José Otero

Genetic learning of accurate and compact fuzzy rule based systems based on the 2-tuples linguistic representation

One of the problems that focus the research in the linguistic fuzzy modeling area is the trade-off between interpretability and accuracy. To deal with this problem, different approaches can be found in the literature. Recently, a new linguistic rule representation model was presented to perform a genetic lateral tuning of membership functions. It is based on the linguistic 2-tuples representation that allows the lateral displacement of a label considering an unique parameter. This way to work involves a reduction of the search space that eases the derivation of optimal models and therefore, improves the mentioned trade-off. Based on the 2-tuples rule representation, this work proposes a new method to obtain linguistic fuzzy systems by means of an evolutionary learning of the data base a priori (number of labels and lateral displacements) and a simple rule generation method to quickly learn the associated rule base. Since this rule generation method is run from each data base definition generated by the evolutionary algorithm, its selection is an important aspect. In this work, we also propose two new ad hoc data-driven rule generation methods, analyzing the influence of them and other rule generation methods in the proposed learning approach. The developed algorithms will be tested considering two different real-world problems.

Obtaining linguistic fuzzy rule-based regression models from imprecise data with multiobjective genetic algorithms

Backfitting of fuzzy rules is an Iterative Rule Learning technique for obtaining the knowledge base of a fuzzy rule-based system in regression problems. It consists in fitting one fuzzy rule to the data, and replacing the whole training set by the residual of the approximation. The obtained rule is added to the knowledge base, and the process is repeated until the residual is zero, or near zero. Such a design has been extended to imprecise data for which the observation error is small. Nevertheless, when this error is moderate or high, the learning can stop early. In this kind of algorithms, the specificity of the residual might decrease when a new rule is added. There may happen that the residual grows so wide that it covers the value zero for all points (thus the algorithm stops), but we have not yet extracted all the information available in the dataset. Focusing on this problem, this paper is about datasets with medium to high discrepancies between the observed and the actual values of the variables, such as those containing missing values and coarsely discretized data. We will show that the quality of the iterative learning degrades in this kind of problems, because it does not make full use of all the available information. As an alternative to sequentially obtaining rules, we propose a new multiobjective Genetic Cooperative Competitive Learning (GCCL) algorithm. In our approach, each individual in the population codifies one rule, which competes in the population in terms of maximum coverage and fitting, while the individuals in the population cooperate to form the knowledge base.

Boosting Fuzzy Rules in Classification Problems under Single-Winner Inference

In previous studies, we have shown that an Adaboost‐based fitness can be successfully combined with a Genetic Algorithm to iteratively learn fuzzy rules from examples in classification problems. Unfortunately, some restrictive constraints in the implementation of the logical connectives and the inference method were assumed. Alas, the knowledge bases Adaboost produces are only compatible with an inference based on the maximum sum of votes scheme, and they can only use the t‐norm product to model the “and” operator. This design is not optimal in terms of linguistic interpretability. Using the sum to aggregate votes allows many rules to be combined, when the class of an example is being decided. Because it can be difficult to isolate the contribution of individual rules to the knowledge base, fuzzy rules produced by Adaboost may be difficult to understand linguistically. In this point of view, single‐winner inference would be a better choice, but it implies dropping some nontrivial hypotheses. In this work we introduce our first results in the search for a boosting‐based genetic method able to learn weighted fuzzy rules that are compatible with this last inference method.

A fast genetic method for inducting descriptive fuzzy models

Under certain inference mechanisms, fuzzy rule bases can be regarded as extended additive models. This relationship can be applied to extend some statistical techniques to learn fuzzy models from data. The interest in this parallelism is twofold: theoretical and practical. First, extended additive models can be estimated by means of the matching pursuit algorithm, which has been related to Support Vector Machines, Boosting and Radial Basis neural networks learning; this connection can be exploited to better understand the learning of fuzzy models. In particular, the technique we propose here can be regarded as the counterpart to boosting fuzzy classifiers in the field of fuzzy modeling. Second, since matching pursuit is very efficient in time, we can expect to obtain faster algorithms to learn fuzzy rules from data. We show that the combination of a genetic algorithm and the backfitting process learns faster than ad hoc methods in certain datasets.

Learning Fuzzy Linguistic Models from Low Quality Data by Genetic Algorithms

Incremental rule base learning techniques can be used to learn models and classifiers from interval or fuzzy-valued data. These algorithms are efficient when the observation error is small. This paper is about datasets with medium to high discrepancies between the observed and the actual values of the variables, such as those containing missing values and coarsely discretized data. We will show that the quality of the iterative learning degrades in this kind of problems, and that it does not make full use of all the available information. As an alternative, we propose a new implementation of a mutiobjective Michigan-like algorithm, where each individual in the population codifies one rule and the individuals in the Pareto front form the knowledge base.

