Generating Interpretable Fuzzy Systems for Classification Problems

En este artículo se presenta un nuevo método para generar sistemas difusos interpretables, a partir de datos experimentalesde entrada y salida, para resolver problemas de clasificación. En la partición antecedente se emplean conjuntos triangulares con interpolación de 0.5 lo cual evita la presencia de solapamientos complejos que suceden en otros métodos. Los consecuentes, tipo Singleton, son generados por la proyección de los valores modales de cada función de membresía triangular en el espacio de salida y se emplea el método de mínimos cuadrados para el ajuste de los consecuentes. El método propuesto consigue una mayor precisión que la alcanzada con los métodos actuales existentes, empleando un número reducido de reglas y parámetros y sin sacrificar la interpretabilidad del modelo difuso. El enfoque propuesto es aplicado a dos problemas clásicos de clasificación: el Wisconsin Breast Cancer (WBC) y el Iris Data Classification Problem, para mostrar las ventajas del método y comparar los resultados con los alcanzados por otros investigadores.This paper presents a new method to generate interpretable fuzzy systems from training data to deal with classification problems. The antecedent partition uses triangular sets with 0.5 interpolations avoiding the presence of complex overlapping that happens in another method. Singleton consequents are generated form the projection of the modal values of each triangular membership function into the output space. Least square method is used to adjust the consequents. The proposed method gets a higher average classification accuracy rate than the existing methods with a reduced number of rules andparameters and without sacrificing the fuzzy system interpretability. The proposed approach is applied to two classical classification problems: Iris data and the Wisconsin Breast Cancer classification problem

Model-Based Feature Selection Based on Radial Basis Functions and Information Measures

In this paper the development of a new embedded feature selection method is presented, based on a Radial-Basis-Function Neural-Fuzzy modelling structure. The proposed method is created to find the relative importance of features in a given dataset (or process in general), with special focus on manufacturing processes. The proposed approach evaluates the impact/importance of processes features by using information theoretic measures to measure the correlation between the process features and the modelling performance. Crucially, the proposed method acts during the training of the process model; hence it is an embedded method, achieving the modelling/classification task in parallel to the feature selection task. The latter is achieved by taking advantage of the information in the output layer of the Neural Fuzzy structure; in the presented case this is a TSK-type polynomial function. Two information measures are evaluated in this work, both based on information entropy: mutual information, and cross-sample entropy. The proposed methodology is tested against two popular datasets in the literature (IRIS - plant data, AirFoil - manufacturing/design data), and one more case study relevant to manufacturing - the heat treatment of steel. Results show the good and reliable performance of the developed modelling structure, on par with existing published work, as well as the good performance of the feature selection task in terms of correctly identifying important process features

Self learning neuro-fuzzy modeling using hybrid genetic probabilistic approach for engine air/fuel ratio prediction

Machine Learning is concerned in constructing models which can learn and make predictions based on data. Rule extraction from real world data that are usually tainted with noise, ambiguity, and uncertainty, automatically requires feature selection. Neuro-Fuzzy system (NFS) which is known with its prediction performance has the difficulty in determining the proper number of rules and the number of membership functions for each rule. An enhanced hybrid Genetic Algorithm based Fuzzy Bayesian classifier (GA-FBC) was proposed to help the NFS in the rule extraction. Feature selection was performed in the rule level overcoming the problems of the FBC which depends on the frequency of the features leading to ignore the patterns of small classes. As dealing with a real world problem such as the Air/Fuel Ratio (AFR) prediction, a multi-objective problem is adopted. The GA-FBC uses mutual information entropy, which considers the relevance between feature attributes and class attributes. A fitness function is proposed to deal with multi-objective problem without weight using a new composition method. The model was compared to other learning algorithms for NFS such as Fuzzy c-means (FCM) and grid partition algorithm. Predictive accuracy and the complexity of the Fuzzy Rule Base System (FRBS) including number of rules and number of terms in each rule were taken as terms of evaluation. It was also compared to the original GA-FBC depending on the frequency not on Mutual Information (MI). Experimental results using Air/Fuel Ratio (AFR) data sets show that the new model participates in decreasing the average number of attributes in the rule and sometimes in increasing the average performance compared to other models. This work facilitates in achieving a self-generating FRBS from real data. The GA-FBC can be used as a new direction in machine learning research. This research contributes in controlling automobile emissions in helping the reduction of one of the most causes of pollution to produce greener environment

Computer Graphic and Photographic Image Classification using Local Image Descriptors

