, while the underlying probability distribution is usually ignored. To address this challenge, we propose a novel generalized contrastive loss for self-supervised learning using the Bregman divergence by investigating the hidden relationship between the contrastive loss and the Bregman divergence. Our method considers the hybrid divergence that leverages the Euclidean-based distance and probabilistic divergence, which improves the quality of self-supervised learned feature representation. Besides theory, extensive experimental results demonstrate the effectiveness of our method compared to other state-of-the-art self-supervised methods.

Recently, deep metric learning techniques received attentions, as the learned distance representations are useful to capture the similarity relationship among samples and further improve the performance of various of supervised or unsupervised learning tasks. We propose a novel supervised metric learning method that can learn the distance metrics in both geometric and probabilistic space for image recognition. In contrast to the previous metric learning methods which usually focus on learning the distance metrics in Euclidean space, our proposed method is able to learn better distance representation in a hybrid approach. To achieve this, we proposed a Generalized Hybrid Metric Loss (GHM-Loss) to learn the general hybrid proximity features from the image data by controlling the trade-off between geometric proximity and probabilistic proximity. To evaluate the effectiveness of our method, we first provide theoretical derivations and proofs of the proposed loss function, then we perform extensive experiments on two public datasets to show the advantage of our method compared to other state-of-the-art metric learning methods.

The paper aims at classifying the learning-skill of driving-learners by utilizing the acquired P300 and N400 event related potentials during the learning phase of a simulated car-driving task. A set of driving stimuli, including braking on sudden appearance of bumpers, steering control at the sharp bending points, and the like, are prepared to experimentally classify the learning skill of the subjects in three distinct classes: Low, Medium and High. The complexity in classifying the subjective learning-skill arises because of intra- and inter-session variations in brain signals due to temporal fluctuation in activation levels of the involved brain lobes. A novel z-slice based model of general type-2 fuzzy set is proposed to represent the intra- and inter-session variations by the footprint of uncertainty and their composite variations by z-slices at different values of a given feature. Further, a novel technique for z-slice based classifier is proposed to classify the learning-skill under intra-and inter-session uncertainty. The proposed classifier is found to outperform traditional and well-known type-2 classifiers for the present learning-skill classification task in Experiments undertaken confirm the frontal and parietal theta (4-7 Hz) activation in discrete learning steps. The proposed research outcome may directly be utilized to certify driving learners with required learning skills.

We present an adaptive hierarchical sliding mode control based on fuzzy neural network (AFNNHSMC) for a class of underactuated nonlinear systems. The approach is applied to the problem of high-precision trajectory tracking. The underactuated nonlinear system is viewed as several subsystems. One subsystem is used to design the first layer sliding surface, which constructs the second layer sliding surface with another subsystem. When the top layer, the nth layer, includes all the subsystems, the design process is finished. Meanwhile, the equivalent control law and the switching control law are achieved at every layer. Because the hierarchical sliding mode control (HSMC) law relies excessively on the requirement of detailed information of the underactuated dynamic system, and because that method causes an inevitable chattering phenomenon, an online fuzzy neural network (FNN) system is applied to mimic the HSMC law. Moreover, the bounds of system uncertainties, time-varying external disturbances, and modeling error caused by the fuzzy neural network system are estimated online by a robust term. The stability of the closed-loop system is guaranteed based on the Lyapunov theory and the Barbalat's Lemma. Finally, the example of a single-pendulum-type overhead crane system is simulated and used to verify the effectiveness and robustness of the proposed method compared with the conventional HSMC method.

We study the vowels detection from brain activation due to vowel sound imageries. At first we experimentally determine the maximum and relatively longer activation that takes place in the frontal or pre frontal lobe during vowel sound Imagination using acquired electroencephalographic signal analysis. Then we capture pre-frontal or frontal vowel sound imagery using a functional near infrared device to extract certain statistical features. Differential evolution based feature selection is used to for dimensionality reduction. The reduced feature set is then used to design an interval type 2 fuzzy classifier to classify the vowels from the pre frontal or frontal f-NIRs response to vowel sound imagination. Experiments undertaken confirm that the proposed classifier outperforms its competitors in classification accuracy for each vowel sound imagery class. They further confirm that the f-NIRs based classification outperforms EEG based modality for better capture of brain activations. Consonants are encoded with two vowel sounds with a space between them. Thus the proposed technique can effectively be used for mind driven type writing of vowels and consonants, serving people suffering from vocal deficiency.

