Fuzzy Cognitive Maps (FCMs) are knowledge-based recurrent neural networks that involve neural concepts and causal relationships. Despite being successful in several domains, classic FCMs often fall behind black-box models in terms of their approximation capabilities. However, the literature only reports a few studies devoted to understanding their theoretical foundations and the cause of their limited performance. In this paper, we prove that FCMs are not universal approximators and base our proof on recent theoretical findings and theorems related to the dynamic behavior of FCM-based models. Our results hold for activation functions that are bounded and monotonically increasing. These analytical findings and the empirical evidence (from the analysis of covering and proximity measures applied to synthetically generated FCMs) show that there are significant state space regions that are never produced for some problems. Consequently, classic FCM models cannot generally approximate these values, thus hindering their predictive capabilities in machine learning tasks. The same theoretical results that exposed the design weaknesses of FCMs can be used to overcome them. As the second contribution of our paper, we propose two enhanced FCM-based classifiers equipped with a quasi-nonlinear reasoning rule, together with a decision-making layer that uses derived analytical results. To fine-tune the classifiers' learnable parameters, we introduce a backpropagation-like algorithm that balances convergence and accuracy. Numerical simulations using realworld datasets indicate that our enhanced FCM-based classifiers significantly outperform the classical model.

This article presents a comprehensive approach for time-series classification. The proposed model employs a fuzzy cognitive map (FCM) as a classification engine. Preprocessed input data feed the employed FCM. Map responses, after a postprocessing procedure, are used in the calculation of the final classification decision. The time-series data are staged using the moving-window technique to capture the time flow in the training procedure. We use a backward error propagation algorithm to compute the required model hyperparameters. Four model hyperparameters require tuning. Two are crucial for the model construction: 1) FCM size (number of concepts) and 2) window size (for the moving-window technique). Other two are important for training the model: 1) the number of epochs and 2) the learning rate (for training). Two distinguishing aspects of the proposed model are worth noting: 1) the separation of the classification engine from pre- and post-processing and 2) the time flow capture for data from concept space. The proposed classifier joins the key advantage of the FCM model, which is the interpretability of the model, with the superior classification performance attributed to the specially designed pre- and postprocessing stages. This article presents the experiments performed, demonstrating that the proposed model performs well against a wide range of state-of-the-art time-series classification algorithms.

Neural networks are considered a black-box model as their strength in modeling complex interactions makes its operation almost impossible to explain. Still, neural networks remain very interesting tools as they have shown promising performance in various classification tasks. Layer-wise relevance propagation is a technique that, based on a propagation approach, is able to explain the predictions obtained by a neural network. In this work, we propose four adaptations of this technique to operate on multi-label neural networks. The proposed methods provide new ways of distributing the relevance between the output layer and the preceding ones. The efficacy of these adaptations is demonstrated after an experimental study. The study is carried out based on existing evaluation criteria in the literature that measure the explanation's quality. These methods are applied to a case study in which a neural network is used to detect secondary coinfections in patients infected with SARS-CoV-2. Overall, the proposed methods provide a post-hoc interpretability stage of the results.

Forecasting windmill time series is often the basis of other processes such as anomaly detection, health monitoring, or maintenance scheduling. The amount of data generated by windmill farms makes online learning the most viable strategy to follow. Such settings require retraining the model each time a new batch of data is available. However, updating the model with new information is often very expensive when using traditional Recurrent Neural Networks (RNNs). In this paper, we use Long Short-term Cognitive Networks (LSTCNs) to forecast windmill time series in online settings. These recently introduced neural systems consist of chained Short-term Cognitive Network blocks, each processing a temporal data chunk. The learning algorithm of these blocks is based on a very fast, deterministic learning rule that makes LSTCNs suitable for online learning tasks. The numerical simulations using a case study involving four windmills showed that our approach reported the lowest forecasting errors with respect to a simple RNN, a Long Short-term Memory, a Gated Recurrent Unit, and a Hidden Markov Model. What is perhaps more important is that the LSTCN approach is significantly faster than these state-of-the-art models.

