The Study Of Graph-Based Brain-Image Functional Alignment And Optimization

With the great advancement of the brain-imaging technology and machine learning,investigations into what is encoding in the human brain has drawn much of attention.There is an increasing number of researchers devoting themselves into leveraging machine learning to help understand how the human brain works.Recently,functional Magnetic Resonance Imaging(fMRI)is becoming a promising technology to aid researchers to decode the human brain,since its high resolution is expected to capture sufficient information of what a human is thinking at a certain time.To reach general and valid findings of the human brain,it is indispensable to aggregate fMRI data from different subjects.The variability of anatomical structures and functional topographies further warrant alignment across neural representational spaces.So far,functional alignment has become the most effective methodology to carry out alignment across subjects.However,the related studies fail to cope with two critical issues:1)The existing works assume that the given fMRI datasets are temporally-aligned,but there are lots of unaligned fMRI datasets.2)The geometry of the stimuli contains some valuable information,but an algorithm leveraging it is missing.To fill the two aforementioned gaps,this paper will develop two more flexible frameworks based on graph-embedding techniques that can suit an assortment of current fMRI datasets.On the other hand,the potential high dimension of the features of fMRI data could lead to small sample size problem,causing that the two proposed optimization models are prone to overfitting.To overcome such an issue,we will theoretically develop a low-dimension assumption that can be used to further refine the two proposed optimization models.The main research works are as follows:1.The previous studies are based on temporally-aligned datasets,but fMRI datasets today could be unaligned.Though an unaligned dataset could be reordered and truncated,or down-sampled,to be aligned,it would lead to an inevitable loss of information.Therefore,temporal-alignment-based methods generally fail to handle unaligned fMRI datasets well.To tackle this scenario,we set up a cross-subject graph to depict the innate structure of an unaligned fMRI dataset,with which a more versatile framework coupled with an efficient optimization algorithm will be developed.The experiment results attest to that the proposed method is able to handle unaligned fMRI datasets much better.2.The geometry of stimuli of different categories could be constructed or inferred in lots of fMRI datasets,but is unemployed in the existing methods.To exploit such a geometry,a graph matrix is used to encode this information,with which a more powerful temporal-alignment-based functional alignment method will be introduced.3.To allow for non-linear feature extraction,kernel method is adopted.Theoretically,however,small sample size problem potentially brought by the high dimension of fMRI will make the two proposed optimization models suffer from overfitting.To overcome this difficulty,a low-dimension assumption,which complies with that the data in the feature space should lie in a low-dimensional manifold,is imposed on the new feature space of each subject.Based on such an assumption,we develop a kernel-based optimization theory that serves as a complement to the two proposed optimization models.The experiments of both proposed methods,even when not facing small sample size problem,demonstrate that such an assumption is able to improve functional alignment significantly.The two frameworks developed in this paper,with the proposed low-dimension assumption theories,will augment the current functional alignment toolbox.Specifically,the low-dimension assumption provides a novel way to effectively cope with small sample size problem.Our experiments attest to that the proposed two frameworks can effectively tackle the aforementioned two issues,and also confirm the effectiveness of the developed low-dimension assumption.