Fuzzy Cognitive Maps (FCMs) are considered a soft computing technique combining elements of fuzzy logic and recurrent neural networks. They found multiple application in such domains as modeling of system behavior, prediction of time series, decision making and process control. Less attention, however, has been turned towards using them in pattern classification. In this work we propose an FCM based classifier with a fully connected map structure. In contrast to methods that expect reaching a steady system state during reasoning, we chose to execute a few FCM iterations (steps) before collecting output labels. Weights were learned with a gradient algorithm and logloss or cross-entropy were used as the cost function. Our primary goal was to verify, whether such design would result in a descent general purpose classifier, with performance comparable to off the shelf classical methods. As the preliminary results were promising, we investigated the hypothesis that the performance of $d$-step classifier can be attributed to a fact that in previous $d-1$ steps it transforms the feature space by grouping observations belonging to a given class, so that they became more compact and separable. To verify this hypothesis we calculated three clustering scores for the transformed feature space. We also evaluated performance of pipelines built from FCM-based data transformer followed by a classification algorithm. The standard statistical analyzes confirmed both the performance of FCM based classifier and its capability to improve data. The supporting prototype software was implemented in Python using TensorFlow library.
FCMpy is an open source package in Python for building and analyzing Fuzzy Cognitive Maps. More specifically, the package allows 1) deriving fuzzy causal weights from qualitative data, 2) simulating the system behavior, 3) applying machine learning algorithms (e.g., Nonlinear Hebbian Learning, Active Hebbian Learning, Genetic Algorithms and Deterministic Learning) to adjust the FCM causal weight matrix and to solve classification problems, and 4) implementing scenario analysis by simulating hypothetical interventions (i.e., analyzing what-if scenarios).
Federal University of Minas Gerais（米纳斯吉拉斯联邦大学）；Federal Institute of Education Science and Technology of Northern Minas Gerais（北米纳斯吉拉斯联邦教育科学与技术学院）
Among various soft computing approaches for time series forecasting, Fuzzy Cognitive Maps (FCM) have shown remarkable results as a tool to model and analyze the dynamics of complex systems. FCM have similarities to recurrent neural networks and can be classified as a neuro-fuzzy method. In other words, FCMs are a mixture of fuzzy logic, neural network, and expert system aspects, which act as a powerful tool for simulating and studying the dynamic behavior of complex systems. The most interesting features are knowledge interpretability, dynamic characteristics and learning capability. The goal …
Tilburg University（蒂尔堡大学）；Eindhoven University of Technology（埃因霍温理工大学）；Hasselt University（哈瑟尔特大学）；Central University of Las Villas（拉斯维亚斯中央大学）；São Paulo State University（圣保罗州立大学）
This paper presents a Fuzzy Cognitive Map model to quantify implicit bias in structured datasets where features can be numeric or discrete. In our proposal, problem features are mapped to neural concepts that are initially activated by experts when running what-if simulations, whereas weights connecting the neural concepts represent absolute correlation/association patterns between features. In addition, we introduce a new reasoning mechanism equipped with a normalization-like transfer function that prevents neurons from saturating. Another advantage of this new reasoning mechanism is that it …
Time series classification is one of the very popular machine learning tasks. In this paper, we explore the application of Hidden Markov Model (HMM) for time series classification. We distinguish between two modes of HMM application. The first, in which a single model is built for each class. The second, in which one HMM is built for each time series. We then transfer both approaches for classifier construction to the domain of Fuzzy Cognitive Maps. The identified four models, HMM NN (HMM, one per series), HMM 1C (HMM, one per class), FCM NN, and FCM 1C are then studied in a series of experime…
RAND Corporation（兰德公司）；Pardee RAND Graduate School（帕迪兰德研究生院）；University of Southern California（南加州大学）
Fuzzy cognitive maps (FCMs) model feedback causal relations in interwoven webs of causality and policy variables. FCMs are fuzzy signed directed graphs that allow degrees of causal influence and event occurrence. Such causal models can simulate a wide range of policy scenarios and decision processes. Their directed loops or cycles directly model causal feedback. Their nonlinear dynamics permit forward-chaining inference from input causes and policy options to output effects. Users can add detailed dynamics and feedback links directly to the causal model or infer them with statistical learning …
Measuring Implicit Bias Using SHAP Feature Importance and Fuzzy Cognitive Maps
Eindhoven University of Technology（埃因霍温理工大学）；Eindhoven Artificial Intelligence Systems Institute（埃因霍温人工智能系统研究院）；Tilburg University（蒂尔堡大学）；Hasselt University（哈塞尔特大学）
Systems Research Institute, Polish Academy of Sciences（波兰科学院系统研究所）
