Computational geometry: an introduction
Computational geometry: an introduction
Constructing higher-dimensional convex hulls at logarithmic cost per face
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Fuzzy clustering with weighting of data variables
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems - special issue on measures and aggregation: formal aspects and applications to clustering and decision
Fuzzy Clustering Models and Applications
Fuzzy Clustering Models and Applications
Efficient and Effective Clustering Methods for Spatial Data Mining
VLDB '94 Proceedings of the 20th International Conference on Very Large Data Bases
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
A new and efficient k-medoid algorithm for spatial clustering
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part III
Nonlinear system modeling by competitive learning and adaptivefuzzy inference system
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
An adaptive fuzzy neural network for MIMO system modelapproximation in high-dimensional spaces
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Reducing the time complexity of the fuzzy c-means algorithm
IEEE Transactions on Fuzzy Systems
A contribution to convergence theory of fuzzy c-means and derivatives
IEEE Transactions on Fuzzy Systems
A fuzzy-logic-based approach to qualitative modeling
IEEE Transactions on Fuzzy Systems
A clustering technique for the identification of piecewise affine systems
Automatica (Journal of IFAC)
Identification of piecewise affine systems via mixed-integer programming
Automatica (Journal of IFAC)
Engineering Applications of Artificial Intelligence
Hybrid-fuzzy modeling and identification
Applied Soft Computing
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This paper presents an identification method for a class of dynamic system known as piecewise affine systems. Such systems are composed of a set of affine maps which relate inputs and outputs. These maps are defined in disjunctive regions in the regression space, itself composed of system inputs and outputs. The aim of the proposed method is to obtain a model of the system from a set of input-output data. This model comprises a set of submodels defined in different regions of the regression space. The proposed method is sequenced according to several stages which identify the set of submodels and the regions in which they are defined. These submodels are obtained by means of an algorithm inspired by competitive learning which rewards those that best fit the data in each region of the regression space. The method uses a process of fuzzy clustering in order to obtain a subset of representatives from the original data set, so reducing the amount of information to be processed while retaining the significant information from the original data and minimizing the effect of noise on the data.