Although there exist recent works on fMRI based cognitive learning, there is a dearth of literature on fNIRs based studies on learning and memory. This paper provides a novel study on the cognitive load detection of subjects engaged in symbol-meaning associative learning tasks from the direct measurement of the hemodynamic response of the brain. The hemodynamic response collected during symbol-meaning associative learning tasks by subjects are pre-processed (filtered from artifacts) for extraction of 112-dimensional features, which are reduced to 20 dimensions by a meta-heuristic optimization algorithm for subsequent transfer to a interval type-2 fuzzy classifier to classify three levels of cognitive loads (High, Low and Moderate) borne by the subjects at different time slots of the learning task. Analysis undertaken reveals that the type-2 fuzzy classifier with the proposed feature selection mechanism has a high performance in classification of the cognitive loads over 89%. Experimental analysis further reveals that the transfer of brain activation from orbitofrontal to ventrolateral prefrontal cortex takes place during transition of cognitive load from high to low. In addition, the activation of dorsolateral prefrontal cortex is also reduced during low cognitive load of subjects. These findings would offer justification of inability to handle high cognitive loads by people with under-developed/damaged orbitofrontal and dorsolateral prefrontal cortex.

The paper attempts to model human working memory using fuzzy relational equation with an aim to retrieve the relevant stored information in the memory from the partial input using the model. Psycho-physiological experiments have been developed to validate the model to match the model generated memory-response with the actual memory response using EEG signals acquired during memory encoding and recall phases. The fuzzy relational equation developed here represents brain connectivity in the fuzzy space between the encoding and the recall instances. The paper introduces a novel approach to compute inverse fuzzy relation with respect to max-min composition operator to determine the short-term memory information from the working memory, when the latter is stimulated with partial faces of people already encoded in the short-term memory. An error metric is defined to measure the error amplitude between the model-predicted encoding pattern and the actual pattern encoded in the short-term memory. A small value in error indicates a good accuracy of the proposed working memory model, and thus can be used to discriminate people with memory failure. Experiments undertaken reveal that the error metric could be used successfully to detect memory failures in five patients, two of which suffer from Parkinson, two from the early Alzheimer's disease and one from frontal lobe damage.

There have been many attempts to classify imbalanced data, since this classification is critical in a wide variety of applications related to the detection of anomalies, failures, and risks. Many conventional methods, which can be categorized into sampling, cost-sensitive, or ensemble, include heuristic and task dependent processes. In order to achieve a better classification performance by formulation without heuristics and task dependence, we propose confusion-matrix-based kernel logistic regression (CM-KLOGR). Its objective function is the harmonic mean of various evaluation criteria derived from a confusion matrix, such criteria as sensitivity, positive predictive value, and others for negatives. This objective function and its optimization are consistently formulated on the framework of KLOGR, based on minimum classification error and generalized probabilistic descent (MCE/GPD) learning. Due to the merits of the harmonic mean, KLOGR, and MCE/GPD, CM-KLOGR improves the multifaceted performances in a well-balanced way. This paper presents the formulation of CM-KLOGR and its effectiveness through experiments that comparatively evaluated CM-KLOGR using benchmark imbalanced datasets.

