Validation of Soft Classification Models using Partial Class Memberships: An Extended Concept of Sensitivity & Co. applied to the Grading of Astrocytoma Tissues

We use partial class memberships in soft classification to model uncertain labelling and mixtures of classes. Partial class memberships are not restricted to predictions, but may also occur in reference labels (ground truth, gold standard diagnosis) for training and validation data. Classifier performance is usually expressed as fractions of the confusion matrix, such as sensitivity, specificity, negative and positive predictive values. We extend this concept to soft classification and discuss the bias and variance properties of the extended performance measures. Ambiguity in reference labels translates to differences between best-case, expected and worst-case performance. We show a second set of measures comparing expected and ideal performance which is closely related to regression performance, namely the root mean squared error RMSE and the mean absolute error MAE. All calculations apply to classical crisp classification as well as to soft classification (partial class memberships and/or one-class classifiers). The proposed performance measures allow to test classifiers with actual borderline cases. In addition, hardening of e.g. posterior probabilities into class labels is not necessary, avoiding the corresponding information loss and increase in variance. We implement the proposed performance measures in the R package "softclassval", which is available from CRAN and at http://softclassval.r-forge.r-project.org. Our reasoning as well as the importance of partial memberships for chemometric classification is illustrated by a real-word application: astrocytoma brain tumor tissue grading (80 patients, 37000 spectra) for finding surgical excision borders. As borderline cases are the actual target of the analytical technique, samples which are diagnosed to be borderline cases must be included in the validation.Comment: The manuscript is accepted for publication in Chemometrics and Intelligent Laboratory Systems. Supplementary figures and tables are at the end of the pd

Marker effects and examination reliability: a comparative exploration from the perspectives of generalizability theory, Rasch modelling and multilevel modelling

This study looked at how three different analysis methods could help us to understand rater effects on exam reliability. The techniques we looked at were: generalizability theory (G-theory) item response theory (IRT): in particular the Many-Facets Partial Credit Rasch Model (MFRM) multilevel modelling (MLM) We used data from AS component papers in geography and psychology for 2009, 2010 and 2011 from Edexcel.</p

The Feasibility of Reclaiming Shell Material from Investment Casting

This report examines the feasibility of investment shell component reclamation. Shell material components and their compositions are investigated with an industry survey, a study of the available literature, and analysis of specimen shell materials. physical properties and factors related to the reclamation and reuse of shell materials are described. Well known mineral processing methods are capable of producing concentrates of the various shell components. The theory and techniques of some applicable processes are discussed to assist with the development of reclamation operations. The recommended methods are; comminution by roll crushing, component concentration by screening, gravity settling or heavy medium separation. Aluminosilicate stucco (a major component of many investment shells) can be recovered in a form suitable for reuse as backup stucco. Zircon (a minor component in many shell compositions) -can be concentrated in an impure form, and subsequent caustic liberation treatments can remove the intermixed silica phases. Reuse of such zircon in investment casting may be possible but will require careful qualification testing. Fused and crystalline silica (major components of most shell compositions) are not reusable for investment casting. The feasibility of reclamation will be influenced by individual foundry choices of materials, composition and shell practice.HWRIC Project No. RRT-10NTIS PB92-16219