Nonparametric discriminant analysis of phytoplankton species using data from analytical flow cytometry

Background: Analytical flow cytometry (AFC) provides rapid and accurate measurement of particles from heterogeneous populations. AFC has been used to classify and identify phytoplankton species, but most methods of discriminant analysis of resulting data have depended on normality assumptions and outcomes have been disappointing. Methods and Results: In this study, we consider nonparametric methods based on density estimation. In addition to the familiar kernel method, methods based on wavelets are also implemented. Full five-dimensional wavelet estimation proves to be computationally prohibitive with current workstation power, so we employ projection pursuit for reduction of dimensionality. AFC typically produces very large samples, so we also investigate data simplification through binning. Further modifications to the discrimination strategy are suggested by specific features of phytoplankton data, namely, a hierarchical group structure, the possible presence of many groups, and the likelihood of encountering an aberrant group in a test sample. Conclusions: We apply all the resultant procedures to appropriate subsets of a very large data set, demonstrate their efficacy, and compare their error rates with those of more conventional methods. We further show that incorporation of the specific features of phytoplankton data into the analysis leads to improved results and provides a general framework for analysis of such data.