Download - Evolving Fuzzy Systems
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Dr. Edwin Lughofer
Evolving Fuzzy Systems (EFS)
Methodologies, Advanced Concepts and Applications
Overview
Dr. Edwin LughoferDepartment of Knowledge-Based Mathematical Systems
Johannes Kepler University, Linz, Austria
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Dr. Edwin Lughofer
Properties of Fuzzy Systems • Models which build upon the concept of Fuzzy Logic (going back to Zadeh: truth values are fuzzified in [0,1] by MFs) •Tradeoff between
» Universal Approximation: Models with arbitrary degree of non-linearity by piecewise local approx.
» Interpretability(Readable Linguistic Terms and Rules)
• (Dark) Gray-Box Models
• Similarities Between Certain Architectures with Certain Types of Neural Networks
• Old-School (70ties, 80ties): Knowledge-Based Input
• New-School (90ties, 00s): Data-Driven Learning with Machine Learning/Optimization Techniques (genfis2, LOLIMOT, FMCLUST, ANFIS)
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Dr. Edwin Lughofer
The Idea of Evolving Fuzzy Systems
Evolving = Evolutionary
Building Up Fuzzy Systems in (Single-Pass) Incremental and Evolving Manner
with On-line Recordings/Data-Streams
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Dr. Edwin Lughofer
Concepts in Evolving Fuzzy Systems
Incrementality accounts for a step-wise (sample or block) processing of data and model building, omitting time-intensive re-training (on-line capability) Adaptivity accounts for (recursively) adapting parameters with newly loaded samples Evolving means that structural components(rules, neurons) are added on demand due to new system states, operating conditions etc. Single-Pass = Sample is loaded, sent into the incremental learning engine and discarded immediately, afterwards (achieving low computation time and virtual memory demand)
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Dr. Edwin Lughofer
Incremental Learning Example (Movement of Decision Boundary)
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Dr. Edwin Lughofer
Some (Industrial) Requirements
• Fast Online Identification of Models/Classifiers (from scratch), usage in On-line Plausibility Analysis/FD• Updating and extending already available models => improvement of generalization capability of models, preventing extrapolation => Higher Process Safety• Hybrid Modelling: Refining Knowledge-based Models with Data• Extracting models from Huge Data Bases (no loading of all data at once possible)• Enhanced Human-Machine Interaction Scenarios• Appropriate handling of drifts/shifts in data streams(gradual forgetting, out-smoothing over time)
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Dr. Edwin Lughofer
Evolving Modelling FrameworkInclusion of target values from measurement/feedback;
Never include estimated/predicted values from models (risk of self-error propagation)
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Dr. Edwin Lughofer
EFS Model Architectures
• Takagi-Sugeno Type: most frequently used, best tradeoff between accuracy and interpretability • Neuro-Fuzzy Approaches: fuzzy components embedded in neural network architecture (layers)• Mamdani Fuzzy Systems (linguistic consequents)• Fuzzy Classifiers
» Single Model Architectures » Multi-Model Architectures » [All-Pairs] (in work)
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Dr. Edwin Lughofer
Definition of a (specific) Takagi-Sugeno Fuzzy Model
Usage of product t-norm and Gaussian funcs as fuzzy sets
C rules
Linear Hyper-planes, in case of polynomials with higher order TSK models
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Dr. Edwin Lughofer
Incremental Learning of Consequent Parameters (in TS fuzzy models)Most of the EFS approaches exploit local learning by a recursive fuzzily weighted least squares (consequ. func. for each rule separately)
Fuzzy Weight
Objective Function
Inverse Hessian Matrix
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Dr. Edwin Lughofer
Local Verus Global Learning (All Params in All Rules at Once)
• More Flexibility during learning: Rules can be added, pruned or merged by not ‚disturbing‘ the recursive parameter update of the others(Global learning requires a spec. Handling of the inverse Hessian in such cases as size changes)• O(C(p+1)^2) versus O((C(p+1))^2)• More stability as dealing with smaller Hessian matrices • Local feature weighing capability (per local region)• Better Interpretability (piecewise linear approx. along real trend of curve)
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Dr. Edwin Lughofer
Comparison Global vs Local Estimation: Consequent Functions
Consequent Functions obtained by global estimation -> not interpretable
Consequent Functions obtained by local estimation -> interpretable (piecewise local tendencies of
variables (gradients))
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Dr. Edwin Lughofer
Success Cases of Consequ. Adaptation
Model Refinement
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Dr. Edwin Lughofer
Success Cases of Consequ. Adaptation
Closure of Data Hole
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Dr. Edwin Lughofer
Success Cases of Consequ. Adaptation
Slight Range Extension
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Dr. Edwin Lughofer
Failure Cases (Consequ. Adaptation)
Strong Changing Behavior
Bad Approx.
