Attention Deficit Hyperactive Disorder (ADHD) is one of the most common diseases in school aged children. In this paper, we consider using fMRI data with classification techniques to aid the diagnosis of ADHD and propose a bi-objective ADHD classification scheme based on L1-norm support vector machine (SVM). In our classification model, two objectives, namely, the margin of separation and the empirical error are considered at the same time. Then the normal boundary intersection (NBI) method of Das and Dennis is used to solve the bi-objective optimization problem. A representative nondominated set which reflects the entire trade-off information between the two objectives is obtained. Each representative nondominated point in the set corresponds to an efficient classifier. Finally a decision maker can choose a final efficient classifier from the set according to the performance of each classifier. Our scheme avoids the trial and error process for regularization hyper-parameter selection. Experimental results show that our bi-objective optimization classification scheme for ADHD diagnosis performs considerably better than some traditional classification methods.

Introduction

Attention Deficit Hyperactivity Disorder (ADHD) is a very common mental disorder in childhood. ADHD symptoms include inattention, hyperactivity, and impulsively. It affects approximately 5–۷% of all school-age children and more than one half of the ADHD children continue to manifest clinically significant symptoms after reaching adulthood [1]. As the pathogenesis is not clear, the main diagnostic method is based on the subjective experience of doctors, which results in many children not being able to receive good treatment in the early stage of ADHD. In addition to the traditional clinical diagnosis, there is a pressing need to find a set of more distinctive and objective features to characterize ADHD that can be used to facilitate ADHD diagnosis. As a promising neuroimaging tool, functional MRI (fMRI) has been widely used to examine the brain of ADHD patients. Abnormal brain activations were found in task-related experiments on the dorsal anterior cingulate cortex (dACC), the ventrolateral prefrontal cortex (VLPFC) and the putamen [2]. Using resting-state fMRI, abnormalities were found in prefrontal cortex, inferior frontal cortex, sensorimotor cortex, anterior cingulated cortex, putamen, temporal cortex and cerebellum. In addition, Castellanos et al. (2008) [3] found ADHD-related decreases of functional connectivity between anterior cingulate and precuneus/posterior cingulate cortex regions, as well as between precuneus and other default-mode network components, including ventromedial prefrontal cortex and portions of posterior cingulate cortex. This suggests that functional connectivity information of functional MRI data can be used as a classification feature for ADHD diagnosis. With the development of machine learning techniques, many efforts have also been made to predict ADHD disease of patients. Mueller et al. [4] have introduced a machine learning system that uses support vector machine (SVM) to differentiate ADHD adults from control groups on the base of the event related potentials that are generated from the EEG measurements. In [5], Peng et al. utilized structural MRI data and ELM for ADHD classification. Dai et al. [6] proposed using multimodal magnetic resonance imaging to classify ADHD children. Mourão-Miranda et al. [7] applied SVM algorithm to perform multivariate classification of brain states from whole fMRI volumes. They demonstrated that SVM outperforms Fisher Linear Discriminant (FLD) classifier in classification performance as well as in robustness of the spatial maps obtained by a comparative analysis. Traditional machine learning classification methods mentioned above for ADHD are based on single optimization technique. One or more hyper-parameters need to be selected before training a classifier. This often leads to time-consuming training sessions and classification inefficiency with changes in sample size. For example, when using a SVM to classify mild cognitive impairment subtypes [8], Haller [9] explored the gamma parameter iteratively from 0.01 to 0.09.