Characterization and detection of noise in clustering
Pattern Recognition Letters
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Estimating the Support of a High-Dimensional Distribution
Neural Computation
KPCA for semantic object extraction in images
Pattern Recognition
Robust kernel PCA using fuzzy membership
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Kernel principal component analysis for content based image retrieval
PAKDD'05 Proceedings of the 9th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining
Outlier resistant PCA ensembles
KES'06 Proceedings of the 10th international conference on Knowledge-Based Intelligent Information and Engineering Systems - Volume Part III
Fuzzy auto-associative neural networks for principal component extraction of noisy data
IEEE Transactions on Neural Networks
Robust principal component analysis by self-organizing rules based on statistical physics approach
IEEE Transactions on Neural Networks
Robust kernel discriminant analysis using fuzzy memberships
Pattern Recognition
Another variant of robust fuzzy PCA with initial membership estimation
ACIIDS'11 Proceedings of the Third international conference on Intelligent information and database systems - Volume Part II
Fuzzy quartile encoding as a preprocessing method for biomedical pattern classification
Theoretical Computer Science
RF-PCA2: an improvement on robust fuzzy PCA
ACIIDS'12 Proceedings of the 4th Asian conference on Intelligent Information and Database Systems - Volume Part II
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Principal component analysis (PCA) is a mathematical method that reduces the dimensionality of the data while retaining most of the variation in the data. Although PCA has been applied in many areas successfully, it suffers from sensitivity to noise and is limited to linear principal components. The noise sensitivity problem comes from the least-squares measure used in PCA and the limitation to linear components originates from the fact that PCA uses an affine transform defined by eigenvectors of the covariance matrix and the mean of the data. In this paper, a robust kernel PCA method that extends the kernel PCA and uses fuzzy memberships is introduced to tackle the two problems simultaneously. We first introduce an iterative method to find robust principal components, called Robust Fuzzy PCA (RF-PCA), which has a connection with robust statistics and entropy regularization. The RF-PCA method is then extended to a non-linear one, Robust Kernel Fuzzy PCA (RKF-PCA), using kernels. The modified kernel used in the RKF-PCA satisfies the Mercer's condition, which means that the derivation of the K-PCA is also valid for the RKF-PCA. Formal analyses and experimental results suggest that the RKF-PCA is an efficient non-linear dimension reduction method and is more noise-robust than the original kernel PCA.