Outlier detection in non-elliptical data by kernel MRCD

The minimum regularized covariance determinant method (MRCD) is a robust estimator for multivariate location and scatter, which detects outliers by fitting a robust covariance matrix to the data. Its regularization ensures that the covariance matrix is well-conditioned in any dimension. The MRCD assumes that the non-outlying observations are roughly elliptically distributed, but many datasets are not of that form. Moreover, the computation time of MRCD increases substantially when the number of variables goes up, and nowadays datasets with many variables are common. The proposed Kernel Minimum Regularized Covariance Determinant (KMRCD) estimator addresses both issues. It is not restricted to elliptical data because it implicitly computes the MRCD estimates in a kernel induced feature space. A fast algorithm is constructed that starts from kernel-based initial estimates and exploits the kernel trick to speed up the subsequent computations. Based on the KMRCD estimates, a rule is proposed to flag outliers. The KMRCD algorithm performs well in simulations, and is illustrated on real-life data.

Visualizing classification results

Classification is a major tool of statistics and machine learning. A classification method first processes a training set of objects with given classes (labels), with the goal of afterward assigning new objects to one of these classes. When running the resulting prediction method on the training data or on test data, it can happen that an object is predicted to lie in a class that differs from its given label. This is sometimes called label bias, and raises the question whether the object was mislabeled.Our goal is to visualize aspects of the data classification to obtain insight. The proposed display reflects to what extent each object's label is (dis)similar to its prediction, how far each object lies from the other objects in its class, and whether some objects lie far from all classes. The display is constructed for discriminant analysis, the k-nearest neighbor classifier, support vector machines, logistic regression, and majority voting. It is illustrated on several benchmark datasets containing images and texts.

Anomaly Detection by Robust Statistics

Real data often contain anomalous cases, also known as outliers. These may spoil the resulting analysis but they may also contain valuable information. In either case, the ability to detect such anomalies is essential. A useful tool for this purpose is robust statistics, which aims to detect the outliers by first fitting the majority of the data and then flagging data points that deviate from it. We present an overview of several robust methods and the resulting graphical outlier detection tools. We discuss robust procedures for univariate, low-dimensional, and high-dimensional data, such as estimating location and scatter, linear regression, principal component analysis, classification, clustering, and functional data analysis. Also the challenging new topic of cellwise outliers is introduced.