Related papers: Multivariate Location and Scatter Matrix Estimatio…
In many applications, when building linear regression models, it is important to account for the presence of outliers, i.e., corrupted input data points. Such problems can be formulated as mixed-integer optimization problems involving cubic…
Multivariate spatially-oriented data sets are prevalent in the environmental and physical sciences. Scientists seek to jointly model multiple variables, each indexed by a spatial location, to capture any underlying spatial association for…
We consider component-wise equivariant estimation of order restricted location/scale parameters of a general bivariate distribution under quite general conditions on underlying distributions and the loss function. This paper unifies various…
There is a great need for robust techniques in data mining and machine learning contexts where many standard techniques such as principal component analysis and linear discriminant analysis are inherently susceptible to outliers.…
Outlier detection in a large-scale database is a significant and complex issue in knowledge discovering field. As the data distributions are obscure and uncertain in high dimensional space, most existing solutions try to solve the issue…
The Projection Congruent Subset (PCS) Outlyingness is a new index of multivariate outlyingness obtained by considering univariate projections of the data. Like many other outlier detection procedures, PCS searches for a subset which…
We define and solve classes of sparse matrix problems that arise in multilevel modeling and data analysis. The classes are indexed by the number of nested units, with two-level problems corresponding to the common situation in which data on…
The M-estimators of multivariate scatter are known to have breakdown points no greater than 1/(p+1), where p is the dimension of the data. In high dimension, the breakdown points are usually considered to be disappointingly low. This paper…
A novel approach to obtain weighted likelihood estimates of multivariate location and scatter is discussed. A weighting scheme is proposed that is based on the distribution of the Mahalanobis distances rather than the distribution of the…
Principal component analysis (PCA) is a fundamental tool for analyzing multivariate data. Here the focus is on dimension reduction to the principal subspace, characterized by its projection matrix. The classical principal subspace can be…
A multilayered particle is illuminated by plane acoustic or electromagnetic waves of one or several frequencies. We consider the inverse scattering problem for the identification of the layers and of the refraction coefficients of the…
When a large body of data from diverse experiments is analyzed using a theoretical model with many parameters, the standard error matrix method and the general tools for evaluating errors may become inadequate. We present an iterative…
How can we detect outliers, both scattered and clustered, and also explicitly assign them to respective micro-clusters, without knowing apriori how many micro-clusters exist? How can we perform both tasks in-house, i.e., without any…
Multivariate Gaussian is often used as a first approximation to the distribution of high-dimensional data. Determining the parameters of this distribution under various constraints is a widely studied problem in statistics, and is often…
This paper studies inference in the high-dimensional linear regression model with outliers. Sparsity constraints are imposed on the vector of coefficients of the covariates. The number of outliers can grow with the sample size while their…
Most multivariate outlier detection procedures ignore the spatial dependency of observations, which is present in many real data sets from various application areas. This paper introduces a new outlier detection method that accounts for a…
Analysis of three-way data is becoming ever more prevalent in the literature, especially in the area of clustering and classification. Real data, including real three-way data, are often contaminated by potential outlying observations.…
We consider the problem of principal component analysis (PCA) in the presence of outliers. Given a matrix $A$ ($d \times n$) and parameters $k, m$, the goal is to remove a set of at most $m$ columns of $A$ (known as outliers), so as to…
We deal with the equivariant estimation of scatter and location for p-dimensional data, giving emphasis to scatter. It it important that the estimators possess both a high efficiency for normal data and a high resistance to outliers, that…
The usual Minimum Covariance Determinant (MCD) estimator of a covariance matrix is robust against casewise outliers. These are cases (that is, rows of the data matrix) that behave differently from the majority of cases, raising suspicion…