An Investigation into Classification of High Dimensional Frequency Data
We desire an algorithm to classify a physical object in ``real-time" using an easily portable probing device. The probe excites a given object at frequencies from 100 MHz up to 800 MHz at intervals of 0.5 MHz. Thus the data used for classification is the 1400-component vector of these frequency responses.
The Interdisciplinary Center for Applied Mathematics (ICAM) was asked to help develop an algorithm and executable computer code for the probing device to use in its classification analysis. Due to these and other requirements, all work had to be done in Matlab. Hence a significant portion of the effort was spent in writing and testing applicable Matlab code which incorporated the various statistical techniques implemented.
We offer three approaches to classification: maximum log-likelihood estimates, correlation coefficients, and confidence bands. Related work included considering ways to recover and exploit certain symmetry characteristics of the objects (using the response data). Present investigations are not entirely conclusive, but the correlation coefficient classifier seems to produce reasonable and consistent results. All three methods currently require the evaluation of the full 1400-component vector. It has been suggested that unknown portions of the vectors may include extraneous and misleading information, or information common to all classes. Identifying and removing the respective components may be beneficial to classification regardless of method. Another advantage of dimension reduction should be a strengthening of mean and covariance estimates.