Euler principal component analysis

Principal Component Analysis (PCA) is perhaps the most prominent learning tool for dimensionality reduction in pattern recognition and computer vision. However, the ℓ 2-norm employed by standard PCA is not robust to outliers. In this paper, we propose a kernel PCA method for fast and robust PCA, which we call Euler-PCA (e-PCA). In particular, our algorithm utilizes a robust dissimilarity measure based on the Euler representation of complex numbers. We show that Euler-PCA retains PCA’s desirable properties while suppressing outliers. Moreover, we formulate Euler-PCA in an incremental learning framework which allows for efficient computation. In our experiments we apply Euler-PCA to three different computer vision applications for which our method performs comparably with other state-of-the-art approaches.