Centrifugation is often applied in laboratories and industries to increase the effective gravity on a particle and hence make it sediment faster. Based on this principle, one may extend the existing optimization techniques, which are driven by only gravitational force (objective values of discovered best solutions), and do not consider application of centrifugal force for faster convergence. We extended the Nelder-Mead's simplex algorithm, by applying an exponentially decaying centrifugal force on each of the computed vertices of the simplex. The proposed centrifugation technique was also applied on other optimization algorithms including differential evolution and gravitational search algorithms. It was seen that application of centrifugal force indeed enhanced the objective values obtained by of all the tested evolutionary algorithms. The comparative performance of the extended Nelder-Mead Algorithm was found to be better among all the tested algorithms. The algorithms were compared on the basis of the best obtained objective value after a fixed number of objective function evaluations (here 20 times the problem dimension). Testing was performed in the real world problem of EEG feature selection (from brain networks), for the classification of memory encoding versus recall using SVM. The average classification accuracy was found to be high (89.97%).

The main notion of this paper is to identify the cognitive load during a mental arithmetic task experiment using fNIRS signals. The first objective is to classify the difficulty level and the state of inactivity during the given task. To identify the classes, the feature vectors have to undergo all the possible steps of a pattern classification problem. In this paper, we have developed a novel Feature Selection technique to reduce the dimension of the feature vectors by omitting the redundant features. For this purpose, an objective function depending upon the class density or likelihood functions is optimized using the well-known Differential Evolution algorithm. General type-2 fuzzy classifier is used for subsequent classification step. The proposed Feature Selection technique gives a satisfactory accuracy results over principal component analysis. The fuzzy classifier outperforms the other well-known classifier like support vector machine, k-nearest neighborhood. Experimental result reveals that the proposed likelihood-based FS induced type 2 fuzzy classifier attains the highest classification accuracy (above 90% in each case) as compared to its standard competitors. The load of a subject undergoing the experiment is measured at a particular class relying upon the mean type- 1 fuzzy value of all feature entities. A clear discrimination in concentration level from 16 channels has been observed for each distinct feature set.

EEG based vowel classification is currently gaining importance for its increasing applications in the next generation mind-driven type-writing. This paper addresses a novel approach to classify the mentally uttered alphabets in a specific three lettered format, where the first and the last letter represent two vowel sounds and the middle is a space, where no character is imagined. Such formatting helps recognizing 26 alphabets in English language using seven vowel sounds only. To eliminate the possible infiltration of noise by parallel thoughts we used a specialized neuro-fuzzy classifier, where the first layer of the classifiers realized with fuzzy logic eliminates the possible creeping of noise due to side active channel interference. Two models of fuzzy preprocessing are used. The first one is realized with type-1 fuzzy logic, whereas the second model is realized with interval type-2 fuzzy sets. The latter model can take care of both intra- and inter-personal level uncertainty in measurements. Experiments undertaken reveal that the proposed type-2 fuzzy classifier outperforms both type-1 and traditional neural classifiers by a significant margin.

This note presents the characterization of a fuzzy variable whose possibility distribution is a convex fuzzy set.

An interval type-2 fuzzy set (IT2 FS) is characterized by its upper and lower membership functions containing all possible embedded fuzzy sets, which together is referred to as the footprint of uncertainty (FOU). The FOU results in a span of uncertainty measured in the defuzzified space and is determined by the positional difference of the centroids of all the embedded fuzzy sets taken together. This paper provides a closed-form formula to evaluate the span of uncertainty of an IT2 FS. The closed-form formula offers a precise measurement of the degree of uncertainty in an IT2 FS with a runtime complexity less than that of the classical iterative Karnik-Mendel algorithm and other formulations employing the iterative Newton-Raphson algorithm. This paper also demonstrates a real-time control application using the proposed closed-form formula of centroids with reduced root mean square error and computational overhead than those of the existing methods. Computer simulations for this real-time control application indicate that parallel realization of the IT2 defuzzification outperforms its competitors with respect to maximum overshoot even at high sampling rates. Furthermore, in the presence of measurement noise in system (plant) states, the proposed IT2 FS based scheme outperforms its type-1 counterpart with respect to peak overshoot and root mean square error in plant response.