Numerous learning methods for fuzzy cognitive maps (FCMs), such as the Hebbian-based and the population-based learning methods, have been developed for modeling and simulating dynamic systems. However, these methods are faced with several obvious limitations. Most of these models are extremely time consuming when learning the large-scale FCMs with hundreds of nodes. Furthermore, the FCMs learned by those algorithms lack robustness when the experimental data contain noise. In addition, reasonable distribution of the weights is rarely considered in these algorithms, which could result in the red…
Federal University of Minas Gerais（米纳斯吉拉斯联邦大学）；Federal Institute of Education Science and Technology of Northern Minas Gerais（北米纳斯吉拉斯联邦教育科技学院）；Universidade Federal de Minas Gerais（米纳斯吉拉斯联邦大学）
Fuzzy Cognitive Maps (FCMs) have emerged as an interpretable signed weighted digraph method consisting of nodes (concepts) and weights which represent the dependencies among the concepts. Although FCMs have attained considerable achievements in various time series prediction applications, designing an FCM model with time-efficient training method is still an open challenge. Thus, this paper introduces a novel univariate time series forecasting technique, which is composed of a group of randomized high order FCM models labeled R-HFCM. The novelty of the proposed R-HFCM model is relevant to merg…
University of Michigan – Ann Arbor（密歇根大学安娜堡分校）；University of Missouri – Rolla（密苏里大学罗拉分校）；GE Global Research（通用电气全球研究中心）
In this paper, we describe an algorithm FARDiff (Fuzzy Adaptive Resonance Dif- fusion) which combines Diffusion Maps and Fuzzy Adaptive Resonance Theory to do clustering on high dimensional data. We describe some applications of this method and some problems for future research.
Convolutional Neural Networks (CNNs) are artificial learning systems typically based on two operations: convolution, which implements feature extraction through filtering, and pooling, which implements dimensionality reduction. The impact of pooling in the classification performance of the CNNs has been highlighted in several previous works, and a variety of alternative pooling operators have been proposed. However, only a few of them tackle with the uncertainty that is naturally propagated from the input layer to the feature maps of the hidden layers through convolutions. In this paper we pre…
Frankfurt School of Finance & Management（法兰克福金融与管理学院）；University of Bologna（博洛尼亚大学）
There are two reasons why uncertainty may not be adequately described by Probability Theory. The first one is due to unique or nearly-unique events, that either never realized or occurred too seldom for frequencies to be reliably measured. The second one arises when one fears that something may happen, that one is not even able to figure out, e.g., if one asks: "Climate change, financial crises, pandemic, war, what next?" In both cases, simple one-to-one cognitive maps between available alternatives and possible consequences eventually melt down. However, such destructions reflect into the cha…
Stanford University（斯坦福大学）；University of Oxford（牛津大学）；University College London（伦敦大学学院）
Learning and interpreting the structure of the environment is an innate feature of biological systems, and is integral to guiding flexible behaviours for evolutionary viability. The concept of a cognitive map has emerged as one of the leading metaphors for these capacities, and unravelling the learning and neural representation of such a map has become a central focus of neuroscience. While experimentalists are providing a detailed picture of the neural substrate of cognitive maps in hippocampus and beyond, theorists have been busy building models to bridge the divide between neurons, computat…
University College London（伦敦大学学院）；Max Planck University College London Centre for Computational Psychiatry and Ageing Research（马克斯·普朗克伦敦大学学院计算精神病学与衰老研究中心）
Since machine learning models have been applied to neuroimaging data, researchers have drawn conclusions from the derived weight maps. In particular, weight maps of classifiers between two conditions are often described as a proxy for the underlying signal differences between the conditions. Recent studies have however suggested that such weight maps could not reliably recover the source of the neural signals and even led to false positives (FP). In this work, we used semi-simulated data from ElectroCorticoGraphy (ECoG) to investigate how the signal-to-noise ratio and sparsity of the neural si…
While the machine learning literature dedicated to fully automated reasoning algorithms is abundant, the number of methods enabling the inference process on the basis of previously defined knowledge structures is scanter. Fuzzy Cognitive Maps (FCMs) are neural networks that can be exploited towards this goal because of their flexibility to handle external knowledge. However, FCMs suffer from a number of issues that range from the limited prediction horizon to the absence of theoretically sound learning algorithms able to produce accurate predictions. In this paper, we propose a neural network …
Cornell University（康奈尔大学）；University of California, Davis（加利福尼亚大学戴维斯分校）；Institute of Infocomm Research (I2R), A*STAR（新加坡科技研究局资讯通信研究院）；Weill Cornell Medicine（威尔康奈尔医学院）
Most neuroimaging experiments are under-powered, limited by the number of subjects and cognitive processes that an individual study can investigate. Nonetheless, over decades of research, neuroscience has accumulated an extensive wealth of results. It remains a challenge to digest this growing knowledge base and obtain new insights since existing meta-analytic tools are limited to keyword queries. In this work, we propose Text2Brain, a neural network approach for coordinate-based meta-analysis of neuroimaging studies to synthesize brain activation maps from open-ended text queries. Combining a…
