Sergiy Peredriy

Arin Chaudhuri, Carol Sadek, Deovrat Kakde et al.

Support vector data description (SVDD) is a popular anomaly detection technique. The SVDD classifier partitions the whole data space into an inlier region, which consists of the region near the training data, and an outlier region, which consists of points away from the training data. The computation of the SVDD classifier requires a kernel function, for which the Gaussian kernel is a common choice. The Gaussian kernel has a bandwidth parameter, and it is important to set the value of this parameter correctly for good results. A small bandwidth leads to overfitting such that the resulting SVDD classifier overestimates the number of anomalies, whereas a large bandwidth leads to underfitting and an inability to detect many anomalies. In this paper, we present a new unsupervised method for selecting the Gaussian kernel bandwidth. Our method exploits a low-rank representation of the kernel matrix to suggest a kernel bandwidth value. Our new technique is competitive with the current state of the art for low-dimensional data and performs extremely well for many classes of high-dimensional data. Because the mathematical formulation of SVDD is identical with the mathematical formulation of one-class support vector machines (OCSVM) when the Gaussian kernel is used, our method is equally applicable to Gaussian kernel bandwidth tuning for OCSVM.

Deovrat Kakde, Sergriy Peredriy, Arin Chaudhuri et al.

Support Vector Data Description (SVDD) is a machine learning technique used for single class classification and outlier detection. SVDD based K-chart was first introduced by Sun and Tsung for monitoring multivariate processes when underlying distribution of process parameters or quality characteristics depart from Normality. The method first trains a SVDD model on data obtained from stable or in-control operations of the process to obtain a threshold $R^2$ and kernel center a. For each new observation, its Kernel distance from the Kernel center a is calculated. The kernel distance is compared against the threshold $R^2$ to determine if the observation is within the control limits. The non-parametric K-chart provides an attractive alternative to the traditional control charts such as the Hotelling's $T^2$ charts when distribution of the underlying multivariate data is either non-normal or is unknown. But there are challenges when K-chart is deployed in practice. The K-chart requires calculating kernel distance of each new observation but there are no guidelines on how to interpret the kernel distance plot and infer about shifts in process mean or changes in process variation. This limits the application of K-charts in big-data applications such as equipment health monitoring, where observations are generated at a very high frequency. In this scenario, the analyst using the K-chart is inundated with kernel distance results at a very high frequency, generally without any recourse for detecting presence of any assignable causes of variation. We propose a new SVDD based control chart, called as $K_T$ chart, which addresses challenges encountered when using K-chart for big-data applications. The $K_T$ charts can be used to simultaneously track process variation and central tendency. We illustrate the successful use of $K_T$ chart using the Tennessee Eastman process data.