Full Information Linked ICA: addressing missing data problem in multimodal fusion

Recent advances in multimodal imaging acquisition techniques have allowed us to measure different aspects of brain structure and function. Multimodal fusion, such as linked independent component analysis (LICA), is popularly used to integrate complementary information. However, it has suffered from missing data, commonly occurring in neuroimaging data. Therefore, in this paper, we propose a Full Information LICA algorithm (FI-LICA) to handle the missing data problem during multimodal fusion under the LICA framework. Built upon complete cases, our method employs the principle of full information and utilizes all available information to recover the missing latent information. Our simulation experiments showed the ideal performance of FI-LICA compared to current practices. Further, we applied FI-LICA to multimodal data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study, showcasing better performance in classifying current diagnosis and in predicting the AD transition of participants with mild cognitive impairment (MCI), thereby highlighting the practical utility of our proposed method.

Nonparametric Independent Component Analysis for the Sources with Mixed Spectra

Independent component analysis (ICA) is a blind source separation method to recover source signals of interest from their mixtures. Most existing ICA procedures assume independent sampling. Second-order-statistics-based source separation methods have been developed based on parametric time series models for the mixtures from the autocorrelated sources. However, the second-order-statistics-based methods cannot separate the sources accurately when the sources have temporal autocorrelations with mixed spectra. To address this issue, we propose a new ICA method by estimating spectral density functions and line spectra of the source signals using cubic splines and indicator functions, respectively. The mixed spectra and the mixing matrix are estimated by maximizing the Whittle likelihood function. We illustrate the performance of the proposed method through simulation experiments and an EEG data application. The numerical results indicate that our approach outperforms existing ICA methods, including SOBI algorithms. In addition, we investigate the asymptotic behavior of the proposed method.