This paper elaborates on the modeling and simulation of complex systems involving uncertainty. More explicitly, we are interested in situations in which experts hesitate about the exact values of variables when designing the model. Such situations can be modeled using Interval-valued Long-term Cognitive Networks (IVLTCNs). In this model, the activation values and the weights between neural concepts are expressed as interval grey numbers. Unlike other grey cognitive networks, our model neither imposes restrictions on the weights nor performs a whitenization process. The second contribution of this paper is a nonsynaptic grey backpropagation algorithm, which allows adjusting the learnable parameters of IVLTCNs under uncertainty conditions. Moreover, this learning algorithm does not alter the linear knowledge representations provided by domain experts during the modeling phase.

Modeling a real-world system by means of a neural model involves numerous challenges that range from formulating transparent knowledge representations to obtaining reliable simulation errors. However, that knowledge is often difficult to formalize in a precise way using crisp numbers. In this paper, we present the long-term grey cognitive networks which expands the recently proposed long-term cognitive networks (LTCNs) with grey numbers. One advantage of our neural system is that it allows embedding knowledge into the network using weights and constricted neurons. In addition, we propose two procedures to construct the network in situations where only historical data are available, and a regularization method that is coupled with a nonsynaptic backpropagation algorithm. The results have shown that our proposal outperforms the LTCN model and other state-of-the-art methods in terms of accuracy.

Fuzzy cognitive maps (FCMs) are recurrent neural networks comprised of well-defined concepts and causal relations. While the literature about real-world FCM applications is prolific, the studies devoted to understanding the foundations behind these neural networks are rather scant. In this article, we introduce several definitions and theorems that unveil the dynamic behavior of FCM-based models equipped with transfer F-functions. These analytical expressions allow estimating bounds for the activation value of each neuron and analyzing the covering and proximity of feasible activation spaces. The main theoretical findings suggest that the state space of any FCM model equipped with transfer F-functions shrinks infinitely with no guarantee for the FCM to converge to a fixed point but to its limit state space. This result in conjunction with the covering and proximity values of FCM-based models helps understand their poor performance when solving complex simulation problems.

Learning FCM models from data without any a priori knowledge and expert intervention remains a considerable problem. This research study utilizes a fully data-based learning method (the glassoFCM) for automatic design of Fuzzy Cognitive Maps (FCM) using large ordinal dataset based on the efficient capabilities of graphical lasso (glasso) models. Therefore, glasso represents its structure as a sparser graph, while maintaining a high likelihood, by producing an adjacent weighted matrix, where relationships are expressed by conditional independences. By minimizing the negative log-likelihood indicates that the model fits better to the data under the assumption that the observed data are the most likely data. The principle questioning is which of the observed concepts is the appropriate to trigger the remaining concepts in the map in order to create the glassoFCMs and obtain reasonable results. The answer derives from the FCM structure analysis based on the strength centrality indices. Moreover, the MAX-threshold algorithm based on the FCM scenario analysis is proposed in order to prune edges and retrieve sparser graphs. This algorithm shrinks the meaningless weights of the FCM, without affecting significantly the outcomes in scenario analysis. The whole approach was implemented in a business intelligence problem of evaluating the attractiveness of Belgian companies.

Fuzzy cognitive maps (FCMs) have gained popularity within the scientific community due to their capabilities in modelling and decision making for complex problems. However, learning FCM models automatically from data without any expert knowledge and/or historical data remains a considerable challenge. For our research, we use the estimated weight matrix from the graphical lasso (glasso) method with the EBIC regulation technique. Particularly, the glasso is a technique originated from machine learning which is used to model a problem by learning the weight matrix directly from a dataset. Moreover, the relationships are expressed by conditional independence among two nodes after conditioning on all the other nodes of the graph. However, the challenging task in this study is the investigation of the suitable transformation of the weight matrix from a symmetric matrix to asymmetric in order to determine the directions of the edges among the concepts and construct the glassoFCM model. For this reason, statistical comparisons are applied to examine if there are significant differences in the value of the output concept when the input concepts are rearranged according to four different cases. The whole approach was implemented in a business intelligence problem of evaluating the willingness of the employees to work in Belgian companies.

