Assessing phenotype order in molecular data

Abstract

Biological entities are key elements of biomedical research. Their definition and their relationships are important in areas such as phylogenetic reconstruction, developmental processes or tumor evolution. Hypotheses about relationships like phenotype order are often postulated based on prior knowledge or belief. Evidence on a molecular level is typically unknown and whether total orders are reflected in the molecular measurements is unclear or not assessed. In this work we propose a method that allows a fast and exhaustive screening for total orders in large datasets. We utilise ordinal classifier cascades to identify discriminable molecular representations of the phenotypes. These classifiers are constrained by an order hypothesis and are highly sensitive to incorrect assumptions. Two new error bounds, which are introduced and theoretically proven, lead to a substantial speed-up and allow the application to large collections of many phenotypes. In our experiments we show that by exhaustively evaluating all possible candidate orders, we are able to identify phenotype orders that best coincide with the high-dimensional molecular profiles.

Ordinal Classification: Working Definition and Detection of Ordinal Structures

“…This fact might sound questionable and unconventional, at first sight. However, Lattke et al [22] and Lausser et al [23] showed that an expected class structure, which is based on the meaning of classes, is not always reflected in the chosen feature space. In such classification tasks, OC-based classification models (CMs) are not able to exploit the given feature space, with respect to the assumed class order, in general.…”

“…The outcomes presented by Lattke et al [22] indicate that one can detect ordinal class structures by applying CCAs, in combination with linear SVM models. Lausser et al [23] showed that this specific approach can be used to assess phenotype order in molecular data. Such kind of data represents one of the many interesting tasks, in which we usually do not have any a priori information about the corresponding structure.…”

“…Lattke et al [22] and Lausser et al [23] proposed to implement pairwise cascaded SVM models to detect ordinal structures. Based on the outcomes of those studies, we believe that one can also approach the whole idea the other way around.…”

“…Each of the two edges can be seen as the starting or end point of the corresponding order. The second FOR-loop of our proposed algorithm constitutes the main difference to the detection methods from [22] and [23]. In both of the related works, one has to consider all possible permutations of the class labels, in general.…”

“…if no ties occur). Moreover, in [22] and [23], each permutation is associated with the (re-)evaluation of the corresponding cascaded classification model. By contrast, in our detection algorithm, we evaluate each of the c(c − 1)/2 binary SVM models exactly one time (in the first FOR-loop).…”