Dynamic Analysis of High Dimensional Microarray Time Series Data Using Various Dimensional Reduction Methods

Abstract

This dissertation focuses on dynamic analysis of reduced dimension models of two microarray time series datasets. Underlying research achieves two main objectives; namely, (1) various dimension reduction techniques used on time series microarray data, and (2) estimating autoregressive coefficients using several penalized regression methods like ridge, SCAD, and lasso.The research methodology includes two research tasks. Firstly, applying several dimension reduction methods on two microarray data sets, and modeling comparisons based on accuracy and computation cost. Secondly, applying the sparse vector autoregressive (SVAR) model to estimate gene regulatory network based on gene expression profile from time series microarray experiment on two datasets and the autoregressive coefficients estimation were calculated using several penalized regression methods, and then performing comparisons among various regression methods for each dimension reduction model.Study results show that the dimension reduction methods producing orthogonal independent variables are performing better because orthogonality leads to reasonable coefficient estimation with low standard errors. On the other hand, regarding dynamic analysis, it could be seen that factor analysis (FA) outperformed the rest of dimension reduction methods with regards to goodness of fit after applying several penalized regression methods on each model. The reason behind this is due to using varimax rotation in FA, in which most of the coordinates are set closer to zero, and in turn makes the data sparser. Hence inducing additional sparsity subject to maintaining a certain goodness of fit.