Low-level interpretability and high-level interpretability: a unified view of data-driven interpretable fuzzy system modelling

This paper aims at providing an in-depth overview of designing interpretable fuzzy inference models from data within a unified framework. The objective of complex system modelling is to develop reliable and understandable models for human being to get insights into complex real-world systems whose first-principle models are unknown. Because system behaviour can be described naturally as a series of linguistic rules, data-driven fuzzy modelling becomes an attractive and widely used paradigm for this purpose. However, fuzzy models constructed from data by adaptive learning algorithms usually suffer from the loss of model interpretability. Model accuracy and interpretability are two conflicting objectives, so interpretation preservation during adaptation in data-driven fuzzy system modelling is a challenging task, which has received much attention in fuzzy system modelling community. In order to clearly discriminate the different roles of fuzzy sets, input variables, and other components in achieving an interpretable fuzzy model, a taxonomy of fuzzy model interpretability is first proposed in terms of low-level interpretability and high-level interpretability in this paper. The low-level interpretability of fuzzy models refers to fuzzy model interpretability achieved by optimizing the membership functions in terms of semantic criteria on fuzzy set level, while the high-level interpretability refers to fuzzy model interpretability obtained by dealing with the coverage, completeness, and consistency of the rules in terms of the criteria on fuzzy rule level. Some criteria for low-level interpretability and high-level interpretability are identified, respectively. Different data-driven fuzzy modelling techniques in the literature focusing on the interpretability issues are reviewed and discussed from the perspective of low-level interpretability and high-level interpretability. Furthermore, some open problems about interpretable fuzzy models are identified and some potential new research directions on fuzzy model interpretability are also suggested. Crown Copyright © 2008

Extracting takagi-sugeno fuzzy rules with interpretable submodels via regularization of linguistic modifiers

In this paper, a method for constructing Takagi-Sugeno (TS) fuzzy system from data is proposed with the objective of preserving TS submodel comprehensibility, in which linguistic modifiers are suggested to characterize the fuzzy sets. A good property held by the proposed linguistic modifiers is that they can broaden the cores of fuzzy sets while contracting the overlaps of adjoining membership functions (MFs) during identification of fuzzy systems from data. As a result, the TS submodels identified tend to dominate the system behaviors by automatically matching the global model (GM) in corresponding subareas, which leads to good TS model interpretability while producing distinguishable input space partitioning. However, the GM accuracy and model interpretability are two conflicting modeling objectives, improving interpretability of fuzzy models generally degrades the GM performance of fuzzy models, and vice versa. Hence, one challenging problem is how to construct a TS fuzzy model with not only good global performance but also good submodel interpretability. In order to achieve a good tradeoff between GM performance and submodel interpretability, a regularization learning algorithm is presented in which the GM objective function is combined with a local model objective function defined in terms of an extended index of fuzziness of identified MFs. Moreover, a parsimonious rule base is obtained by adopting a QR decomposition method to select the important fuzzy rules and reduce the redundant ones. Experimental studies have shown that the TS models identified by the suggested method possess good submodel interpretability and satisfactory GM performance with parsimonious rule bases. © 2006 IEEE

Constructing accurate and parsimonious fuzzy models with distinguishable fuzzy sets based on an entropy measure

Parsimony is very important in system modeling as it is closely related to model interpretability. In this paper, a scheme for constructing accurate and parsimonious fuzzy models by generating distinguishable fuzzy sets is proposed, in which the distinguishability of input space partitioning is measured by a so-called "local" entropy. By maximizing this entropy measure the optimal number of merged fuzzy sets with good distinguishability can be obtained, which leads to a parsimonious input space partitioning while preserving the information of the original fuzzy sets as much as possible. Different from the existing merging algorithms, the proposed scheme takes into account the information provided by input-output samples to optimize input space partitioning. Furthermore, this scheme possesses the ability to seek a balance between the global approximation ability and distinguishability of input space partitioning in constructing Takagi-Sugeno (TS) fuzzy models. Experimental results have shown that this scheme is able to produce accurate and parsimonious fuzzy models with distinguishable fuzzy sets. © 2005 Elsevier B.V. All rights reserved

Constructing L2-SVM-based fuzzy classifiers in high-dimensional space with automatic model selection and fuzzy rule ranking

In this paper, a new scheme for constructing parsimonious fuzzy classifiers is proposed based on the L2-support vector machine (L2-SVM) technique with model selection and feature ranking performed simultaneously in an integrated manner, in which fuzzy rules are optimally generated from data by L2-SVM learning. In order to identify the most influential fuzzy rules induced from the SVM learning, two novel indexes for fuzzy rule ranking are proposed and named as α-values and ω-values of fuzzy rules in this paper. The α-values are defined as the Lagrangian multipliers of the L2-SVM and adopted to evaluate the output contribution of fuzzy rules, while the ω-values are developed by considering both the rule base structure and the output contribution of fuzzy rules. As a prototype-based classifier, the L2-SVM-based fuzzy classifier evades the curse of dimensionality in high-dimensional space in the sense that the number of support vectors, which equals the number of induced fuzzy rules, is not related to the dimensionality. Experimental results on high-dimensional benchmark problems have shown that by using the proposed scheme the most influential fuzzy rules can be effectively induced and selected, and at the same time feature ranking results can also be obtained to construct parsimonious fuzzy classifiers with better generalization performance than the well-known algorithms in literature. © 2007 IEEE

