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P. Bauer,
E.P. Klement,
A. Leikermoser,
and B. Moser.
Interpolation and approximation of real input-output functions using fuzzy rule bases.
In Kruse R.,
J. Gebhardt,
and R. Palm, editors,Fuzzy Systems in Computer Science,
pages 245--254.
1994.
Keywords:
Fuzzy Models.
| Abstract: |
It is shown how fuzzy controllers, in particular the Mamdani and Sugeno controller, can be used to interpolate and approximate control functions, i.e., input-output functions which assign to each input value a real output value. |
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W. Brian Arthur.
Complexity Reasoning and Bounded Rationality.
Complexity in Economic Theory,
84(2):406--411,
1994.
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Bhavik R. Bakshi and George Stephanopoulos.
Representation of Process Trends -- Part IV. Induction of Real-Time Patterns from Operating Data for Diagnosis and Supervisory Control.
CCE,
18(4):303--332,
1994.
Keywords:
Decision Trees.
| Abstract: |
A methodology for pattern-based supervisory control and fault diagnosis is presented, based on the multi-scale extraction of trends from process data described in Part III of this series \cite{Bakshi:CCE:18:4a}. An explicit mapping is learned between the features extracted at multiple scales, and the corresponding process conditions, using the technique of induction by decision trees. Simple rules may be derived from the induced decision tree, to relate the relevant qualitative or quantitative features in the measured process data to process conditions. Industrial case studies from fine chemicals manufacturing, reactive crystallization and fed-batch fermentation are used to illustrate the characteristics of the pattern-based learning methodology and its application to process supervision and diagnosis. |
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Bhavik R. Bakshi and George Stephanopoulos.
Representation of Process Trends -- Part III. Multiscale Extraction of Trends from Process Data.
CCE,
18(4):267--302,
1994.
Keywords:
Wavelets,
Multiscale Analysis.
| Abstract: |
This paper presents a formal methodology for the analysis of process signals and the automatic extraction of temporal features contained in a record of measured data. It is based on the multiscale analysis of the measured signals using wavelets, which allows the extraction of significant temporal features that are localized in the frequency domain, from segments of the record of measured data (i.e.\ localized in the time domain). The paper provides a concise framework for the multiscale extraction and description of temporal process trends. The resulting algorithms are analytically sound, computationally very efficient and can be easily integrated with a large variety of methods for the interpretation of process trends and the automatic learning of relationships between causes and symptoms in a dynamic environment. A series of examples illustrate the characteristics of the approach and outline its use in various settings for the solution of industrial problems. |
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Gerardo Beni and Xiaomin Liu.
A Least Biased Fuzzy Clustering Method.
TPAMI,
16(9):954--960,
1994.
Keywords:
Clustering,
Cluster Validity Measures,
Fuzzy Clustering,
Multiscale Analysis.
| Abstract: |
A new operational definition of cluster is proposed, and a fuzzy clustering algorithm with minimal biases is formulated by making use of the Maximum Entropy Principle to maximize the entropy of the centroids with respect to the data points ({\sl clustering} entropy). We make no assumptions on the number of clusters or their initial positions. For each value of an adimensional scale parameter $\beta'$, the clustering algorithm makes each data point iterate towards one of the cluster's centroids, so that both hard and fuzzy partitions are obtained. Since the clustering algorithm can make a multiscale analysis of the given data set we can obtain both hierarchy and partitioning type clustering. The relative stability with respect to $\beta'$ of each cluster structure is defined as the measurement of cluster validity. We determine the specific value of $\beta'$ which corresponds to the optimal positions of cluster centroids by minimizing the entropy of the data points with respect to the centroids ({\sl clustered} entropy). Examples are given to show how this least-biased method succeeds in getting perceptually correct clustering results. |
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Stephen L. Chui.
Fuzzy Model Identification based on cluster estimation.
JIFS,
2:267--278,
1994.
Keywords:
Clustering,
Fuzzy c-Means,
Mountain Method,
Fuzzy Models,
Sequential/Temporal Data.
| Abstract: |
We present an efficient mountain method for estimating cluster centers of numerical data. This method can be used to determine the number of clusters and their initial values for initializing iterative optimization-based clustering algorithms such as fuzzy c-means. Here we use the cluster estimation method as the basis of a fast and robust algorithm for identifying fuzzy models. A benchmark problem involving the prediction of a chaotic time series shows this model identification method compares favourably with others, more computationally intensive methods. We also illustrate an application of this method in modeling the relationship between automobile trips and demographic factors. |
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Pau-Choo Chung,
Ching-Tsorng Tsai,
E-Liang Chen,
and Yung-Nien Sun.
Polygonal Approximation using a Competitive Hopfield Neural Network.
PR,
27(11):1505--1512,
1994.
Keywords:
Neural Networks.
| Abstract: |
Polygonal approximation plays an important role in pattern recognition and computer vision. In this paper, a parallel method using a Competitive Hopfield Neural Network (CHNN) is proposed for polygonal approximation. Based on the CHNN, the polygonal approximation is regarded as a minimization of a criterion function which is defined as the arc-to-chord deviation between the curve and the polygon. The CHNN differs from the original Hopfield network in that a competitive winner-take-all mechanism is imposed. The winner-take-all mechanism adeptly precludes the necessity of determining the values for the weighting factors in the energy function in maintaining a feasible result. The proposed method is compared to several existing methods by the approximation error norms $L_2$ and $L_\infty$ with the result that promising approximation polygons are obtained. |
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Mohamed S. Kamel and Shokri Z. Selim.
New Algorithms for Solving the Fuzzy Clustering Problem.
PR,
27(3):421--428,
1994.
Keywords:
Clustering,
Fuzzy Clustering,
Fuzzy c-Means.
| Abstract: |
Two new algorithms for fuzzy clustering are presented. Convergence of the proposed algorithms is proved. An empirical study of their convergence behaviour is discussed. The performance of the new algorithms is compared with the fuzzy c-means algorithm by testing them on four published data sets. Experimental results show that the new algorithms are faster and lead to computational savings. |
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Yael Man and Isak Gath.
Detection and Separation of Ring-Shaped Clusters Using Fuzzy Clustering.
TPAMI,
16(8):855--861,
1994.
Keywords:
Clustering,
Fuzzy Clustering,
Image Data.
| Abstract: |
A new fuzzy clustering algorithm, designed to detect and characterize ring-shaped clusters and combinations of ring-shaped and compact spherical clusters, has been developed. This FKR algorithm includes automatic search for proper initial conditions in the two cases of concentric and excentric (intersected) combinations of clusters. Validity criteria based on total fuzzy area and fuzzy density are used to estimate the optimal number of substructures in the data set. The FKR algorithm has been tested on a variety of simulated combinations of ring-shaped and compact spherical clusters, and its performance proved to be very good, both in identifying the input shapes and in recovering the input parameters. Application of the FKR algorithm to an MRI image of the heart's left ventricle was aimed to investigate the possibility of using this algorithm as an aid im image processing. |
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Norman Ramsey.
Literate programming simplified.
IEEE Transactions on Software,
11(5):97--105,
1994.
Keywords:
Literate Programming.
|