Outlier Detection of Functional Data Using Reproducing Kernel Hilbert Space

Abstract

The problem of finding the pattern that deviates from other observation is termed as outlier. The detection of outlier is getting importance in research area nowadays due to the reason that the technique has been used in various mission critical applications such as military, health care, fault recovery, and many. The analysis of functional data and its depth function plays a crucial role in statistical model for detecting outlier. The depth values alone not enough for finding outliers, since all the low depth values not be an outlier. The main problem of using classical model is that it cannot cop up with the high dimensionality of the data This paper proposed a novel technique based on Reproducing Kernel Hilbert Space curve (RKHS) for detecting outliers in functional data. The proposed RKHS model is based on a special Hilbert space curve associated with a kernel so that it reproduces each function in the space to enhance the performance of data depth function. The proposed method uses distance weighted discrimination classification that avoids overfitting the model and provides better generalizability in high dimensions. The kernel depths perform better performances for detection of outlier in a number of artificial and real data sets.

Recovery of Outliers in Water Environment Monitoring Data

“…The outliers in the large-scale data are recovered with the fitting method [3,4] and the prediction method [5][6][7][8] to improve the reliability of the data, but the outside factors such as pollution and weather greatly influence the water environment monitoring data, which lead to the error in the long-term model, and the outliers in water environment monitoring data will lead to the failure of the prediction method. The first step of outlier recovery is outlier detection [9]; traditional outlier detection techniques (based on classification [10], distance [11], clustering [12] and Information theory [13], etc.) are not sufficient, and some targeted methods are necessary for outlier detection in specific situations [14,15].…”