On the interpretability of fuzzy cognitive maps

This paper proposes a post-hoc explanation method for computing concept attribution in Fuzzy Cognitive Map (FCM) models used for scenario analysis, based on SHapley Additive exPlanations (SHAP) values. The proposal is inspired by the lack of approaches to exploit the often-claimed intrinsic interpretability of FCM models while considering their dynamic properties. Our method uses the initial activation values of concepts as input features, while the outputs are considered as the hidden states produced by the FCM model during the recurrent reasoning process. Hence, the relevance of neural concepts is computed taking into account the model’s dynamic properties and hidden states, which result from the interaction among the initial conditions, the weight matrix, the activation function, and the selected reasoning rule. The proposed post-hoc method can handle situations where the FCM model might not converge or converge to a unique fixed-point attractor where the final activation values of neural concepts are invariant. The effectiveness of the proposed approach is demonstrated through experiments conducted on real-world case studies

Measuring Implicit Bias Using SHAP Feature Importance and Fuzzy Cognitive Maps

In this paper, we integrate the concepts of feature importance with implicit bias in the context of pattern classification. This is done by means of a three-step methodology that involves (i) building a classifier and tuning its hyperparameters, (ii) building a Fuzzy Cognitive Map model able to quantify implicit bias, and (iii) using the SHAP feature importance to active the neural concepts when performing simulations. The results using a real case study concerning fairness research support our two-fold hypothesis. On the one hand, it is illustrated the risks of using a feature importance method as an absolute tool to measure implicit bias. On the other hand, it is concluded that the amount of bias towards protected features might differ depending on whether the features are numerically or categorically encoded

Forward Composition Propagation for Explainable Neural Reasoning

This paper proposes an algorithm called Forward Composition Propagation (FCP) to explain the predictions of feed-forward neural networks operating on structured classification problems. In the proposed FCP algorithm, each neuron is described by a composition vector indicating the role of each problem feature in that neuron. Composition vectors are initialized using a given input instance and subsequently propagated through the whole network until reaching the output layer. The sign of each composition value indicates whether the corresponding feature excites or inhibits the neuron, while the absolute value quantifies its impact. The FCP algorithm is executed on a post-hoc basis, i.e., once the learning process is completed. Aiming to illustrate the FCP algorithm, this paper develops a case study concerning bias detection in a fairness problem in which the ground truth is known. The simulation results show that the composition values closely align with the expected behavior of protected features. The source code and supplementary material for this paper are available at https://github.com/igraugar/fcp

Online learning of windmill time series using Long Short-term Cognitive Networks

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 on 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, update the model with the new information is often very expensive to perform 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 with 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

Towards Swarm Diversity: Random Sampling in Variable Neighborhoods Procedure Using a Lévy Distribution

Abstract. Particle Swarm Optimization (PSO) is a nondirect search method for numerical optimization. The key advantages of this metaheuristic are principally associated to its simplicity, few parameters and high convergence rate. In the canonical PSO using a fully connected topology, a particle adjusts its position by using two attractors: the best record stored for the current agent, and the best point discovered for the entire swarm. It leads to a high convergence rate, but also progressively deteriorates the swarm diversity. As a result, the particle swarm frequently gets attracted by sub-optimal points. Once the particles have been attracted to a local optimum, they continue the search process within a small region of the solution space, thus reducing the algorithm exploration. To deal with this issue, this paper presents a variant of the Random Sampling in Variable Neighborhoods (RSVN) procedure using a Lévy distribution, which is able to notably improve the PSO search ability in multimodal problems. Keywords. Swarm diversity, local optima, premature convergence, RSVN procedure, Lévy distribution. Hacia la diversidad de la bandada: procedimiento RSVN usando una distribución de Lévy Resumen. Particle Swarm Optimization (PSO) es un método de búsqueda no directo para la optimización numérica. Las principales ventajas de esta metaheurística están relacionadas principalmente con su simplicidad, pocos parámetros y alta tasa de convergencia. En el PSO canónico usando una topología totalmente conectada, una partícula ajusta su posición usando dos atractores: el mejor registro almacenado por el individuo y el mejor punto descubierto por la bandada completa. Este esquema conduce a un alto factor de convergencia, pero también deteriora la diversidad de la población progresivamente. Como resultado la bandada de partículas frecuentemente es atraída por puntos subóptimos. Una vez que las partículas han sido atraídas hacia un óptimo local, ellas continúan el proceso de búsqueda dentro de una región muy pequeña del espacio de soluciones, reduciendo las capacidades de exploración del algoritmo. Para tratar esta situación este artículo presenta una variante del procedimiento Random Sampling in Variable Neighborhoods (RSVN) usando una distribución de Lévy. Este algoritmo es capaz de mejorar notablemente la capacidad de búsqueda de los algoritmos PSO en problemas multimodales de optimización. Palabras clave. Diversidad de la bandada, óptimos locales, convergencia prematura, procedimiento RSVN, distribución de Lévy

