A maximum margin-based kernel width estimator and its application to the response to neoadjuvant chemotherapy

ABSTRACT

INTRODUCTION: Function induction problems are frequently represented by affinity measures between the elements of the inductive sample set, and kernel matrices are a well-known example of affinity measures. METHODS: The objective of the present work is to obtain information about the relations between data from a calculated kernel matrix by initially assuming that those geometric relations are consistent with known labels. To assess the relation between the data structure and the labels, a classifier based on kernel density estimation (KDE) was used. The performance of the selected width using the method presented in this paper was compared to the performance of a method described in the literature; the literature method was based on minimizing error minimization and balancing bias and variance. The main case study, which was to predict the response to neoadjuvant chemotherapy treatment, consists of evaluating whether a set of training data from genomic expression data from breast tumors and the genomic expression from the tumor of one patient can be used to determine whether there will be a pathological complete response. RESULTS: For the tested databases, the proposed method showed statistically equivalent results with the literature method; however, in some cases, the proposed method had a better overall performance when considering both large and small classes. CONCLUSION: The results demonstrate the feasibility of selecting models by directly calculating densities and the geometry from the class separation.