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Dr. Edwin Lughofer
Failure Cases (Consequ. Adaptation)
Significant Range Extension
Bad Approx.
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Dr. Edwin Lughofer
Failure Cases (Consequ. Adaptation)
FAZIT: Consequent adaptation not sufficient => Evolving Components Required
Bad Approx.
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Dr. Edwin Lughofer
Advanced Issues in Consequent Adaptation Orthogonal Regressors: If regressors could be made orthogonal (in incremental manner synchronously to the model updates), dynamic feature selection (discarding, adding features)would be possible as each consequent parameter can be estimated separately
Possibility: via Principal Fuzzy Component Regression using iPCA + EFS
Jth Consequent in Ith Rule
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Dr. Edwin Lughofer
Advanced Issues in Consequent Adaptation Alternative Optimization Function: including punishment terms as least squares is biased towards over-fitting (fits error on training data)
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Dr. Edwin Lughofer
Possible Alternatives
In-Sample Error:
Rule-Based Constrained Least-Squares (Solution in Batch exists: SparseFIS)
Generalized Total Least Squares (Modeling error in inputs)
No incremental/recursive optimization method exists for these
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Dr. Edwin Lughofer
Incremental Learning of Non-Linear Antecedent Parameters
Update of only one
param in one cycle
Recursive LM (used in EFP)
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Dr. Edwin Lughofer
EFS Approaches (Alphabetically)
DENFIS (Kasabov) ePL (Lima, Ballini and Gomide) eTS (Angelov and Filev) FLEXFIS (Lughofer) SAFIS (Rong et al.) SEIT2FNN (Juang, Tsao) SOFNN (Leng et al.) SONFIN (Juang and Lin)
Bottom Line: Most of these are using TS fuzzy systems and R(FW)LS; antecedent learning and rule evolutionare performed with different concepts
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Dr. Edwin Lughofer
FLEXFIS: Antecedent Learning (AL) and Rule Evolution (RE)
AL and RE is performed in the Clustering Space => each cluster is associated with one rule (local region) evolving version of Vector Quantization (basic) (eVQ, Lughofer 2008): Three central steps: Checking whether new sample fits into current cluster
parition (distance to nearest cluster higher than vigilance) Movement of winning = nearest cluster towards current
sample
Update of ranges of influence of winning cluster
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Dr. Edwin Lughofer
Example Rule Evolution / Update
Movement Horizon (bounded by vigilance)
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Dr. Edwin Lughofer
Cluster Projection => Forming Fuzzy Sets and Rules
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Dr. Edwin Lughofer
Extensions to eVQ
Deletion of Cluster Satellites
Usage of Mahalanobis Distance (Ellip. in Arb. Pos.) New Distance Measure Concept (to Surface instead of Center) Integration of Feature Weights for Classification (preventing generation of superfluous clusters due to large distances in unimportant dimensions)
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Dr. Edwin Lughofer
Feature Weight Integration (Example)
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Dr. Edwin Lughofer
Combining Antecedent with Consequent Learning
Problem: structural change in Fuzzy Systems in each inc. learning cycle => Convergence to Optimality in LS sense not guaranteed Integration of Correction Terms (before RFWLS)
No explicit calculation of correction terms achieved so far, but partial results: Decreasing sequence of correction terms towards 0 In a Quasi-monotonic fashion => Sum of correction
terms bounded
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Dr. Edwin Lughofer
Block-size versus Accuracy (Example)
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Dr. Edwin Lughofer
Success of Update with FLEXFIS
Update Params only Update Structure + Params
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Dr. Edwin Lughofer
Success of Update with FLEXFIS
Update Params only Update Structure + ParamsUpdate Structure + Params
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Dr. Edwin Lughofer
Variants of FLEXFIS (FLEXFIS Family)
FLEXFIS for Regression (previous Slides)Edwin Lughofer. FLEXFIS: A Robust Incremental Learning Approach for Evolving
TS Fuzzy Models, IEEE Trans. On Fuzzy Systems, vol. 16 (6), pp. 1393-1410, 2008
FLEXFIS for Classification using Single-Model Architectures (FLEXFIS-Class SM)
