Hypergraph based multi-task feature selection for multimodal classification of Alzheimer's disease
Introduction
Alzheimer's disease (AD), which is usually associated with elderly people, is the sixth leading cause of death in the United States (Association, 2012). The progression of AD gradually leads to a widespread loss of mental function such as memory loss, language impairment, disorientation and personality change, ultimately leading to death. In Association (2013), it was reported that the total estimated prevalence of AD is expected to be 13.8 million by 2050. However, no treatment has so far been reported to be able to reverse or stop the progress of AD. Therefore, many studies focus on the early diagnosis of AD and MCI based on neuroimaging data (Sui et al., 2012, Ye et al., 2011) which plays a crucial role in the later treatments.
Neuroimaging which offers great potential to discover features corresponding to the early course of dementing illness is a powerful tool for disease diagnosis in neurodegenerative diseases such as AD. Recently, magnetic resonance imaging (MRI) and positron emission topography (PET) are indicated to be useful to investigate neurophysiological characteristics of AD and MCI (Davatzikos et al., 2011, Fan et al., 2008, Chetelat et al., 2003, Foster et al., 2007). Furthermore, multiple biomarkers have been shown to be sensitive to the diagnosis of AD and MCI by neuroimaging, such as the structural atrophy, pathological amyloid depositions, and metabolic alterations in the brain.
In recent decades, machine learning and pattern recognition methods have been widely used in neuroimaging analysis of AD and MCI, including group-based comparison approaches and individual classification (Ye et al., 2011, Orrú et al., 2012). However, most of the existing studies mainly focus on extracting features from single modality. For example, researchers extracted the features from the structural MRI, such as voxel-wise tissue (Desikan et al., 2009, Fan et al., 2007) and hippocampal volumes (Gerardin et al., 2009) for diagnosis of AD. In addition to the structural MRI, PET images are also utilized for the classification of AD and MCI (Chetelat et al., 2003, Foster et al., 2007, Hinrichs et al., 2009).
However, since the structure and function of brain are very complex, it is challenging to accurately detect all the disease-related features from single modality. Recently, with the development of biomedical imaging techniques, multi-modality based methods are promising in the field of medical image analysis since multi-modality information is naturally available in the data acquisition procedures of various clinical tasks. Different modalities can provide different views of brain structure or function and reveal different aspects of pathological changes related to AD. For example, structural MRI provides information related to the tissue type of brain, while the FDG-PET measures the cerebral metabolic rate for glucose. Numerous studies have shown that the complementary neuroimaging modalities can help to discover the hidden information which may be ignored by the single modality, and the fusion of the information from different modalities can enhance the diagnostic performance. Hence, multiple modalities are preferred to improve the accuracy of AD diagnosis (Liu et al., 2014, Liu et al., 2015, Suk et al., 2014, Zhu et al., 2014, Gray et al., 2013, Ahmed et al., 2017, Lei et al., 2017). For instance, Liu et al. (2015) and Suk et al. (2014) used two modalities including MRI and PET for the diagnosis of AD. Zhu et al. (2014) combined MRI, PET and cerebrospinal fluid (CSF) for the regression and classification of AD. Gray et al. (2013) used MRI, PET, CSF and categorical genetic information for AD/MCI classification.
Although the existing multi-modality based methods have achieved promising results, there are still some problems which may limit the classification performance. For neuroimaging, even after feature extraction, the feature dimension is relatively high compared to the sample size, and the subsequent classification performance may be poor because of the redundant or irrelative features. Therefore, feature selection which removes the redundant or irrelative features has become an important step in the diagnosis of AD. Some feature selection methods have been used for identifying the corresponding disease-related regions in AD. For example, Zhu et al. (2016) combined two subspace learning methods, namely, linear discriminant analysis and locality preserving projection to select features in neuroimaging. Jie et al. (2015) proposed a manifold regularized multitask feature learning method which uses multi-task learning and manifold based Laplacian regularization to preserve both the intrinsic relatedness among multiple modalities of data and the data distribution information in each modality and thus induces more discriminative features. Zu et al. (2016) proposed a label-aligned multi-task feature learning method which adds a new label-aligned regularization term to the objective function of standard multi-task feature selection to ensure that all multi-modal subjects with the same class labels should be close in the new feature-reduced space.
