Diego S. Comas

Automatic design of interpretable fuzzy predicate systems for clustering using self-organizing maps

Abstract In the area of pattern recognition, clustering algorithms are a family of unsupervised classifiers designed with the aim to discover unrevealed structures in the data. While this is a never ending research topic, many methods have been developed with good theoretical and practical properties. One of such methods is based on self organizing maps (SOM), which have been successfully used for data clustering, using a two levels clustering approach. Newer on the field, clustering systems based on fuzzy logic improve the performance of traditional approaches. In this paper we combine both approaches. Most of the previous works on fuzzy clustering are based on fuzzy inference systems, but we propose the design of a new clustering system in which we use predicate fuzzy logic to perform the clustering task, being automatically designed based on data. Given a datum, degrees of truth of fuzzy predicates associated with each cluster are computed using continuous membership functions defined over data features. The predicate with the maximum degree of truth determines the cluster to be assigned. Knowledge is discovered from data, obtained using the SOM generalization aptitude and taking advantage of the well-known SOM abilities to discover natural data grouping when compared with direct clustering. In addition, the proposed approach adds linguistic interpretability when membership functions are analyzed by a field expert. We also present how this approach can be used to deal with partitioned data. Results show that clustering accuracy obtained is high and it outperforms other methods in the majority of datasets tested.

A survey of medical images and signal processing problems solved successfully by the application of Type-2 Fuzzy Logic

Typical problems concerning to Digital Image Processing (DIP) and to Digital Signals Processing require specific models for each particular problem and the characteristics of the data involved. However, usually these data show a high degree of uncertainty due to the acquisition system itself, noise or uncertainties related to the nature of the problem. They often require considering different points of view of experts in a single model to determine a set of rules or predicates that would achieve the desired solution. Type-2 fuzzy sets can adequately model such uncertainties. This paper presents a study on different applications of type-2 fuzzy sets in image and signal processing, analyzing the main advantages of this type of fuzzy sets in modeling uncertainties. We also review the definitions of type-2 fuzzy sets, their main properties and operations between them.

Type-2 Fuzzy Logic in Decision Support Systems

Decision Support Systems have been widely used in expert knowledge modeling. One of the known implementation approaches is through definition of Fuzzy Sets and Fuzzy Predicates, whose evaluation determines the system’s output. Despite Type-1 Fuzzy Sets have been widely used in this type of implementation, there are uncertainty sources that cannot be adequately modeled when using expert knowledge minimizing their effect on system’s output, especially when it comes from several experts opinions. Type-2 Fuzzy Sets deal with fuzzy membership degrees, which can represent adequately the typical uncertainties of these systems. In this chapter, we generalize the operators of Fuzzy Logic in order to evaluate Fuzzy Predicates with Type-2 Fuzzy Sets and we define measures to assess the degree of truth of these predicates to define the theoretical background of the Decision Support Systems using this methodology. We present an example application of decision-making and a brief discussion of the results.

Using SOM as a Tool for Automated Design of Clustering Systems Based on Fuzzy Predicates

Clustering task is a never-ending research topic. New methods are permanently proposed. In particular, Fuzzy Logic and Self-organizing Maps and their mutual cooperation have demonstrated to be interesting paradigms. We propose a general approach to obtain membership functions for a ranked clustering system based on fuzzy predicates logical operations, considering Gaussian-shaped curves. We find membership functions parameters from trained Self-organizing Maps, which generalize the statistical characteristics of data. The system is self-configured and it has the advantages of other fuzzy approaches. Clustering quality is assessed by labeled data, which allow computing accuracy. The proposal must be tested with more real datasets, though the preliminary results obtained in well-known datasets suggest that it is a promising clustering scheme.

Discovering knowledge from data clustering using automatically-defined interval type-2 fuzzy predicates

