In many applications, especially in cancer treatment and diagnosis, investigators are interested in classifying patients into various diagnosis groups on the basis of molecular data such as gene expression or proteomic data. Often, some of the diagnosis groups are known to be related to higher or lower values of some of the predictors. The standard methods of classifying patients into various groups do not take into account the underlying order. This could potentially result in high misclassification rates, especially when the number of groups is larger than two. In this article, we develop classification procedures that exploit the underlying order among the mean values of the predictor variables and the diagnostic groups by using ideas from order-restricted inference. We generalize the existing methodology on discrimination under restrictions and provide empirical evidence to demonstrate that the proposed methodology improves over the existing unrestricted methodology. The proposed methodology is applied to a bladder cancer data set where the researchers are interested in classifying patients into various groups.

Classification rules that incorporate additional information usually present in discrimination problems are receiving certain attention during the last years as they perform better than the usual rules in poor discrimination problems. Fernández et al (2006) proved that these rules have a lower unconditional misclassification probability than the usual Fisher's rule but they did not consider the estimation of the conditional error probability when a training sample is given (the so-called true error rate) which is a very interesting parameter in practice.In this paper we consider the problem of estimating the true error rate of these classification rules in the classical topic of discrimination among two normal populations. We prove theoretical results on the apparent error rate of the rules that expose the need of new estimators of their true error rate. Our proposal is to also consider the additional information in the definition of the true error rate estimators. We propose four such new estimators. Two of them are defined incorporating the additional information into the leave-one-out-bootstrap. The other two are the corresponding cross-validation after bootstrap versions. We compare these new estimators with the usual ones in a simulation study and in a cancer trial application, showing the very good behavior, in terms of mean square error, of the leave-one-out bootstrap estimators that incorporate the available additional information.

No abstract

The incorporation of additional information into discriminant rules is receiving increasing attention as the rules including this information perform better than the usual rules. In this paper we introduce an R package called dawai, which provides the functions that allow to define the rules that take into account this additional information expressed in terms of restrictions on the means, to classify the samples and to evaluate the accuracy of the results. Moreover, in this paper we extend the results and definitions given in previous papers (Fernández,

A multispectral system based on a monochrome camera and an adaptive illumination source is presented in this paper. Its preliminary application is focused on material discrimination for food and beverage industries, where monochrome, color and infrared imaging have been successfully applied for this task. This work proposes a different approach, in which the relevant wavelengths for the required discrimination task are selected in advance using a Sequential Forward Floating Selection (SFFS) Algorithm. A light source, based on Light Emitting Diodes (LEDs) at these wavelengths is then used to sequentially illuminate the material under analysis, and the resulting images are captured by a CCD camera with spectral response in the entire range of the selected wavelengths. Finally, the several multispectral planes obtained are processed using a Spectral Angle Mapping (SAM) algorithm, whose output is the desired material classification. Among other advantages, this approach of controlled and specific illumination produces multispectral imaging with a simple monochrome camera, and cold illumination restricted to specific relevant wavelengths, which is desirable for the food and beverage industry. The proposed system has been tested with success for the automatic detection of foreign object in the tobacco processing industry.