However, one disadvantage of the existing methods is that they only considered the pairwise relationships between subjects, while ignoring the high-order relationships which are a kind of important prior information for the learning task. In many real-world problems, relationships among the objects of interest are more complex than pairwise. Naively squeezing the complex relationships into pairwise ones inevitably leads to the information loss which can be expected valuable for our learning tasks (Zhou et al., 2007). Intuitively, modeling the high-order relationships among subjects can induce more discriminative features and further boost the performance of subsequent classification. In many applications, researchers use hypergraph to model the complex relationships among subjects, where a hyperedge can connect more than two vertices at the same time and capture the high-order structure. For example, Bu et al. (2010) adopted hypergraph for music recommendation. Hong et al. (2016) proposed to recovery human pose via hypergraph Laplacian.
In this paper, we propose a hypergraph based multi-task feature selection method where a hypergraph-based regularization is developed to explicitly depict the high-order relationship in each modality. Specifically, our proposed method contains three steps: (1) hypergraph construction, (2) hypergraph based multi-task feature learning, (3) multimodal classification. Specifically, we first construct a hypergraph in each modality by constructing multiple hyperedges that reflect the high-order relationships among subjects. Then we treat feature learning in each modality as a single learning task and formulate the multimodal classification as the multi-task learning (MTL) problem. MTL exploits the intrinsic task relatedness, based on which the information from each task can be shared across multiple tasks and thus facilitates the individual task learning. Specifically, the norm is introduced to select features jointly, which can guarantee the features of different modalities in the same brain regions are selected at the same time. Then, we add hypergraph-based regularization terms to the standard multi-task objective function. Finally, we use the multi-kernel support vector machine SVM to fuse the selected features from multimodal data for final classification. To validate our method, we conduct experiments on the ADNI dataset and the experimental results show the efficiency of the proposed method compared with the start-of-the-art methods.
Section snippets
Method
Fig. 1 illustrates the framework of the proposed method, which includes three main steps: hypergraph construction, feature selection and classification. In this section, we first introduce the dataset used in our experiments and then details of the proposed method will be given.
Experiments and results
To validate the effectiveness of our proposed method, we perform experiments in different scenarios, including AD vs. NC, LMCI vs. NC and EMCI vs. LMCI. Classification performance is accessed on the MRI and FDG-PET modalities from ADNI participants. In our experiments, 10-fold cross-validation strategy is adopted to evaluate the classification performance. Specifically, the whole set is equally divided into subsets. For each cross-validation, we take subsets as the training set and the
Discussion
In this paper, we propose a new multi-modality based classification framework, that is, hypergraph based multimodal classification. Our proposed method includes three steps, hypergraph construction, hypergraph based multi-task feature selection and multi-kernel classification. To validate the effectiveness our proposed method, three sets of experiments are performed on the 831 subjects of ADNI dataset. The results show that the proposed method can not only take advantage of the multi-modality
Conclusion
In summary, this paper proposed a novel multi-task learning method to jointly select features from multimodal neuroimaging data for AD/MCI classification. MTL captures the intrinsic task relatedness, based on which the information from each task can be shared across multiple tasks. By introducing the hypergraph based regularization term into the multi-task learning framework, the proposed method can utilize the high-order relationships among the subjects to seek the most discriminative brain
Conflict of interest
The authors of this manuscript have nothing to disclose.
Acknowledgements
This work was supported by the the National Natural Science Foundation of China (Nos. 61902183, 61876082, 61861130366, 61732006) and National Key Research and Development Program of China (Nos. 2018YFC2001600, 2018YFC2001602), the Royal Society-Academy of Medical Sciences Newton Advanced Fellowship (No. NAFR1180371), and China Postdoctoral Science Foundation funded project (No. 2019M661831)
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