It is proposed a new clustering method based on interval type-2 fuzzy predicates. Fuzzy predicates are automatically generated from data describing clusters. Interval type-2 membership functions model variability and vagueness in clusters. Linguistic descriptions and knowledge are extracted from predicates. The method can be applied to data analysis applications. In data clustering fuzzy predicates act as cluster descriptors providing linguistically expressed knowledge which indicates how features are related to each cluster. Fuzzy predicates directly and automatically obtained from data enable discovering knowledge inside clusters, even when there is no prior-information about the clustering problem. In this work a new method for automatic discovering of interval type-2 fuzzy predicates in data clustering is proposed, called Type-2 Data-based Fuzzy Predicate Clustering (T2-DFPC). In a first stage, a data analysis is performed by making a random partition of the original data and running a clustering scheme that automatically determines the suitable number of clusters. From this stage, interval type-2 fuzzy predicates are discovered. Results obtained on very different clustering datasets show that the T2-DFPC method was consistently one of the best in terms of accuracy. The method preserves all known advantages of the interval type-2 FL to deal with problems with vagueness, quantifying the degree of truth of the fuzzy predicates and modelling the variability of the data inside the clusters. The proposed method is a fast, useful, general, and unsupervised approach for interpretable data clustering, being the knowledge-extracting capabilities one of the main contributions. Linguistic expressions can be easily adapted to match the terminology used in the field the data are related to. The predicates are able to generalize the knowledge for new cases (new data), as an intelligent system. This new approach might be surprisingly useful in contexts where, besides the clustering partition, summary information from data is of interest.

Fuzzy Mathematical Morphology Toolbox and Graphical Interface

The task of solving problems using Digital Image Processing requires of the choice of the correct methodology for the issues to be tackled, and a sound selection of parameters for each algorithm to be used. Fuzzy Mathematical Morphology is one of the existing techniques for image processing, being already applied with success on several problems of medical images analysis. However, the selection and use of its operators requires of the continual observation of the results, over a varied range of parameters, for the selection of the optimal ones. Toward that goal, in this work we develop a library of Fuzzy Mathematical Morphology operators, plus a flexible graphical interface, which is of great help in the selection of the optimal parameters and the implementation of Fuzzy operators, with the addition of several classical Image Processing operators. We describe the properties of the library and analyze the simplicity of the graphical interface.

Interpretable interval type-2 fuzzy predicates for data clustering: A new automatic generation method based on self-organizing maps

A new clustering based on interval type-2 fuzzy predicates and SOMs is proposed.SOMs are automatically configured and trained.Fuzzy predicates are generated using cluster prototypes extracted from SOMs.Linguistic knowledge is obtained from the predicates automatically generated.The proposed method overcome existing clustering methods based on fuzzy predicates. In previous works, we proposed two methods for data clustering based on automatically discovered fuzzy predicates which were referred to as SOM-based Fuzzy Predicate Clustering (SFPC) [Meschino et al., Neurocomputing, 147, 4759 (2015)] and Type-2 Data-based Fuzzy Predicate Clustering (T2-DFPC) [Comas et al., Expert Syst. Appl., 68, 136150 (2017)]. In such methods, fuzzy predicates allow both data clustering and knowledge discovering about the obtained clusters. This last feature constitutes novelty comparing to other existing approaches and it is a major contribution in the data clustering field. Based on these previous methods, in the present paper a new automatic clustering method based on fuzzy predicates is proposed which uses Self-Organizing Maps (SOMs) and is called Type-2 SOM-based Fuzzy Predicate Clustering (T2-SFPC). The new method does not require any prior knowledge about the clustering addressed. First, a random partition is defined on the dataset to be clustered and SOMs are configured and trained using the resulting data subsets. Second, an automatic clustering approach is applied on the SOM codebooks, discovering representative data of the different clusters, which are called cluster prototypes. Third, interval type-2 membership function formed by Gaussian-shape sub-functions and fuzzy predicates are defined, allowing data clustering and its interpretation. The proposed method preserves all the advantages of the previous methods SFPC and T2-DFPC in relation to the knowledge extraction capabilities and their potential application on distributed clustering and parallel computing, but results obtained on several public datasets tested showed more compactness and separation of the clusters defined by the T2-SFPC, outperforming both the previous methods and the several classical clustering approaches tested, considering internal and external validation indices. Additionally, both clustering interpretation and optimization capabilities are improved by the proposed method when compared to the methods SFPC and T2-DFPC.

Classification of Cattle Coat Color Based on Genotype Using Pattern Recognition Methods

Several current research projects are focused on the creation of haplotype maps to identify and describe common genetic variation in some species. Studies on haplotype maps are key in understanding how natural selection has produced genomic differences between subspecies of a given species. Important insight can be obtained by determining which variations in the genotype are associated with important phenotypical differences between individuals. Pattern recognition theory and machine learning techniques are useful tools to reveal this connection from a large amount of data provided by haplotype maps. In this work, we applied discrete classifiers and feature selection techniques for the prediction of cattle coat color from genotypes. We compared the performance of different classification rules and showed the feasibility of this approach for the prediction of phenotype based on genotype.