We introduce a neural cognitive mapping technique named long-term cognitive network (LTCN) that is able to memorize long-term dependencies between a sequence of input and output vectors, especially in those scenarios that require predicting the values of multiple dependent variables at the same time. The proposed technique is an extension of a recently proposed method named short-term cognitive network that aims at preserving the expert knowledge encoded in the weight matrix while optimizing the nonlinear mappings provided by the transfer function of each neuron. A nonsynaptic, backpropagation-based learning algorithm powered by stochastic gradient descent is put forward to iteratively optimize four parameters of the generalized sigmoid transfer function associated with each neuron. Numerical simulations over 35 multivariate regression and pattern completion data sets confirm that the proposed LTCN algorithm attains statistically significant performance differences with respect to other well-known state-of-the-art methods.

Pattern classification is a popular research field within the Machine Learning discipline. Black-box models have proven to be potent classifiers in this particular field. However, their inability to provide a transparent decision mechanism is often regarded as an undesirable feature. Fuzzy-Rough Cognitive Networks are granular classifiers that have proven competitive and effective in such tasks. In this paper, we examine the contribution of the FRCN's main building blocks, being the causal weight matrix and the activation values of the neurons, to the model's average performance. Noise injection is employed to this end. Our findings suggest that optimising the weight matrix might not be as beneficial to the model's performance as suggested in previous research. Furthermore, we found that a powerful activation of the neurons included in the model topology is crucial to performance, as expected. Further research should as such focus on finding more powerful ways to activate these neurons, rather than focus on optimising the causal weight matrix.

In contrast with the extense variety of machine learning algorithms, to fully automate the reasoning process, only a few can take advantage of the expert knowledge. Fuzzy Cognitive Maps (FCMs) are neural networks that can naturally integrate this kind of knowledge in the inference process. Nevertheless, FCMs have serious drawbacks difficult to overcome from the absence of an intrinsically learning algorithm or limited prediction horizon of the activation space of the neurons. Recently, some variants of the FCMs like Short-Term Cognitive Networks (STCN) and Long Term Cognitive Networks (LTCN) have been proposed to solve these problems. In this paper, we propose a new neural network model as a variant of LTCNs called Long-Term Cognitive Networks with Inputs (LTCNIs). A new kind of input neuron which is not present in the traditional FCMs approach or the derived algorithms STCNs and LTCNs is introduced, in order to model inputs like energy or mass in physical systems. The performance of the method is discussed through the modeling of a passive circuit problem. As a second contribution, a new flexible reasoning strategy, which preserves the expert knowledge through synaptic learning is presented. A synaptic learning based on a gradient descent method is implemented limited by a set of restrictions that preserves the model semantics.

Recently, a learning procedure to improve the overall convergence of sigmoid fuzzy cognitive maps used in pattern classification was proposed. The algorithm estimates the slope of each sigmoid neuron while preserving the causal weights. This paper proposes a more realistic error function for this algorithm, which is based on 1) the dissimilarity between two consecutive responses, and 2) the dissimilarity between the current output and the expected one. As a second contribution, we introduce sufficient conditions to arrive at stability features. These conditions allow assessing the accuracy-convergence tradeoff attached to the proposed learning procedure.

