Kernel-based methods for source identification using very small particles from carpet fibers

Abstract The objective comparison of complex signals in chemistry, and more particularly in forensic chemistry, with the view of inferring the source of a particular ‘trace’ object is an ongoing issue. In this paper, we propose a method that enables to assign a probability distribution to control material from any given source based on its chemical signal and to subsequently infer the source of a trace object using a simple Bayes classifier. Our method takes advantage of the dimension reduction and discriminative powers of kernels, and only requires the estimation of three parameters (once a kernel is chosen). We illustrate the application of our method to the inference of the source of trace objects based on very small particles (VSP) that can be found on their surfaces. VSPs are picked up in the environment(s) where the trace object has been in. These VSPs can (1) offer information about the geographic origins of the objects; (2) help discriminate between multiple mass-manufactured objects that would be otherwise identical. In this project, we use VSPs recovered from carpet fibers throughout the United States and apply our method to (1) reduce the complexity of compositional data obtained by SEM/EDS; (2) infer the source of the trace material. This method can be extended to VSPs found on other types of recovered forensic materials such as weapons, drugs, or IEDs (improvised explosive device), and to other types of chemical signals.