An Extended Multi-scale Principal Component Analysis Method and Application in Anomaly Detection

Multi-scale principal component analysis (MSPCA) can well implement multivariate information extracting on different scales, but theory foundation of MSPCA is still an open question. Using spectral decomposition of a matrix and multi-scale representation of spectral as well as multi-scale transform of a signal, an Extended multi-scale PCA (EMSPCA) method is proposed to analyze the reason why multi-scale detection method does well than single scale method. Under the uniform projection frame of EMSPCA, the relation between multi-scale detection model and those on each scale is established. Thus multi-scale anomaly detection can be implemented without establishing another new PCA model of the reconstructed data. Simulation shows the efficiency of EMSPCA anomaly detection algorithm.