Biomarker selection and a prospective metabolite-based machine learning diagnostic for lyme disease.

We provide a pipeline for data preprocessing, biomarker selection, and classification of liquid chromatography-mass spectrometry (LCMS) serum samples to generate a prospective diagnostic test for Lyme disease. We utilize tools of machine learning (ML), e.g., sparse support vector machines (SSVM), iterative feature removal (IFR), and k-fold feature ranking to select several biomarkers and build a discriminant model for Lyme disease. We report a 98.13% test balanced success rate (BSR) of our model based on a sequestered test set of LCMS serum samples. The methodology employed is general and can be readily adapted to other LCMS, or metabolomics, data sets.

Modeling multivariate time series on manifolds with skew radial basis functions.

We present an approach for constructing nonlinear empirical mappings from high-dimensional domains to multivariate ranges. We employ radial basis functions and skew radial basis functions for constructing a model using data that are potentially scattered or sparse. The algorithm progresses iteratively, adding a new function at each step to refine the model. The placement of the functions is driven by a statistical hypothesis test that accounts for correlation in the multivariate range variables. The test is applied on training and validation data and reveals nonstatistical or geometric structure when it fails. At each step, the added function is fit to data contained in a spatiotemporally defined local region to determine the parameters--in particular, the scale of the local model. The scale of the function is determined by the zero crossings of the autocorrelation function of the residuals. The model parameters and the number of basis functions are determined automatically from the given data, and there is no need to initialize any ad hoc parameters save for the selection of the skew radial basis functions. Compactly supported skew radial basis functions are employed to improve model accuracy, order, and convergence properties. The extension of the algorithm to higher-dimensional ranges produces reduced-order models by exploiting the existence of correlation in the range variable data. Structure is tested not just in a single time series but between all pairs of time series. We illustrate the new methodologies using several illustrative problems, including modeling data on manifolds and the prediction of chaotic time series.

Geometric subspace methods and time-delay embedding for EEG artifact removal and classification.

Generalized singular-value decomposition is used to separate multichannel electroencephalogram (EEG) into components found by optimizing a signal-to-noise quotient. These components are used to filter out artifacts. Short-time principal components analysis of time-delay embedded EEG is used to represent windowed EEG data to classify EEG according to which mental task is being performed. Examples are presented of the filtering of various artifacts and results are shown of classification of EEG from five mental tasks using committees of decision trees.