71,368 research outputs found
Kernel Ellipsoidal Trimming
Ellipsoid estimation is an issue of primary importance in many practical areas such as control, system identification, visual/audio tracking, experimental design, data mining, robust statistics and novelty/outlier detection. This paper presents a new method of kernel information matrix ellipsoid estimation (KIMEE) that finds an ellipsoid in a kernel defined feature space based on a centered information matrix. Although the method is very general and can be applied to many of the aforementioned problems, the main focus in this paper is the problem of novelty or outlier detection associated with fault detection. A simple iterative algorithm based on Titterington's minimum volume ellipsoid method is proposed for practical implementation. The KIMEE method demonstrates very good performance on a set of real-life and simulated datasets compared with support vector machine methods
The Ellipsoid Factor for quantification of rods, plates and intermediate forms in 3D geometries
The Ellipsoid Factor (EF) is a method for the local determination of the rod- or plate-like nature of porous or spongy continua. EF at a point within a 3D structure is defined as the difference in axis ratios of the greatest ellipsoid which fits inside the structure and which contains the point of interest, and ranges from -1 for strongly oblate (discus-shaped) ellipsoids, to +1 for strongly prolate (javelin-shaped) ellipsoids. For an ellipsoid with axes a ≤ b ≤ c, EF = a/b – b/c. Here, EF is demonstrated in a Java plugin, Ellipsoid Factor for ImageJ, distributed in the BoneJ plugin collection. Ellipsoid Factor utilises an ellipsoid optimisation algorithm which assumes that maximal ellipsoids are centred on the medial axis, then dilates, rotates and translates slightly each ellipsoid until it cannot increase in volume any further. Ellipsoid Factor successfully identifies rods, plates and intermediate structures within trabecular bone, and summarises the distribution of geometries with an overall EF mean and standard deviation, EF histogram and Flinn diagram displaying a/b versus b/c. Ellipsoid Factor is released to the community for testing, use, and improvement
Scalable Ellipsoidal Classification for Bipartite Quantum States
The Separability Problem is approached from the perspective of Ellipsoidal
Classification. A Density Operator of dimension N can be represented as a
vector in a real vector space of dimension , whose components are the
projections of the matrix onto some selected basis. We suggest a method to test
separability, based on successive optimization programs. First, we find the
Minimum Volume Covering Ellipsoid that encloses a particular set of properly
vectorized bipartite separable states, and then we compute the Euclidean
distance of an arbitrary vectorized bipartite Density Operator to this
ellipsoid. If the vectorized Density Operator falls inside the ellipsoid, it is
regarded as separable, otherwise it will be taken as entangled. Our method is
scalable and can be implemented straightforwardly in any desired dimension.
Moreover, we show that it allows for detection of Bound Entangled StatesComment: 8 pages, 5 figures, 3 tables. Revised version, to appear in Physical
Review
The ellipsoid method redux
We reconsider the ellipsoid method for linear inequalities. Using the
ellipsoid representation of Burrell and Todd, we show the method can be viewed
as coordinate descent on the volume of an enclosing ellipsoid, or on a
potential function, or on both. The method can be enhanced by improving the
lower bounds generated and by allowing the weights on inequalities to be
decreased as well as increased, while still guaranteeing a decrease in volume.
Three different initialization schemes are described, and preliminary
computational results given. Despite the improvements discussed, these are not
encouraging.Comment: 29 pages, 4 table
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