Abstract For a given multidimensional data set (point cloud), we investigate methods for computing the minimum-volume enclosing ellipsoid (MVEE), which provides an efficient representation of that is useful in many applications, including analysis, optimal design, and computational geometry. Contrary to conventional wisdom, demonstrate careful exploitation problem structure can enable high-orde...

Minimum Volume Embedding (MVE) is an algorithm for non-linear dimensionality reduction that uses semidefinite programming (SDP) and matrix factorization to find a low-dimensional embedding that preserves local distances between points while representing the dataset in many fewer dimensions. MVE follows an approach similar to algorithms such as Semidefinite Embedding (SDE), in that it learns a k...

Two different methods for computing the covering ellipses of a set of points are presented. The first method finds the optimal ellipsoids with the minimum volume. The second method uses the first and second moments of the data points to compute the parameters of an ellipsoid that covers most of the points. A MATLAB software is written to verify the results.

Given a probability measure P and a reference measure μ, one is often interested in the minimum μ-measure set with P -measure at least α. Minimum volume sets of this type summarize the regions of greatest probability mass of P , and are useful for detecting anomalies and constructing confidence regions. This paper addresses the problem of estimating minimum volume sets based on independent samp...

We develop an optimization model based on Markovian approach to determine the optimum value of thresholds in a proposed acceptance sampling design. Consider an acceptance sampling plan where items are inspected and when the number of conforming items between successive defective items falls below a lower control threshold value, then the batch is rejected, and if it falls above a control thresh...