abstract
- This paper proposes a new robust approach to nonlinear clustering based on the Principal Component Analysis (PCA) approach. A robust c-means partition is derived by using the natural PCA noise-rejection mechanism and the nonlinearity captured by a sliding process of the clusters prototype. A non-linear extension of PCA has been developed for detecting the lower-dimensional representation of real world data sets. For these cases local linear approaches are used widely because of their computational simplicity and understandability. We will present a new method that joins (merges) the fuzzy clustering algorithm with a local sliding PCA analysis. With this strategy it is possible to identify the non-linear relations and obtain morphological information of the data. The Sliding PCA-Fuzzy cluster algorithm (SPCA-FCA) is a fuzzy clustering algorithm that estimates local principal component vectors as the vectors spanning prototypes of clusters, performed on the neighborhood of the center of cluster and normal approximations in order to estimate a tangent surface that characterizes the trend and curvature of the data points or contours region. Numerical experiments demonstrate that the proposed method is useful for capturing cluster cores by rejecting noise samples, and we can easily assess cluster validity by using cluster-crossing curves.