A recurrent neural network model is designed to classify (pretrained) aromatic stimuli and discriminate noisy stimuli of both similar and different genres, using EEG analysis of the experimental subjects. The design involves determining the weights of the selected recurrent dynamics so that for a given base stimulus, the dynamics converges to one of several optima (local attractors) on the given Lyapunov energy surface. Experiments undertaken reveal that for small noise amplitude below a selected threshold, the dynamics essentially converges to fixed stable attractor. However, with a slight increase in noise amplitude above the selected threshold, the local attractor of the dynamics shifts in the neighborhood of the attractor obtained for the noise-free standard stimuli. The other important issues undertaken in this paper include a novel algorithm for evolutionary feature selection and data-point reduction from multiple experimental EEG trials using principal component analysis. The confusion matrices constructed from experimental results show a marked improvement in classification accuracy in the presence of data point reduction algorithm. Statistical tests undertaken indicate that the proposed recurrent classifier outperforms its competitors with classification accuracy as the comparator. The importance of this paper is illustrated with a tea-taster selection problem, where an olfactory perceptual-ability measure is used to rank the tasters.

The paper proposes a novel approach to recognize smell stimuli from the electroencephalogram (EEG) signals acquired during the period of inhalation. The main contribution of the paper lies in feature selection by an evolutionary algorithm and pattern classification by Differential Evolution induced Hopfield neural network. One additional merit of the work lies in data point reduction by Principal component analysis. Experiments undertaken on 25 subjects with 10 smell stimuli indicate that the proposed scheme of feature selection, data point reduction and classification outperforms the traditional approach by a wide margin. Experimental results confirm that the smell stimuli excites the pre frontal lobe of the human brain and is responsible for a special type of brain rhythms (EEG signal) in alpha-band, theta-band and delta-band.

Social networks such as Facebook, LinkedIn, or Twitter have nowadays a global reach that surpassed all previous expectations. Many social networks gather confidential information of their users, and as a result, the privacy in social networks has become a topic of general interest. To defend against

Hybrid intelligent systems play an important role in the survival prediction of breast cancer. The life-expectancy prediction of a patient is highly significant in decision making for treatments, medications and therapies. This paper addresses the motivation behind the need of hybrid model approach to survival prediction for breast cancer. The conventional approach of survival prediction faces difficulties in handling complex non-linear correlation between the prognostic factors and tumor progression, the censoring issue in medical data and the need to process the growing number of macro-scale and molecular-scale prognostic factors. The issues in breast cancer survivability are discussed with some examples of prominent works from machine learning approaches. Current trends and advancements of hybrid intelligent system are also presented.

Survival analysis is a procedure of data analysis focusing on time until an event occurs. In the medical field, predicted life expectancy is a highly significant factor in the decision making process for both the patient and the medical practitioner i.e. when making decision on palliative care and hospice referral, initiation of medications, and avoidance of aggressive therapies. The conventional statistical approach faces many challenges in handling the nature of the survival analysis datasets which often are censored data, and the difficulties in managing the complex, non-linear relationships between the prognostic factors and the patient's tumor progression. Also the statistical approach omits the need in prediction of the patient's prognosis since it does not take into account that all patients are individual and unique cases. The aim of this study is to develop a survival prediction model for breast cancer patients using Fuzzy Classifier (FC). The FC method applied is a new approach to classifying datasets with imbalanced and overlapping problems which is particularly effective in managing survival data since the data is widely known as imbalanced in nature and very rarely normally distributed. The results from a comparative study on FC, PNN and CART using Wisconsin breast cancer datasets are presented, where FC classification yields better results than the other two methods.

A problem of information separation in multichannel recordings is important in engineering applications such as brain computer/machine interfaces (BCI/BMI). Whereas this problem is not entirely new, engineering approaches connecting the mental states of humans and the observed electroencephalography (EEG) recordings are still in their infancy, mostly due to problems with electrophysiological denoising. The electrophysiological signals captured in form of the EEG carry brain activity in form of the neurophysiological components which are usually embedded in much higher power electrical muscle activity components (electromyography - EMG; electrooculography - EOG; etc.). In this paper we present an approach to remove muscular interference caused by eye-movements from EEG recorded during auditory experiments in an eight channel recording setting. This is achieved by analyzing the correlation of the oscillatory modes within a multichannel signal in the Hilbert domain. Simulations in a real world auditory BCI setting support the analysis.

