Optimal multivariate classification by linear thresholding

The purpose of this paper is two-fold: 1. We pose the problem of linear thresholding, a classification scheme that uses a threshold variable on multivariate measurements. We begin with formalizing the problem for dichotomy (i.e., with two options, such as true or false), then further generalize the problem for trichotomy (i.e., with three options, such as true, false, or unknown). We present necessary conditions for optimality along with numerical examples. 2. We pose the problem of linear mixed-initiative nested thresholding, a classification architecture that exploits a primary, workload-independent, trichotomous classifier and a secondary, workload-dependent, dichotomous classifier in a nested structure with multivariate measurements. We provide necessary conditions for optimality and proof-of-concept numerical examples.