Sample-poor estimation of order and common signal subspace with application to fusion of medical imaging data

Abstract

Due to their data-driven nature, multivariate methods such as canonical correlation analysis (CCA) have proven very useful for fusion of multimodal neurological data. However, being able to determine the degree of similarity between datasets and appropriate order selection are crucial to the success of such techniques. The standard methods for calculating the order of multimodal data focus only on sources with the greatest individual energy and ignore relations across datasets. Additionally, these techniques as well as the most widely-used methods for determining the degree of similarity between datasets assume sufficient sample support and are not effective in the sample-poor regime. In this paper, we propose to jointly estimate the degree of similarity between datasets and their order when few samples are present using principal component analysis and canonical correlation analysis (PCA-CCA). By considering these two problems simultaneously, we are able to minimize the assumptions placed on the data and achieve superior performance in the sample-poor regime compared to traditional techniques. We apply PCA-CCA to the pairwise combinations of functional magnetic resonance imaging (fMRI), structural magnetic resonance imaging (sMRI), and electroencephalogram (EEG) data drawn from patients with schizophrenia and healthy controls while performing an auditory oddball task. The PCA-CCA results indicate that the fMRI and sMRI datasets are the most similar, whereas the sMRI and EEG datasets share the least similarity. We also demonstrate that the degree of similarity obtained by PCA-CCA is highly predictive of the degree of significance found for components generated using CCA.

Keywords: EEG; Multimodal fusion; PCA-CCA; Schizophrenia; fMRI; sMRI.

Figure 1

Generative model for multimodal fusion using CCA. Note that this model is obtained after spatial dimension reduction through PCA, i.e., X̃^[1] and X̃^[2] are both r × M matrices.

Figure 2

Probability of correctly detecting the number of common components versus the dimension of the datasets, m and n, when the latent sources are (a) Gaussian, (b) uniformly, and (c) Laplacian distributed. Note that for these simulations, m = n.

Figure 3

Meaningful and statistically significant components generated using CCA with pairwise combinations of the three modalities. The uncorrected significance (p-values) for the components are (a) 0.027 for the fMRI-sMRI component, (b) 0.003 for the fMRI-ERP component, and (c) 0.018 for the sMRI-ERP component. All spatial maps are Z-maps threshold at Z=3.5.

Figure 4

Meaningful and statistically significant components generated using MCCA with GENVAR. The uncorrected significance (p-values) for the components are (a) 0.014 for the first component and (b) 0.018 for the second component. All spatial maps are Z-maps thesholded at Z=3.5.