Learning a Functional Alignment Model with a Semi-Supervised Approach

A few days ago, our paper “A Semi-supervised Method for Multi-Subject fMRI Functional Alignment” was accepted to the IEEE International Conference on Acoustics, Speech and Signal Processing that will be held next March in New Orleans, Louisiana, USA. This work presents an extension to the original Shared Response Model (SRM), an unsupervised method for multi-subject functional alignment of fMRI data. Using a semi-supervised approach, we show how to train SRM taking into consideration data from a supervised task (multi-label classification). In this way, we need almost half the number of unlabeled samples to achieve the same accuracy level, or achieve higher accuracy with the same number of unlabeled samples.

The method extends the deterministic SRM formulation with a Multinomial Logistic Regression penalty. The semi-supervised SRM inherits the characteristics of the SRM problem, defining a non-convex optimization problem. We solve it using a block-coordinate descent approach, where each block is an unknown matrix. We show similarities to the SRM and MLR, and note that finding the mappings requires to solve an optimization problem in the Stiefel manifold. While this has an closed-form in the SRM case, in the SS-SRM this requires general techniques to solve it. We use the excellent pymanopt package that allowed us to implement a solution for python. Also, the source code of SS-SRM has been published as part of the Brain Imaging Analysis Kit (BrainIAK).