We consider concept representation in the framework of conceptual spaces. We propose the introduction of fuzzy sets to express the entries of the concept (co-occurrence) matrix as fuzzy probabilities. Initial experimental results indicate that the proposed approach can support a much more sophisticated and useful concept representation.

Measuring proximity (or similarity) underlies many algorithms in information processing (by humans or indeed animals, or by machines). When the data involved are heterogeneous this issue is further complicated. This paper discusses some of the difficulties of measuring similarity between heterogeneous data and possible directions for addressing these difficulties using computational intelligence/fuzzy set based techniques. An important concept underlying the discussion is that of consistent meaning of proximity.

We define a fuzzy subspace skeleton of data points and propose an algorithm for finding it. Such a skeleton is connected with data representation: if the data points (represented as columns of a given matrix X) belong exactly to this fuzzy skeleton, then under some mild conditions we can represent X of the form X = AS uniquely (up to scaling and permutation), where the matrices A and S with dimensions m times m and m times N respectively (often called mixing matrix or dictionary and source matrix) are such that S is r-sparse in sense that each column of S has at most m - r nonzero elements. In this paper we consider the case r ges 2 and develop a fuzzy algorithm for clustering over subspaces, which is essential for identification of the mixing matrix A. The idea of this clustering is the same as in the classical fuzzy clustering problem, but instead of balls, here we cluster over subspaces with co-dimension r. For identification of the source matrix, we apply a special source recovery algorithm. We illustrate our algorithms with examples. We note that our method is quite general, since the sparseness conditions could be obtained with some preprocessing methods and no independence conditions for the source signals are imposed (in contrast to independent component analysis).

Conceptual spaces have been introduced to provide a geometrical knowledge representation. Based on it and on the fuzzy graph representation on unit space, J. T. Rickart proposed a 2-dimensional concept matrix representation across the domains used to define a concept. This paper proposes a multidimensional extension of this concept matrix.

A comparison of Bayesian and fuzzy classifiers requires a framework in which a fuzzy set can be related to a probability distribution. This study describes such a framework in which the Bayesian classifier corresponds to a particular choice of the fuzzy classifier. The proposed framework and related concepts is illustrated on a specific classification problem on a well known data set.

Banknote validation systems are used to discriminate between genuine and counterfeit banknotes. The paper proposes a one-class classifier for genuine class using a new similarity measure based on the fuzzy Hamming distance. For each banknote several regions are considered (corresponding to security features) and each region is split in m times n partitions, to include position information. The feature space used by the classifier consists of color histograms of each partition. The fuzzy Hamming distance proves to have a good discrimination power being able to completely discriminate between the genuine and counterfeit banknotes

This study evaluates the robustness of a fuzzy classifier when class distribution of the training set varies. The analysis of the results is based on the classification accuracy and ROC curves. The experimental results reported here show that fuzzy classifiers are less variant with the class distribution and less sensitive to the imbalance factor than decision trees

This work presents a road map of knowledge management for network security. To handle real-time manners and unpredictable distributions of network traffic, a sophisticated artificial intelligence needs to underlie a multi agent system architecture served as a middleware of knowledge management operations. To realize this, soft computing intrinsically plays the key roles in the most of primary knowledge management tasks.

The performance of content-based image retrieval (CBIR) systems mainly depends on the image similarity measure that it uses. The fuzzy Hamming distance (D) is an extension of the Hamming distance for real-valued vectors. Because the feature space of each image is real-valued, the fuzzy Hamming distance can be successfully used as an image similarity measure. The current study reports on the results of applying D as a similarity measure between the color histograms of two images. The fuzzy Hamming distance is suitable for this application because it can take into account not only the number of different colors but also the magnitude of this difference.