FLEXFIS for Classification using Multi-Model Architectures (FLEXFIS-Class MM) K TS-Fuzzy Models based on Indicator Entries for K Classes One-versus-rest classificationEdwin Lughofer, Plamen Angelov and Xiaowei Zhou.Evolving Single- and Multi-Model Fuzzy
Classifiers with FLEXFIS-Class, in Proceedings of FUZZ-IEEE 2007, pp. 363-368, London, UK, 2007
eVQ-Class (Clustering-based Classifier)Edwin Lughofer, On-line Evolving Image Classifiers and Their Application to Surface
Inspection, Image and Vision Computing, Vol. 28 (7), pp. 1065-1079, 2010
Singleton Consequents
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Dr. Edwin Lughofer
FLEXFIS-Class MM: Solving Masking Effect of Linear Regression by Indicator
Linear Regr. By Indicator matrix, 3 classes => red class nowhere
maximal (masking)
Fuzzy regression by indicator matrix, 3 classes
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Dr. Edwin Lughofer
eVQ-Class: Classification Strategy Variant B (distance and class weight)
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Dr. Edwin Lughofer
Advanced Concepts (For more Process-Safety and Robustness) • Instabilities in the learning process (ill-posed problems)
• Solution by regularization (Tichonov, sparsity constraints, parameter choice rules)
• Upcoming drifts and shifts in on-line data streams» Solution by Drift detection (rule ages) and reaction
(gradual forgetting) (Lughofer and Angelov, ASOC, 2010)
• Situations causing an unlearning effect (in steady states) (Lughofer, EFS’06, Book Chapter EIS 2010)
» Solution by Updating only significantly firing rules• Outliers and faults in on-line data streams
» Rule base procrastination » Features characterizing outlook/behav. of clusters/rules
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Dr. Edwin Lughofer
Drift Reaction - Example
Conventional Update =>
cluster joins both distribution
Update with forgetting => Cluster covers new
distribution (old samples
completely forgotten
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Dr. Edwin Lughofer
Outlier and Faults in Regression Modelling (Example)
Single Outlier Systematic Faults
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Dr. Edwin Lughofer
Advanced Concepts (For more Process-Safety and Robustness)
Uncertainties in the models due to high noise levels or lack of data Adaptive local error bars in regression problems (for
evolving TS fuzzy models) (Lughofer, Guardiola EFS’ 08) Concept of conflict and ignorance, confidence levels
in class responses account for conflict, maximal firing degree of rules for ignorance
Extrapolation situations for new samples to be predicted (regression problems) (Lughofer, 2006/2010) Omittance of reactivation of inner Fuzzy Sets
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Dr. Edwin Lughofer
Adaptive Local Error Bars (Example)
Constant Error bands Adaptive Local error bars
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Dr. Edwin Lughofer
Reactivation Inner Sets
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Dr. Edwin Lughofer
Improving Performance and Increasing Useability
Dynamic (On-line) rule split-and-merge Strategies overcoming local redundancies (Lughofer and Bouchot, IEEE SMC-B
2011, submitted) and changing distributions over time
Dynamic soft dimension reduction with incremental feature weighting (Lughofer, Fuzzy Sets and Systems, 2010) Contributes to changing feature importance levels = weights during
incremental learning in smooth manner
Active and semi-supervised learning (for reducing annotation effort of operators) (Lughofer, ICMLA 2010)
Incremental Classifier Fusion (Sannen, Lughofer et al, IDA, 2010): exploiting diversity of classifiers for boosting performance
Alternatives to Incremental/Evolving Learning: Lazy Learning
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Dr. Edwin Lughofer
Problem of Rule Update/Movement
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Dr. Edwin Lughofer
Example Merged Solutions (Strongly Overlapping Rules)
Merging formula of two clusters
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Dr. Edwin Lughofer
Motivation Soft Dimension Reduction
Task: Combining Dimensionality Reduction with On-Line Evolution of Classifiers in an Incremental andHomogenous Manner
• One Possibility: A Priori Feature Selection (as Filters, Expert-Knowledge) keeping fixed during Incremental Learning Phase => static, no exchange of inputs
• Another Poss. : Incremental Feature SelectionSynchronously to Update of Fuzzy Classifiers
Problem with Inc. Feature Selection: How to exchange input features in EFC dynamically, on-the-fly without re-training phase??