Daño en semillas de Erythrina americana Mill., (Leguminosae: Faboideae: Erythrininae) por el brúquido Specularius impressithorax (Pic, 1932) (Coleoptera: Bruchidae) y su efecto en la germinación

The seeds of Erythrina americana Mill. are consumed by the bruchid Specularius impressithorax. Hence to evaluate the effect that the beetles can have on the sedes, the percentage of damage to E. americana seeds in the pre-dispersal stage was determined, as well as the accumulated damage during one year caused by S. impressithorax. The germination percentage of healthy and damaged seeds were evaluated. The seeds were collected in the Tulancingo Valley, Hidalgo, Mexico in December 2017. 1,272 seeds had been collected from nine different trees, which remained at least 500 m away from each other. The number of holes were counted in the seeds, that is, the number of bruchids that emerged from each seed (n = 269). The average damage percentage during the pre-dispersal of the seeds was 17.4% and for the post-dispersal stage it was 83.1%. Seeds with a bruchid exit hole germinated in 66.6%. The undamaged seeds presented a germination percentage of 2.2%, because the E. americana seeds present dormancy. The percentage of germination of the seeds with an emergency hole caused by S. impressithorax (66.6%), indicates that when an E. americana seed is consumed by a bruchid, it does not damage the embryo, and emulates a natural scarification process.Las semillas de Erythrina americana Mill., son consumidas por el brúquido Specularius impressithorax, por lo que para evaluar el efecto que pueden tener los escarabajos sobre las semillas se determinó el porcentaje de daño en semillas de E. americana en la etapa de pre-dispersión, así como el daño acumulado durante un año causado por S. impressithorax. Se evaluó el porcentaje de germinación de semillas sanas y dañadas. Las semillas se colectaron en el valle de Tulancingo, Hidalgo, México en diciembre de 2017. Se colectaron 1,272 semillas provenientes de nueve árboles diferentes, los cuales se encontraban como mínimo a 500 m de distancia uno de otro. A las semillas se les conto el número de orificios, es decir el número de brúquidos que emergieron de cada semilla (n = 269). El porcentaje de daño promedio durante la pre-dispersión de las semillas fue de 17.4 % y para la etapa post-dispersión fue de 83.1 %. Las semillas con un orificio de salida de un brúquido germinaron en un 66.6 %. Las semillas sin daño presentaron un porcentaje de germinación de 2.2 %, debido a que las semillas de E. americana presentan dormancia. El porcentaje de germinación de las semillas con un orificio de emergencia causado por S. impressithorax (66.6 %), indica que cuando una semilla de E. americana es consumida por un brúquido, éste no daña el embrión, y emula un proceso de escarificación natural

Métodos clásicos de nicho para optimización multimodal: una breve revisión

<p>En las últimas dos décadas los métodos poblacionales de optimización han sido muy usados por su capacidad para encontrar buenas soluciones con un esfuerzo bajo, convergiendo a un único óptimo global. En muchos problemas prácticos, multimodales por naturaleza, es importante hallar varias soluciones óptimas, sean locales o globales. Los métodos de nicho permiten ubicar múltiples soluciones al mantener diversidad entre los individuos de la población. En este trabajo son abordados los métodos clásicos de nicho para optimización multimodal. Además, se discuten las principales limitaciones de estas técnicas y se presentan aspectos a considerar cuando se analiza su comportamiento.</p