Measuring the likeness between data in different ways is an important part of pattern recognition and, over the years, many such measures have been developed. This paper proposes an asymmetric measure of likeness based on the concept of context dependent divergence. This is used to construct a numerical descriptor for images and, in conjunction with fuzzy sets, to develop a supervised learning algorithm. When applied to the problem of handwritten digit recognition, the algorithm produces promising and highly accurate results.

This paper deals with the learning concept in the presence of noise (overlap) and imbalance in the training set. The starting assumption is that recognition of the smaller class is much more important than that of the larger class. A fuzzy classifier capable of achieving this based on the relation between fuzzy sets and probability distributions as mediated by the theory of mass assignment. Two approaches to construct fuzzy sets - basic and modified - using the lpd and mpd selection rules are investigated. Preliminary results suggest that the use of mpd selection rule in conjunction with the modified approach is better for recalling the small class at a small cost to the recognition of the negative class.

We present an adjustment-to-user facility of a facial images database system in order to improve retrieval performance. The system uses linguistic (qualitative) descriptions, both in the data model and in the query language. These descriptions are internally represented as fuzzy sets. As the same linguistic descriptions can be used by different users to describe different values, the need of adjusting fuzzy sets, such that the user’s meaning is represented arises. We provide a method which, upon repeated queries by the same user, finds the best representation (as fuzzy set) of the linguistic descriptions given by the user in question. The method is based on an extension of the inverse problem of matching of fuzzy sets. Experiments show that when compared with the unadjusted system, significantly better results are obtained during the process of finding the best representation, and much better results after the best representation (given the whole database) is found.

We propose a new iterative method for inducing classification knowledge from symbolic data. Our method generates a hierarchy of clusters and does not assume a particular knowledge representation formula (e.g., a conjunctive formula, a linear discriminant function). Our method consists of two stages, i.e., the optimization and clustering stages. The first stage maps the symbolic problem into the numerical domain based on an optimization approach. In the second stage, the examples are clustered into positive, negative, and fuzzy zones using induced membership degrees. This learning procedure is iterated until the fuzzy zone becomes empty. Out method learns "topological knowledge" which is found to be useful for the evaluation of the training data quality. Further, we show that our method is useful using real world data of an industrial knowledge acquisition problem.

This paper is concerned with the integration of knowledge intensive methods with low level image processing, in order to achieve a top-down image processing system. The knowledge part contains information about the object to be recognized, the model, expressed here as a part-of hierarchy, and expert knowledge on image processing. Both of these bodies of knowledge are allowed to be imprecise and/or incomplete, in which case fuzzy logic based methods are used for representation and inference. As a consequence, uncertainty management issues, such as partial matching, and evidence combination must be addressed. The approach proposed is most suitable for complex/natural objects and is illustrated for the task of recognizing a human face.

An improved synthesis method for the multilayered neural network (NN) as function approximator is proposed. The method offers a translation mechanism that maps the qualitative knowledge into a multilayered NN structure. Qualitative knowledge is expressed in the form of representative points, which can be linguistically described as, 'when x is around x/sub i/, then y/sub i/ is around y'. Synthesis equations for the translation mechanism are provided. After the direct synthesis of the initial NN, the NN is tuned by backpropagation (BP), using the training data. The direct synthesis decreases the burden on BP and contributes to improved learning efficiency, accuracy, and stability. It is demonstrated that the translation mechanism is also useful for incremental modeling, i.e., increasing the number of neurons, or representative points, based on the results of BP.>

A connectionist mechanism for an inference problem alternative to the usual chaining method is described. The inference problem is within the scope of propositional logic that contains no variables and with some enhanced knowledge representation facilities. The method is an application of mathematical programming where knowledge and data are transformed into constraint equations. In the network, the nodes represent propositions and constraint equations, and the violation of constraints is formulated as an energy function. The inference is realized as a minimization process of the energy function using the relaxation method to search for a truth value distribution that achieves the optimum consistency with the given knowledge and data. A modified relaxation method is proposed to improve the computational inefficiencies associated with the optimization process. The behavior of the method is analyzed through examples of deductive and abductive inference and of inference with unorganized knowledge.