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With rapid progress in high-throughput genotyping and neuroimaging, researches of complex brain disorders, such as Alzheimer’s Disease (AD), have gained significant attention in recent years. Many prediction models have been studied to relate neuroimaging measures to cognitive status over the progressions when these disease develops. Missing data is one of the biggest challenge in accurate cognitive score prediction of subjects in longitudinal neuroimaging studies. To tackle this problem, in this paper we propose a novel formulation to learn an enriched representation for imaging biomarkers that can simultaneously capture both the information conveyed by baseline neuroimaging records and that by progressive variations of varied counts of available follow-up records over time. While the numbers of the brain scans of the participants vary, the learned biomarker representation for every participant is a fixed-length vector, which enable us to use traditional learning models to study AD developments. Our new objective is formulated to maximize the ratio of the summations of a number of L1-norm distances for improved robustness, which, though, is difficult to efficiently solve in general. Thus we derive a new efficient iterative solution algorithm and rigorously prove its convergence. We have performed extensive experiments on the Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset. A performance gain has been achieved to predict four different cognitive scores, when we compare the original baseline representations against the learned representations with enrichments. These promising empirical results have demonstrated improved performances of our new method that validate its effectiveness. 

Alzheimer's Disease (AD) is a chronic neurodegenerative disease that severely impacts patients' thinking, memory and behavior. To aid automatic AD diagnoses, many longitudinal learning models have been proposed to predict clinical outcomes and/or disease status, which, though, often fail to consider missing temporal phenotypic records of the patients that can convey valuable information of AD progressions. Another challenge in AD studies is how to integrate heterogeneous genotypic and phenotypic biomarkers to improve diagnosis prediction. To cope with these challenges, in this paper we propose a longitudinal multi-modal method to learn enriched genotypic and phenotypic biomarker representations in the format of fixed-length vectors that can simultaneously capture the baseline neuroimaging measurements of the entire dataset and progressive variations of the varied counts of follow-up measurements over time of every participant from different biomarker sources. The learned global and local projections are aligned by a soft constraint and the structured-sparsity norm is used to uncover the multi-modal structure of heterogeneous biomarker measurements. While the proposed objective is clearly motivated to characterize the progressive information of AD developments, it is a nonsmooth objective that is difficult to efficiently optimize in general. Thus, we derive an efficient iterative algorithm, whose convergence is rigorously guaranteed in mathematics. We have conducted extensive experiments on the Alzheimer's Disease Neuroimaging Initiative (ADNI) data using one genotypic and two phenotypic biomarkers. Empirical results have demonstrated that the learned enriched biomarker representations are more effective in predicting the outcomes of various cognitive assessments. Moreover, our model has successfully identified disease-relevant biomarkers supported by existing medical findings that additionally warrant the correctness of our method from the clinical perspective. 

Many existing studies on complex brain disorders, such as Alzheimer's Disease, usually employed regression analysis to associate the neuroimaging measures to cognitive status. However, whether these measures in multiple modalities have the predictive power to infer the trajectory of cognitive performance over time still remain under-explored. In this paper, we propose a high-order multi-modal multi-mask feature learning model to uncover temporal relationship between the longitudinal neuroimaging measures and progressive cognitive output scores. The regularizations through sparsity-induced norms implemented in the proposed learning model enable the selection of only a small number of imaging features over time and capture modality structures for multi-modal imaging markers. The promising experimental results in extensive empirical studies performed on the ADNI cohort have validated the effectiveness of the proposed method.