Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence
Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence
Fuzzy logic: intelligence, control, and information
Fuzzy logic: intelligence, control, and information
Support vector domain description
Pattern Recognition Letters - Special issue on pattern recognition in practice VI
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Advanced Methods in Neural Computing
Advanced Methods in Neural Computing
Time Series Analysis, Forecasting and Control
Time Series Analysis, Forecasting and Control
Sparse Greedy Matrix Approximation for Machine Learning
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Efficient Biased Sampling for Approximate Clustering and Outlier Detection in Large Data Sets
IEEE Transactions on Knowledge and Data Engineering
Approximate minimum enclosing balls in high dimensions using core-sets
Journal of Experimental Algorithmics (JEA)
Core Vector Machines: Fast SVM Training on Very Large Data Sets
The Journal of Machine Learning Research
Estimating the Support of a High-Dimensional Distribution
Neural Computation
Multiclass core vector machine
Proceedings of the 24th international conference on Machine learning
Simpler core vector machines with enclosing balls
Proceedings of the 24th international conference on Machine learning
Application of Fuzzy Logic to Approximate Reasoning Using Linguistic Synthesis
IEEE Transactions on Computers
CATSMLP: Toward a Robust and Interpretable Multilayer Perceptron With Sigmoid Activation Functions
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
A new kernel-based fuzzy clustering approach: support vector clustering with cell growing
IEEE Transactions on Fuzzy Systems
Support vector learning for fuzzy rule-based classification systems
IEEE Transactions on Fuzzy Systems
From a Gaussian mixture model to additive fuzzy systems
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
Probability density estimation from optimally condensed data samples
IEEE Transactions on Pattern Analysis and Machine Intelligence
Generalization of adaptive neuro-fuzzy inference systems
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Generalized Core Vector Machines
IEEE Transactions on Neural Networks
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While fuzzy inference systems (FISs) have been extensively studied in the past decades, the minimum enclosing ball (MEB) problem was recently introduced to develop fast and scalable methods in pattern classification and machine learning. In this paper, the relationship between these two apparently different data modeling techniques is explored. First, based on the reduced-set density estimator, a bridge between the MEB problem and the FIS is established. Then, an important finding that the Mamdani-Larsen FIS (ML-FIS) can be translated into a special kernelized MEBproblem, i.e., a center-constrainedMEB problem under some conditions, is revealed. Thus, fast kernelized MEB approximation algorithms can be adopted to construct ML-FIS in an efficient manner. Here, we propose the use of a core vector machine (CVM), which is a fast kernelized MEB approximation algorithm for support vector machine (SVM) training, to accomplish this task. The proposed fast ML-FIS training algorithm has the following merits: 1) the number of fuzzy rules can be automatically determined by the CVM training and 2) fast ML-FIS training on large datasets can be achieved as the upper bound on the time complexity of learning the parameters in ML-FIS is linear with the dataset size N and the upper bound on the corresponding space complexity is theoretically independent of N. Our experiments on simulated and real datasets confirm these advantages of the proposed training method, and demonstrate its superior robustness as well. This paper not only represents a very first study of the relationship between MEB and FIS, but it also points out the mutual transformation between kernel methods and FISs under the framework of the Gaussian mixture model and MEB.