This research study proposes a new method for automatic design of Fuzzy Cognitive Maps (FCM) using ordinal data based on the efficient capabilities of mixed graphical models. The approach is able to model all variables on the proper domain of ordinal data by combining a new class of Mixed Graphical Models (MGMs) with a structure estimation approach based on generalized covariance matrices. It can work with a large amount of categorical data. It represents its structure as a sparser graph, while maintaining a high likelihood, by producing an adjacent weight matrix, where relationships are expressed by conditional independences. By maximizing the likelihood indicates that the model fits better to the data under the assumption that the observed data are the most likely data. The whole approach was implemented in a business intelligence problem of evaluating the attractiveness of Belgian companies. Through the analysis of results and conducted scenarios, the usefulness of the proposed MGM method for designing FCM capable to make decisions, is demonstrated. Comparisons with the previous known methodology for automatic construction of FCMs based on distance-based algorithm, showed that the proposed approach provides more understandable/useful relationships among nodes, through a less complex structure for making decisions.

After 30 years of research, challenges and solutions, Fuzzy Cognitive Maps (FCMs) have become a suitable knowledgebased methodology for modeling and simulation. This technique is especially attractive when modeling systems that are characterized by ambiguity, complexity and non-trivial causality. FCMs are well-known due to the transparency achieved during modeling tasks. The literature reports successful studies related to the modeling of complex systems using FCMs. However, the situation is not the same when it comes to software implementations where domain experts can design FCM-based systems, run simulations or perform more advanced experiments. The existing implementations are not proficient in providing many options to adjust essential parameters during the modeling steps. The gap between the theoretical advances and the development of accurate, transparent and sound FCM-based systems advocates for the creation of more complete and flexible software products. Therefore, the goal of this paper is to introduce FCM Expert, a software tool for fuzzy cognitive modeling oriented to scenario analysis and pattern classification. The main features of FCM Expert rely on Machine Learning algorithms to compute the parameters defining the model, optimize the network topology and improve the system convergence without losing information. On the other hand, FCM Expert allows performing WHAT-IF simulations and studying the system behavior through a friendly, intuitive and easy-to-use graphical user interface.

Resources can organise their work in batches, i.e. perform activities on multiple cases simultaneously, concurrently or intentionally defer activity execution to handle multiple cases (quasi-) sequentially. As batching behaviour influences process performance, efforts to gain insight on this matter are valuable. In this respect, this paper uses event logs, data files containing process execution information, as an information source. More specifically, this work (i) identifies and formalises three batch processing types, (ii) presents a resource-activity centered approach to identify batching behaviour in an event log and (iii) introduces batch processing metrics to acquire knowledge on batch characteristics and its influence on process execution. These contributions are integrated in the Batch Organisation of Work Identification algorithm (BOWI), which is evaluated on both artificial and real-life data.

In a multilabel classification problem, each object gets associated with multiple target labels. Graded multilabel classification (GMLC) problems go a step further in that they provide a degree of association between an object and each possible label. The goal of a GMLC model is to learn this mapping while minimizing a certain loss function. In this paper, we tackle GMLC problems from a Granular Computing perspective for the first time. The proposed schemes, termed as partitive granular cognitive maps (PGCMs), lean on Fuzzy Cognitive Maps (FCMs) whose input concepts represent cluster prototypes elicited via Fuzzy C-Means whereas the output concepts denote the set of existing labels. We consider three different linkages between the FCM's input and output concepts and learn the causal connections (weight matrix) through a Particle Swarm Optimizer (PSO). During the exploitation phase, the membership grades of a test object to each fuzzy cluster prototype in the PGCM are taken as the initial activation values of the recurrent network. Empirical results on 16 synthetically generated datasets show that the PGCM architecture is capable of accurately solving GMLC instances.

During the last decade Fuzzy Cognitive Maps (FCM) have become a useful tool for solving unstructured problems. In a few words they could be defined as Recurrent Neural Networks for simulating complex systems, where neurons denote concepts, objects or entities of the investigated system. Normally FCM are entirely designed using the best knowledge of a group of experts in a given domain, so frequently learning algorithms for tuning the model parameters are required. Despite the theoretical advances in such fields, the lack of a suitable computational framework for handling FCM-based systems is still an open problem. This paper introduces a novel tool for designing and simulating FCM which gathers several learning algorithms for adjusting the introduced parameters. More specifically, the framework includes supervised and unsupervised learning algorithms for computing the causal weights, algorithms for optimizing the network topology in large FCM (without losing significant information) and also methods for improving the global convergence on continuous FCM. It should be stated that these algorithms are oriented to prediction tasks, but they could be easily extended to other fields.