Taximeter verification using imprecise data from GPS

Until recently, local governments in Spain were using machines with rolling cylinders for testing and verification of taximeters. However, the tyres condition can lead to errors in the process and the mechanical construction of the test equipment is not compatible with certain vehicles. Thus, a new measurement device should be designed. In our opinion, the verification of a taximeter will not be reliable unless measurements taken on an actual taxi run are used. Global positioning system (GPS) sensors are intuitively well suited for this process, because they provide the position and the speed with independence from those car devices that are under test. Nevertheless, since GPS measurements are inherently imprecise, GPS-based sensors are difficult to homologate. In this paper we will show how these legal problems can be solved. We propose a method for computing an upper bound of the length of the trajectory, taking into account the vagueness of the GPS data. The uncertainty in the GPS data will be modelled by fuzzy techniques. The upper bound will be computed using a multiobjective evolutionary algorithm. The accuracy of the measurements will be improved further by combining it with restrictions based on the dynamic behavior of the vehicles.

Longest path estimation from inherently fuzzy data acquired with GPS using genetic algorithms

Measuring the length of a path that a taxi must fare for is not an obvious task. When driving lower than certain threshold the fare is time dependent, but at higher speeds the length of the path is measured, and the fare depends on such measure. When passing an indoor MOT test, the taximeter is calibrated simulating a cab run, while the taxi is placed on a device equipped with four rotating steel cylinders in touch with the drive wheels. This indoor measure might be inaccurate, as information given by the cylinders is affected by tires inflating pressure, and only straight trajectories are tested. Moreover, modern vehicles with driving aids such as ABS, ESP or TCS might have their electronics damaged in the test, since two wheels are spinning while the others are not. To overcome these problems, we have designed a small, portable GPS sensor that periodically logs the coordinates of the vehicle and computes the length of a discretionary circuit. We show that all the legal issues with the tolerance of such a procedure (GPS data are inherently imprecise) can be overcome if genetic and fuzzy techniques are used to preprocess and analyze the raw data

Bootstrap analysis of multiple repetitions of experiments using an interval-valued multiple comparison procedure

A new bootstrap test is introduced that allows for assessing the significance of the differences between stochastic algorithms in a cross-validation with repeated folds experimental setup. Intervals are used for modeling the variability of the data that can be attributed to the repetition of learning and testing stages over the same folds in cross validation. Numerical experiments are provided that support the following three claims: (1) Bootstrap tests can be more powerful than ANOVA or Friedman test for comparing multiple classifiers. (2) In the presence of outliers, interval-valued bootstrap tests achieve a better discrimination between stochastic algorithms than nonparametric tests. (3) Choosing ANOVA, Friedman or Bootstrap can produce different conclusions in experiments involving actual data from machine learning tasks.

A low-cost 3D human interface device using GPU-based optical flow algorithms

Except for a few cases, nowadays it is very common to find a camera embedded in a consumer grade laptop, notebook, mobile internet device MID, mobile phone or handheld game console. Some of them also have a Graphic Processing Unit GPU to handle 3D graphics and other related tasks. This trend will probably continue in the next future and the pair camera+GPU will be more and more frequent in the market. Because of this, the proposal of this work is to use these resources in order to build a low-cost software-based 3D Human Interface Device 3D HID able to run in this kind of devices, in real time without degrading the overall performance. This is achieved implementing a parallel version of an existing Optical Flow Algorithm that runs fully in the GPU without using it at full power. In this way, usual graphic processes coexist with Optical Flow computations. To the best of authors knowledge, this approach a software-based 3D HID that runs fully in a GPU is not found in academic research nor in commercial products prototypes. Indeed, this is the salient contribution of this paper. The performance of the proposal is good enough to achieve real time in low grade computers.

Fuzzy-genetic optimization of the parameters of a low cost system for the optical measurement of several dimensions of vehicles

When designing optical measurement systems, it is common to use cameras, lenses and frame grabbers specially designed for metrology applications. These devices are expensive, therefore optical metrology is not the technology of choice in low cost applications. On the contrary to this, surveillance video cameras and home oriented frame grabbers are cheap, but imprecise. Their use introduces inaccuracies in the measurements, that sometimes can be compensated by software. Following this last approach, in this paper it is proposed to use fuzzy techniques to exploit the tolerance for imprecision of a practical metrology application (to automate the measurement of vehicle dimensions in Technical Inspection of Vehicles in Spain, the equivalent of the Ministry Of Transport Test or MOT Test in UK) and to find an economic solution. It will be shown that a genetic algorithm (GA), guided by a fuzzy characterization of the sources of error, can optimize the placement of the video cameras in a station so that these mentioned sensors can be used to take measurements within the required tolerance.