Classifying mental tasks based on features of higher-order statistics from EEG signals in brain-computer interface

In order to characterize the non-Gaussian information contained within the EEG signals, a new feature extraction method based on bispectrum is proposed and applied to the classification of right and left motor imagery for developing EEG-based brain-computer interface systems. The experimental results on the Graz BCI data set have shown that based on the proposed features, a LDA classifier, SVM classifier and NN classifier outperform the winner of the BCI 2003 competition on the same data set in terms of either the mutual information, the competition criterion, or misclassification rate. © 2007 Elsevier Inc. All rights reserved

Ultrasonic guided waves propagation analysis under different load tension levels in multi-wire cables

Power line structures made of multi-wire cables are normally subject to adverse environmental conditions that can affect their integrity. The applicability of several techniques has been studied as a possible structural health monitoring solution. Amongst these, Ultrasonic Guided Waves have shown great potential. The complex geometry of the multi-element cable structures complicates the waves’ propagation behaviour and therefore the signal analysis, making the monitoring of the structural integrity of the cables a challenging task. This research presents the enhancements obtained through the use of a specially designed multiple transducer collar for the inspection of the wires. The waves’ excitation capabilities of the system are experimentally evaluated under different axial unload and load tension levels. The influence of these conditions on wave propagation is analysed. The results show the technique’s long range capabilities as well as its limitations and will thereby contribute towards the design of a future structural health monitoring system.This work is part of MOSAIC project, funded by the UK government under the Innovate UK Programme. MOSAIC is a collaboration between the following organisations: Plant Integrity Ltd (Pi), Brunel Innovation Centre (BIC) Brunel University London, and Applied Inspection® (AI)

The dependence of low redshift galaxy properties on environment

We review recent results on the dependence of various galaxy properties on environment at low redshift. As environmental indicators, we use group mass, group-centric radius, and the distinction between centrals and satellites; examined galaxy properties include star formation rate, colour, AGN fraction, age, metallicity and concentration. In general, satellite galaxies diverge more markedly from their central counterparts if they reside in more massive haloes. We show that these results are consistent with starvation being the main environmental effect, if one takes into account that satellites that reside in more massive haloes and at smaller halo-centric radii on average have been accreted a longer time ago. Nevertheless, environmental effects are not fully understood yet. In particular, it is puzzling that the impact of environment on a galaxy seems independent of its stellar mass. This may indicate that the stripping of the extended gas reservoir of satellite galaxies predominantly occurs via tidal forces rather than ram-pressure.Comment: Invited Review given at the Workshop "Environment and the Formation of Galaxies: 30 years later" held in Lisbon, 6-7 September 2010. 10 pages, 5 figure

Generation of photovoltage in graphene on a femtosecond time scale through efficient carrier heating

Graphene is a promising material for ultrafast and broadband photodetection. Earlier studies addressed the general operation of graphene-based photo-thermoelectric devices, and the switching speed, which is limited by the charge carrier cooling time, on the order of picoseconds. However, the generation of the photovoltage could occur at a much faster time scale, as it is associated with the carrier heating time. Here, we measure the photovoltage generation time and find it to be faster than 50 femtoseconds. As a proof-of-principle application of this ultrafast photodetector, we use graphene to directly measure, electrically, the pulse duration of a sub-50 femtosecond laser pulse. The observation that carrier heating is ultrafast suggests that energy from absorbed photons can be efficiently transferred to carrier heat. To study this, we examine the spectral response and find a constant spectral responsivity between 500 and 1500 nm. This is consistent with efficient electron heating. These results are promising for ultrafast femtosecond and broadband photodetector applications.Comment: 6 pages, 4 figure

Construction and Application of an Electronic Spatiotemporal Expression Profile and Gene Ontology Analysis Platform Based on the EST Database of the Silkworm, Bombyx mori

An Expressed Sequence Tag (EST) is a short sub-sequence of a transcribed cDNA sequence. ESTs represent gene expression and give good clues for gene expression analysis. Based on EST data obtained from NCBI, an EST analysis package was developed (apEST). This tool was programmed for electronic expression, protein annotation and Gene Ontology (GO) category analysis in Bombyx mori (L.) (Lepidoptera: Bombycidae). A total of 245,761 ESTs (as of 01 July 2009) were searched and downloaded in FASTA format, from which information for tissue type, development stage, sex and strain were extracted, classified and summed by running apEST. Then, corresponding distribution profiles were formed after redundant parts had been removed. Gene expression profiles for one tissue of different developmental stages and from one development stage of the different tissues were attained. A housekeeping gene and tissue-and-stage-specific genes were selected by running apEST, contrasting with two other online analysis approaches, microarray-based gene expression profile on SilkDB (BmMDB) and EST profile on NCBI. A spatio-temporal expression profile of catalase run by apEST was then presented as a three-dimensional graph for the intuitive visualization of patterns. A total of 37 query genes confirmed from microarray data and RT—PCR experiments were selected as queries to test apEST. The results had great conformity among three approaches. Nevertheless, there were minor differences between apEST and BmMDB because of the unique items investigated. Therefore, complementary analysis was proposed. Application of apEST also led to the acquisition of corresponding protein annotations for EST datasets and eventually for their functions. The results were presented according to statistical information on protein annotation and Gene Ontology (GO) category. These all verified the reliability of apEST and the operability of this platform. The apEST can also be applied in other species by modifying some parameters and serves as a model for gene expression study for Lepidoptera