A New SVDD-Based Multivariate Non-parametric Process Capability Index

Process capability index (PCI) is a commonly used statistic to measure ability of a process to operate within the given specifications or to produce products which meet the required quality specifications. PCI can be univariate or multivariate depending upon the number of process specifications or quality characteristics of interest. Most PCIs make distributional assumptions which are often unrealistic in practice. This paper proposes a new multivariate non-parametric process capability index. This index can be used when distribution of the process or quality parameters is either unknown or does not follow commonly used distributions such as multivariate normal

Automatic Hyperparameter Tuning Method for Local Outlier Factor, with Applications to Anomaly Detection

In recent years, there have been many practical applications of anomaly detection such as in predictive maintenance, detection of credit fraud, network intrusion, and system failure. The goal of anomaly detection is to identify in the test data anomalous behaviors that are either rare or unseen in the training data. This is a common goal in predictive maintenance, which aims to forecast the imminent faults of an appliance given abundant samples of normal behaviors. Local outlier factor (LOF) is one of the state-of-the-art models used for anomaly detection, but the predictive performance of LOF depends greatly on the selection of hyperparameters. In this paper, we propose a novel, heuristic methodology to tune the hyperparameters in LOF. A tuned LOF model that uses the proposed method shows good predictive performance in both simulations and real data sets.Comment: 15 pages, 5 figure

Fast Incremental SVDD Learning Algorithm with the Gaussian Kernel

Support vector data description (SVDD) is a machine learning technique that is used for single-class classification and outlier detection. The idea of SVDD is to find a set of support vectors that defines a boundary around data. When dealing with online or large data, existing batch SVDD methods have to be rerun in each iteration. We propose an incremental learning algorithm for SVDD that uses the Gaussian kernel. This algorithm builds on the observation that all support vectors on the boundary have the same distance to the center of sphere in a higher-dimensional feature space as mapped by the Gaussian kernel function. Each iteration involves only the existing support vectors and the new data point. Moreover, the algorithm is based solely on matrix manipulations; the support vectors and their corresponding Lagrange multiplier $\alpha_i$'s are automatically selected and determined in each iteration. It can be seen that the complexity of our algorithm in each iteration is only $O(k^2)$, where $k$ is the number of support vectors. Experimental results on some real data sets indicate that FISVDD demonstrates significant gains in efficiency with almost no loss in either outlier detection accuracy or objective function value.Comment: 18 pages, 1 table, 4 figure

Peak Criterion for Choosing Gaussian Kernel Bandwidth in Support Vector Data Description

Support Vector Data Description (SVDD) is a machine-learning technique used for single class classification and outlier detection. SVDD formulation with kernel function provides a flexible boundary around data. The value of kernel function parameters affects the nature of the data boundary. For example, it is observed that with a Gaussian kernel, as the value of kernel bandwidth is lowered, the data boundary changes from spherical to wiggly. The spherical data boundary leads to underfitting, and an extremely wiggly data boundary leads to overfitting. In this paper, we propose empirical criterion to obtain good values of the Gaussian kernel bandwidth parameter. This criterion provides a smooth boundary that captures the essential geometric features of the data