In previous work, semi-supervised Fuzzy c-means (ssFCM) was used as an automatic classification technique to classify the Nottingham Tenovus Breast Cancer (NTBC) dataset as no method to do this currently exists. However, the results were poor when compared with semi-manual classification. It is known that the NTBC data is highly non-normal and it was suspected that this affected the poor result...

In this contribution, we show that the incorporation of nonlinear dynamical measures into a multivariate discrimination provides a signal classification system that is robust to additive noise. The signal library was composed of nine groups of signals. Four groups were generated computationally from deterministic systems (van der Pol, Lorenz, Rössler and Hénon). Four groups were generated compu...

1. Compact operators on Banach spaces 2. Appendix: total boundedness and Arzela-Ascoli [Fredholm 1900/1903] treated compact operators as limiting cases of finite-rank operators. [1] [Riesz 1917] defined and made direct use of the compactness condition, more apt for Banach spaces. See [Riesz-Nagy 1952] for extensive discussion in the Hilbert-space situation, and many references to original paper...

where L is a symmetric elliptic operator and r is a locally integrable function on Rn. If r is of constant sign then this problem leads to a selfadjoint problem in the Hilbert space L2(|r|). In this note we are interested in the case when r takes both positive and negative values on sets of positive measure. Then the spectrum of the problem (1) is not necessarily real any more. Moreover it is n...

The use of the Mahalanobis distance in a lookup table approach to retrieval of in-water Inherent Optical Properties (IOPs) led to significant improvements in the accuracy of the retrieved IOPs, as high as 50% in some cases, with an average improvement of 20% over a wide range of case II waters. Previous studies have shown that inherent noise in hyperspectral data can cause significant errors in...

This paper discusses the application of the newly developed Mahalanobis distance-based ARTMAP (MART) network to the predication of sickle cell anemia patients’ response to Hydroxyurea treatment. Mahalanobis distance-based ARTMAP is a modified version of the Fuzzy ARTMAP networks where the activation and choice function are the same and equal to the Mahalanobis distance between the pattern and t...

The covariance matrix in the Mahalanobis distance can be trained by semi-definite programming, but training for a large size data set is inefficient. In this paper, we constrain the covariance matrix to be diagonal and train Mahalanobis kernels by linear programming (LP). Training can be formulated by ν-LP SVMs (support vector machines) or regular LP SVMs. We clarify the dependence of the solut...

Ellipsoid estimation is important in many practical areas such as control, system identification, visual/audio tracking, experimental design, data mining, robust statistics and statistical outlier or novelty detection. A new method, called Kernel Minimum Volume Covering Ellipsoid (KMVCE) estimation, that finds an ellipsoid in a kernel-defined feature space is presented. Although the method is v...

The report of the IAU Working Group on Nutation endorsed by Commissions 4, 8, 19 and 31 at the 1979 General Assembly points out that "... the complete theory of the general nutational motion of the Earth about its center of mass may be described by the sum of two components, astronomical nutation, commonly referred to as nutation, which is nutation with respect to a space-fixed coordinate syste...

Symmetry simplifications are introduced in configuration interaction (CI) by reducing the number of symmetry-allowed space types if there is degeneracy in some of the molecular orbitals by constructing the unique space types. A new symmetry group which we call the configuration symmetry group is defined and is shown to be expressible as a generalized wreath product group. Generating functions a...