Fuzzy Cognitive Maps (FCM) may be defined as Recurrent Neural Networks that allow causal reasoning. According to the transformation function used for updating the activation value of concepts they can be characterized as discrete or continuous. It is remarkable that FCM having discrete neurons never exhibit chaotic states, but this premise cannot be guaranteed for FCM having continuous concepts. On the other hand, complex Sigmoid FCM resulting from experts or learning algorithms often show chaotic or cyclic patterns, therefore leading to confusing interpretation of the investigated system. The first contribution of this paper is focused on explaining why most studies on FCM stability are not applicable to FCM used on classification or decision-making tasks. Next we describe a non-direct learning methodology based on Swarm Intelligence for improving the system stability once the causal weight estimation is done. The objective here is to find a specific threshold function for each map neuron simulating an external stimulus, instead of using the same transformation function for all concepts. At the end, we can compute more stable maps, so better consistency in hidden patterns is achieved.

The goal of this article is to introduce a collaborative clustering approach to the domain of ubiquitous knowledge discovery. This clustering approach is suitable in peer-to-peer networks where different data sites want to cluster their local data as

Article Free Access Share on A data mining framework for optimal product selection in retail supermarket data: the generalized PROFSET model Authors: Tom Brijs Limburg University Centre, Universitaire Campus, B-3590 Diepenbeek Limburg University Centre, Universitaire Campus, B-3590 DiepenbeekView Profile , Bart Goethals Limburg University Centre, Universitaire Campus, B-3590 Diepenbeek Limburg University Centre, Universitaire Campus, B-3590 DiepenbeekView Profile , Gilbert Swinnen Limburg University Centre, Universitaire Campus, B-3590 Diepenbeek Limburg University Centre, Universitaire Campus, B-3590 DiepenbeekView Profile , Koen Vanhoof Limburg University Centre, Universitaire Campus, B-3590 Diepenbeek Limburg University Centre, Universitaire Campus, B-3590 DiepenbeekView Profile , Geert Wets Limburg University Centre, Universitaire Campus, B-3590 Diepenbeek Limburg University Centre, Universitaire Campus, B-3590 DiepenbeekView Profile Authors Info & Claims KDD '00: Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data miningAugust 2000 Pages 300–304https://doi.org/10.1145/347090.347156Online:01 August 2000Publication History 56citation1,552DownloadsMetricsTotal Citations56Total Downloads1,552Last 12 Months49Last 6 weeks5 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

It has been claimed that the discovery of association rules is well-suited for applications of market basket analysis to reveal regularities in the purchase behaviour of customers. Moreover, recent work indicates that the discovery of interesting rules can in fact only be addressed within a microeconomic framework. This study integrates the discovery of frequent itemsets with a (microeconomic) model for product selection (PROFSET). The model enables the integration of both quantitative and qualitative (domain knowledge) criteria. Sales transaction data from a fullyautomated convenience store is used to demonstrate the effectiveness of the model against a heuristic for product selection based on product-specific profitability. We show that with the use of frequent itemsets we are able to identify the cross-sales potential of product items and use this information for better product selection. Furthermore, we demonstrate that the impact of product assortment decisions on overall assortment profitability can easily be evaluated by means of sensitivity analysis.

This paper describes in full detail an analysis of two expert system shells: Level 5 Object and Kappa PC. The major components of these tools (knowledge representation, inference and control, developer interface, user interface and explanation facility, interface to external data sources, support and documentation) were studied and tested by means of small prototypes. Results and experiences of this work are given together with some software engineering remarks.