Data Visualization using Linear and Non-linear Dimensionality Reduction Methods

Abstract

As the large amount of data can be efficiently stored, the methods extracting meaningful features from big data has become important. Especially, the techniques of converting high- to low-dimensional data are crucial for the 'Data visualization'. In this study, principal component analysis (PCA; linear dimensionality reduction technique) and Isomap (non-linear dimensionality reduction technique) are introduced and applied to neural big data obtained by the functional magnetic resonance imaging (fMRI). First, we investigate how much the physical properties of stimuli are maintained after the dimensionality reduction processes. We moreover compared the amount of residual variance to quantitatively compare the amount of information that was not explained. As result, the dimensionality reduction using Isomap contains more information than the principal component analysis. Our results demonstrate that it is necessary to consider not only linear but also nonlinear characteristics in the big data analysis.