Input Features Cycle #1: 1, 5, 9, 15, 20
Input Features Cycle #2: 1, 5, 9, 12, 20Exchange of Feat #12 with #15 in the list
of 5 most important ones
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Dr. Edwin Lughofer
Our Approach SummaryExploiting Generalization Concept of IncrementalFeature Selection = Incremental Feature Weighting=> Assigning Weights in [0,1] to Features According to
their Importance Levels (0 = Not important, 1 = veryimportant) – measured by LOFO and Dy-Brodley‘s sep. criterionAchievements (Lughofer, Fuzzy Sets and Systems 2010):
• Soft Dimension Reduction (Features whose weightsare approaching 0 are nearly discarded)
• Dynamic Dimension Reduction (Feature Weightsare incrementally updated)
• Smooth Learning Behavior: sample-wise inc. learning changes the impact of features step-wisecontinuously
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Dr. Edwin Lughofer
Interpretability Issues (To be handled in current FWF/DFG Project) Reduction of Unnecessary Complexity
Methods for improving Interpretability of EFS Linguistic interpretability (readability,
understandability of the rules and granules, consistency)
Visual interpretability (tracking development of fuzzy sets, rules over time, visual transparency in GUI)
Reliability issues (how reliable is the evolved model in its predictions)
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Dr. Edwin Lughofer
Applications (Overview) On-line System Identification and Prediction Multi-Channel Measurement Systems (static) Prediction Models for NOx Emission (static+dynamic+mixed) Prediction Models for Resistance Value (dynamic)
On-line Fault and Anomaly Detection In stationary data (from multi-channel system) In time series data (dynamic modelling) In audio data (noise detection, analogue tapes)
Visual Inspection Systems On-line Image Classification in Surface Inspection Problems Emotion-based perception modelling (for visual textures)
Potential Future Applications Chemometric Modelling (high-dim spectral data) Enhanced Human-Machine Interaction Systems
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Dr. Edwin Lughofer
Results NOx Prediction Models(Comparison Physical versus EFS)
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Dr. Edwin Lughofer
Results Non-Linear Dynamic SysID
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Dr. Edwin Lughofer
Results Rolling Mills (Prediction of Resistance Values)
Drift of the Error as no forgetting of older stitches takes place
No drift of the error as forgetting older stitches
achieves more flex.
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Dr. Edwin Lughofer
Online FD Framework
Anomaly Detection in Res Signal
FLEXFIS
Adaptive Local Error Bars
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Dr. Edwin Lughofer
On-line Image Classification Framework (for Surface Inspection)
HMI 1: Incorporating On-Line Operator‘s(s‘) Feedback into Classifier: Inc./Evolv Classifiers
HMI 2: Handling Input from Multiple Operators
HMI 3: Handling Variable Levels of Detail in Operators Inputs
HMI 4: Accomodating Partial Confidence of Operators
HMI 5: Operator Insight and Enhanced Interaction (Model Level)
E. Lughofer, J.E. Smith, M. A. Tahir, C. Eitzinger, D. Sannen, „Human–Machine Interaction Issues in Quality ControlBased on On-Line Image Classification“, IEEE Trans. On Systems, Man and Cybernetics, part A: Systems and
Humans, vol. 39(5), pp. 960-971, 2009
Deviation to Master
Automatic ROI extraction
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Dr. Edwin Lughofer
CV Accuracies Surface Inspection Problems (class. into good and bad)
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Dr. Edwin Lughofer
Accuracies on Separate Test Data Static vs. Evolved Image Classifiers
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Dr. Edwin Lughofer
Impact of Incremental Feature Weighting
Evolution of Test Accuracies
for Egg Data Set
Number of features with weights more than 0.05 resp. 0.8
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Dr. Edwin Lughofer
Impact Incremental Classifier Fusion
Evolution of Test Accuracies using 3 base
classifiers
Evolution of Test Accuracies using
ensemble classifiers (exploiting diversity of
base cl.)
