Fuzzy PCA-Guided Robust $k$ -Means Clustering

This paper proposes a new approach to robust clustering, in which a robust k-means partition is derived by using a noise-rejection mechanism based on the noise-clustering approach. The responsibility weight of each sample for the k-means process is estimated by considering the noise degree of the sample, and cluster indicators are calculated in a fuzzy principal-component-analysis (PCA) guided manner, where fuzzy PCA-guided robust k-means is performed by considering responsibility weights of samples. Then, the proposed method achieves cluster-core estimation in a deterministic way. The validity of the derived cluster cores is visually assessed through distance-sensitive ordering, which considers responsibility weights of samples. 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.