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Alzheimer’s disease (AD) is a degenerative brain disease that affects millions of people around the world. As populations in the United States and worldwide age, the prevalence of Alzheimer’s disease will only increase. In turn, the social and financial costs of AD will create a difficult environment for many families and caregivers across the globe. By combining genetic information, brain scans, and clinical data, gathered over time through the Alzheimer’s Disease Neuroimaging Initiative (ADNI), we propose a new Joint High-Order Multi-Modal Multi-Task Feature Learning method to predict the cognitive performance and diagnosis of patients with and without AD.

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Metric Learning, which aims at learning a distance metric for a given data set, plays an important role in measuring the distance or similarity between data objects. Due to its broad usefulness, it has attracted a lot of interest in machine learning and related areas in the past few decades. This paper proposes to learn the distance metric from the side information in the forms of must-links and cannot-links. Given the pairwise constraints, our goal is to learn a Mahalanobis distance that minimizes the ratio of the distances of the data pairs in the must-links to those in the cannot-links. Different from many existing papers that use the traditional squared L2-norm distance, we develop a robust model that is less sensitive to data noise or outliers by using the not-squared L2-norm distance. In our objective, the orthonormal constraint is enforced to avoid degenerate solutions. To solve our objective, we have derived an efficient iterative solution algorithm. We have conducted extensive experiments, which demonstrated the superiority of our method over state-of-the-art.

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