A Validity Measure for Fuzzy Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
A robust algorithm for automatic extraction of an unknown number of clusters from noisy data
Pattern Recognition Letters
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
ACM Computing Surveys (CSUR)
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
Advances in Feedforward Neural Networks: Demystifying Knowledge Acquiring Black Boxes
IEEE Transactions on Knowledge and Data Engineering
Fuzzy Sets and Systems - Clustering and modeling
Segmentation Using Eigenvectors: A Unifying View
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
The Journal of Machine Learning Research
A cluster validity index for fuzzy clustering
Pattern Recognition Letters
Estimation of Dependences Based on Empirical Data: Springer Series in Statistics (Springer Series in Statistics)
Learning Eigenfunctions Links Spectral Embedding and Kernel PCA
Neural Computation
New indices for cluster validity assessment
Pattern Recognition Letters
Performance evaluation of fuzzy classification methods designed for real time application
International Journal of Approximate Reasoning
Clustering by competitive agglomeration
Pattern Recognition
On cluster validity for the fuzzy c-means model
IEEE Transactions on Fuzzy Systems
Survey of clustering algorithms
IEEE Transactions on Neural Networks
A novel training algorithm for RBF neural network using a hybrid fuzzy clustering approach
Fuzzy Sets and Systems
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This method clusters data when the number of classes is unknown. We partition a data set with a Gaussian radial basis kernel function on pairs of feature vectors from a reduced sample to obtain a fuzzy connectivity matrix. The matrix entries are fuzzy truths that the row-column vector pairs belong to the same classes. To reduce the matrix size when the data set is large, we obtain a smaller set of representative vectors by first grouping the feature vectors into many small pre-clusters based on a new robust similarity measure. Then we use the pre-cluster centers as the reduced sample. We next map pairs of the centers via the kernel function to form the connectivity matrix entries of fuzzy values from which we determine the classes and the number of classes. Afterward, when an unknown feature vector is input for recognition, we find its nearest pre-cluster center and assign that center's class to the unknown vector. We demonstrate the method first on a simple set of linearly nonseparable synthetic data to show how it works and then apply it to the well-known difficult iris data. We also apply it to the more substantial and noisy Wisconsin breast cancer data.