Learning Independent Components with Tensor-based Modelling for Big fMRI Data

Functional magnetic resonance imaging (fMRI) is a popular neuroimaging technique for un- derstanding human brain functions and activities. However, fMRI data are big and difficult to deal with directly. For example, an fMRI sequence of size 128 × 128 × 32 with 100 time points has 52,428,800 voxels, and an fMRI scan can generate several gigabytes of data in two hours. Nonetheless, the increasing availability of public, open fMRI data has made it easier for machine learning researchers to contribute to this field. Therefore, in this project, we aim to develop machine learning methods for big fMRI data.

Independent component analysis (ICA) is an important blind source separation (BSS) method for finding representational components of data with maximum statistical indepen- dence. ICA is a popular tool for analyzing multiple brain activities in fMRI data, and usually takes vector-valued observation data as input. However, it is impractical to represent a full 4D fMRI scan sequence or even a 3D fMRI image as a vector for input to ICA. Accordingly, ICA is only applied to vectors formed with selected fMRI voxels. Moreover, with vector represen- tations, the original 4D/3D structure and respective correlations are broken. In contrast, in this project, we focus on the natural tensor (multidimensional array) representations of fMRI, and revisit the use of ICA for big fMRI data from a tensor-based perspective.

The goal of this project is to investigate the use of tensor-based models and algorithms for learning the independent components of big fMRI data to separate their multiple sources. This challenging problem poses three exciting research questions:
1. How to model independence and extract independent components for multidimensional (tensorial) representations of fMRI data.
2. How to enhance the tensor-based ICA models to achieve better discriminability for clas- sification and better robustness against noise and outliers.
3. How to improve the scalability of the proposed tensor-based ICA algorithms for the effi- cient processing and analysis of big fMRI data.

We will use a tensor-based approach to directly perform ICA on multidimensional, ten- sor representations of fMRI without vectorization, based on the PI’s expertise in tensor-based learning. Previous attempts in this direction either still represent 3D fMRI data as vectors first or have no BSS capability, whereas in our preliminary studies in ECMLPKDD2013, we pro- posed a model that both works on tensors and can perform BSS. We plan to systematically study this approach in three phases:
• To learn independent components from tensorial fMRI data using a basic multilinear mixing model and varying architectures.
• To build discriminative and robust ICA models for tensorial fMRI data through class- specific learning and trace-norm minimization, and derive respective algorithms.
• To develop scalable versions of the proposed algorithms for big fMRI data using the alternating direction method of multipliers (ADMM) and parallel processing.

Our proposed models and algorithms are general in nature and will provide new machine learning tools. We will perform evaluations on synthetic and public real fMRI data and dis- tribute our software freely for others’ verification and comparison. The expected project out- comes will particularly benefit big data applications in areas such as neuroimaging, telecom- munications, and finance. For the educational component, the PI will incorporate developments from this project into course work as case studies or small projects.