Multi-task linear programming discriminant analysis for the identification of progressive MCI individuals

Abstract

Accurately identifying mild cognitive impairment (MCI) individuals who will progress to Alzheimer's disease (AD) is very important for making early interventions. Many classification methods focus on integrating multiple imaging modalities such as magnetic resonance imaging (MRI) and fluorodeoxyglucose positron emission tomography (FDG-PET). However, the main challenge for MCI classification using multiple imaging modalities is the existence of a lot of missing data in many subjects. For example, in the Alzheimer's Disease Neuroimaging Initiative (ADNI) study, almost half of the subjects do not have PET images. In this paper, we propose a new and flexible binary classification method, namely Multi-task Linear Programming Discriminant (MLPD) analysis, for the incomplete multi-source feature learning. Specifically, we decompose the classification problem into different classification tasks, i.e., one for each combination of available data sources. To solve all different classification tasks jointly, our proposed MLPD method links them together by constraining them to achieve the similar estimated mean difference between the two classes (under classification) for those shared features. Compared with the state-of-the-art incomplete Multi-Source Feature (iMSF) learning method, instead of constraining different classification tasks to choose a common feature subset for those shared features, MLPD can flexibly and adaptively choose different feature subsets for different classification tasks. Furthermore, our proposed MLPD method can be efficiently implemented by linear programming. To validate our MLPD method, we perform experiments on the ADNI baseline dataset with the incomplete MRI and PET images from 167 progressive MCI (pMCI) subjects and 226 stable MCI (sMCI) subjects. We further compared our method with the iMSF method (using incomplete MRI and PET images) and also the single-task classification method (using only MRI or only subjects with both MRI and PET images). Experimental results show very promising performance of our proposed MLPD method.

Figure 1

Left: Histogram of the canonical correlations between MRI features and PET features; Middle: Histogram of the number of selected MRI features for task 1 based on 50 times simulation. Each time we chose 76 pMCI subjects and 76 sMCI subjects randomly in task 1; Right: Histogram of the number of selected MRI features for task 2 based on 50 times simulation. Each time we chose 76 pMCI subjects and 76 sMCI subjects randomly in task 2. For the middle and right plots, the LASSO method is used for feature selection and 10-fold cross validation is used to choose the optimal number of features.

Figure 2. Classification accuracy of MLPD and SLPD with respect to different predefined threshold .