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Dr. Edwin Lughofer
List of References• Basic Algos (FLEXFIS):• Edwin Lughofer. FLEXFIS: A Robust Incremental Learning Approach for Evolving TS Fuzzy Models, IEEE
Transactions on Fuzzy Systems, vol. 16 (6), pp. 1393-1410, 2008• Edwin Lughofer. Extensions of Vector Quantization for Incremental Clustering, Pattern Recognition, vol. 41(3),
pp. 995-1011, 2008• Edwin Lughofer, Plamen Angelov, Xiaowei Zhou. Evolving Fuzzy Classifiers using Different Model
Architectures, Fuzzy Sets and Systems, vol.159 (23), pp. 3160-3182, 2008• Edwin Lughofer, Plamen Angelov and Xiaowei Zhou, Evolving Single- and Multi-Model Classifiers with
FLEXFIS-Class, in Proceedings of FUZZ-IEEE 2007, pp. 363-368, London, UK, 2007• Edwin Lughofer. Evolving Vector Quantization for Classification of On-line Data Streams, Proc. of the
International Conference on Computational Intelligence for Modelling, Control and Automation (CIMCA), pp. 780-786, Vienna, 2008
• Advanced Concepts in EFS:• Edwin Lughofer, On-line Incremental Feature Weighting in Evolving Fuzzy Classifiers, Fuzzy Sets and
Systems, to appear• Edwin Lughofer and Plamen Angelov, Handling Drifts and Shifts in On-Line Data Streams with Evolving Fuzzy
Systems, Applied Soft Computing, in press• Davy Sannen, Edwin Lughofer and Hendrik van Brussel, Towards Incremental Classifier Fusion, Intelligent Data
Analysis, Vol. 14 (1), pp. 3-30, 2010• Edwin Lughofer. Towards Robust Evolving Fuzzy Systems, book chapter in Evolving Intelligent Systems –
Methodologies and Applications, editors: Plamen Angelov, Dimitar Filev and Nik Kasabov, John Wiley and Sons, 2010, pp. 87-126
• Edwin Lughofer. Process Safety Enhancements for Data-Driven Evolving Fuzzy Models. In Proceedings of the International Symposium on Evolving Fuzzy Systems (EFS), pp. 42-48, Lake District, UK, September 2006 (awarded as best paper)
• Edwin Lughofer, Jean-Luc Bouchot, On-line Elimination of Local Redundancies in Evolving Fuzzy Systems, IEEE Transactions on Systems, Man and Cybernetics, part B: Cybernetics, submitted
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Dr. Edwin Lughofer
List of References (cont‘d)
• Applications:
• Edwin Lughofer, On-line Evolving Image Classifiers and Their Application to Surface Inspection, Image and Vision Computing (special issue of on-line pattern recognition and machine learning techniques for computer vision), Vol. 28 (7), pp. 1065-1079, 2010
• Edwin Lughofer, Carlos Guardiola, Vicente Macian, Erich Peter Klement, Identifying Static and Dynamic Prediction Models for NOx emissions, in revision, Applied Soft Computing
• E. Lughofer, J.E. Smith, M. A. Tahir, C. Eitzinger, D. Sannen, Human–Machine Interaction Issues in Quality Control Based on On-Line Image Classification, IEEE Trans. On Systems, Man and Cybernetics, part A: Systems and Humans, vol. 39(5), pp. 960-971, 2009
• Christian Eitzinger, Wolfgang Heidl, Edwin Lughofer, Stefan Raiser, James E. Smith, Muhammad A. Tahir, Davy Sannen and Hendrik van Brussel, Assessment of the Influence of Adaptive Components in Trainable Surface Inspection Systems, Machine Vision and Applications, Vol. 21 (5), pp. 613-626, 2010
• Edwin Lughofer and Carlos Guardiola. On-Line Fault Detection with Data-Driven Evolving Fuzzy Models. Control and Intelligent Systems, vol. 36 (4), pp. 307-317, 2008
• D. Sannen, M. Nuttin, J.E. Smith, M.A. Tahir, P. Caleb-Solly, E. Lughofer, C. Eitzinger. An On-line Self-adaptive and Interactive Image Classification Framework, in International Conference on Computer Vision Systems 2008, A. Gasteratos, M. Vincze, J.K. Tsotsos (Eds.), Springer Lecture Notes 5008, pp. 171-180, Santorini Island, Greece
• Edwin Lughofer and Carlos Guardiola. Applying Evolving Fuzzy Models with Adaptive Local Error Bars to On-line Fault Detection, in Proc. of the 3rd International Workshop on Genetic and Evolving Fuzzy Systems, GEFS 2008, pp. 35-40, Witten-Bommerholz (Germany) (awarded as best paper finalist)
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Dr. Edwin Lughofer
Monography
Edwin Lughofer
Evolving Fuzzy Systems Methodologies Advanced Concepts Applications
To be submitted to Springer (Heidelberg) in November 2010 (approx. 150 figures, 250 images, 460 pages)
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Dr. Edwin Lughofer
Thank you for your attention!