Fuzzy Weighted Principal Component Analysis for Anomaly Detection

Principal Component Analysis (PCA) is one of the most famous unsupervised dimensionality reduction algorithms and has been widely used in many fields. However, it is very sensitive to outliers, which reduces the robustness of the algorithm.. In recent years, many studies have tried to employ \(\ell_{1}\) -norm to improve the robustness of PCA, but they all lack rotation invariance or the solution is expensive. In this paper, we propose a novel robust principal component analysis, namely, Fuzzy Weighted Principal Component Analysis (FWPCA), which still uses squared \(\ell_{2}\) -norm to minimize reconstruction error and maintains rotation invariance of PCA. The biggest bright spot is that the contribution of data is restricted by fuzzy weights, so that the contribution of normal samples are much greater than noise or abnormal data, and realizes anomaly detection. Besides, a more reasonable data center can be obtained by solving the optimal mean to make projection matrix more accurate. Subsequently, an effective iterative optimization algorithm is developed to solve this problem, and its convergence is strictly proved. Extensive experimental results on face datasets and RGB anomaly detection datasets show the superiority of our proposed method.