Inflationary dynamics for matrix eigenvalue problems

Dimensionality reduction of fMRI time series data using locally linear embedding

OBJECTIVE

Data-driven methods for fMRI analysis are useful, for example, when an a priori model of signal variations is unavailable. However, activation sources are typically assumed to be linearly mixed, although non-linear properties of fMRI data, including resting-state data, have been observed. In this work, the non-linear locally linear embedding (LLE) algorithm is introduced for dimensionality reduction of fMRI time series data.

MATERIALS AND METHODS

LLE performance was optimised and tested using simulated and volunteer data for task-evoked responses. LLE was compared with principal component analysis (PCA) as a preprocessing step to independent component analysis (ICA). Using an example data set with known non-linear properties, LLE-ICA was compared with PCA-ICA and non-linear PCA-ICA. A resting-state data set was analysed to compare LLE-ICA and PCA-ICA with respect to identifying resting-state networks.

RESULTS

LLE consistently found task-related components as well as known resting-state networks, and the algorithm compared well to PCA. The non-linear example data set demonstrated that LLE, unlike PCA, can separate non-linearly modulated sources in a low-dimensional subspace. Given the same target dimensionality, LLE also performed better than non-linear PCA.

CONCLUSION

LLE is promising for fMRI data analysis and has potential advantages compared with PCA in terms of its ability to find non-linear relationships.