With the tremendous development of computer graphic rendering technology, photorealistic computer graphic images are difficult to differentiate from photo graphic images. In this article, a method is proposed based on discrete wavelet transform based binary statistical image features to distinguish computer graphic from photo graphic images using the support vector machine classifier. Textural descriptors extracted using binary statistical image features are different for computer graphic and photo graphic which are based on learning of natural image statistic filters. Input RGB image is first converted into grayscale and decomposed into sub-bands using Haar discrete wavelet transform and then binary statistical image features are extracted. Fuzzy entropy based feature subset selection is employed to choose relevant features. Experimental results using Columbia database show that the method achieves good detection accuracy

Diagnóstico del cáncer de mama empleando clasificador difuso

Los sistemas de clasificación difusa generados a partir de datos experimentales presentan una alta precisión pero a costa de sacrificar la integridad semántica del modelo difuso obtenido. En este artículo se presenta un método novedoso para generar sistemas de clasificación difusa a partir de datos, que superan el conflicto entre precisión e interpretabilidad, obteniendo modelos con particiones triangulares de solapamiento 0.5 en sus antecedentes y consecuentes tipo singleton. Para la ponderación de los antecedentes se utiliza un operador de combinación en vez de una T-norma, lo que contribuye a una reducción sustancial en el número de reglas

Attributes regrouping in Fuzzy Rule Based Classification Systems: an intra-classes approach

International audienceFuzzy rule-based classification systems (FRBCS) are able to build linguistic interpretable models, they automatically generate fuzzy if-then rules and use them to classify new observations. However, in these supervised learning systems, a high number of predictive attributes leads to an exponential increase of the number of generated rules. Moreover the antecedent conditions of the obtained rules are very large since they contain all the attributes that describe the examples. Therefore the accuracy of these systems as well as their interpretability degraded. To address this problem, we propose to use ensemble methods for FRBCS where the decisions of different classifiers are combined in order to form the final classification model. We are interested in particular in ensemble methods which split the attributes into subgroups and treat each subgroup separately. We propose to regroup attributes by correlation search among the training set elements that belongs to the same class, such an intra-classes correlation search allows to characterize each class separately. Several experiences were carried out on various data. The results show a reduction in the number of rules and of antecedents without altering accuracy, on the contrary classification rates are even improved

A Fuzzy Entropy-Based Thematic Classification Method Aimed at Improving the Reliability of Thematic Maps in GIS Environments

Thematic maps of spatial data are constructed by using standard thematic classification methods that do not allow management of the uncertainty of classification and, consequently, eval uation of the reliability of the resulting thematic map. We propose a novel fuzzy-based thematic classification method applied to construct thematic maps in Geographical Information Systems. An initial fuzzy partition of the domain of the features of the spatial dataset is constructed using triangular fuzzy numbers; our method finds an optimal fuzzy partition evaluating the fuzziness of the fuzzy sets by using a fuzzy entropy measure. An assessment of the reliability of the final thematic map is performed according to the fuzziness of the fuzzy sets. We implement our method on a GIS framework, testing it on various vector and image spatial datasets. The results of these tests confirm that our thematic classification method provide thematic maps with a higher reliability with respect to that obtained through fuzzy partitions constructed by expert users

A Rapid Soft Computing Approach to Dimensionality Reduction in Model Construction

A rapid soft computing method for dimensionality reduction of data sets is presented. Traditional approaches usually base on factor or principal component analysis. Our method applies fuzzy cluster analysis and approximate reasoning instead, and thus it is also viable to nonparametric and nonlinear models. Comparisons are drawn between the methods with two empiric data sets.Peer reviewe

A New Feature Selection Method based on Intuitionistic Fuzzy Entropy to Categorize Text Documents

Selection of highly discriminative feature in text document plays a major challenging role in categorization. Feature selection is an important task that involves dimensionality reduction of feature matrix, which in turn enhances the performance of categorization. This article presents a new feature selection method based on Intuitionistic Fuzzy Entropy (IFE) for Text Categorization. Firstly, Intuitionistic Fuzzy C-Means (IFCM) clustering method is employed to compute the intuitionistic membership values. The computed intuitionistic membership values are used to estimate intuitionistic fuzzy entropy via Match degree. Further, features with lower entropy values are selected to categorize the text documents. To find the efficacy of the proposed method, experiments are conducted on three standard benchmark datasets using three classifiers. F-measure is used to assess the performance of the classifiers. The proposed method shows impressive results as compared to other well known feature selection methods. Moreover, Intuitionistic Fuzzy Set (IFS) property addresses the uncertainty limitations of traditional fuzzy set