Classification Using A Functional Partial Least Squares Logistic Regression Method

Abstract

Statistical analysis of functional data has been explored extensively over the last decade and functional partial least squares regression has emerged as a popular choice for classification problems. In partial least squares algorithms, uncorrelated components are derived iteratively by finding linear combinations of the predictors that maximize the variance between the predictors and the response. In this paper, we will develop a method to extract the components that explicitly considers the predictive power of the individual predictors. If an individual predictor does not display high predictive power as well as high covariance with the response, then their coefficients will be set to zero. This modified partial least squares method will be used to develop a set of uncorrelated latent variables, called mPLS components. The mPLS components will be used as the predictor variables in the logistic regression model. The efficacy of our algorithm will be assessed using fractional anisotropy data.