Multi-task fused sparse learning for mild cognitive impairment identification

2.1Proposed framework

Figure 1 shows the flowchart of the proposed method. We preprocess multiple time points rs-fMRI data to build the FC network.

2.2Subjects and data acquisition

Our study is based on the data obtained from the ADNI database created and updated since 2004. The six-year study received $60 million from the public and private sectors, including the National Institute of Aging (NIA), the National Institute of Biomedical Imaging and Bioengineering (NIBIB), and the Food and Drug Administration. The main goal of the ADNI database is to use the continuous MRI and PET images as well as other biomarkers for the clinical and neuropsychological assessment of early AD and MCI progression. Specific and sensitive markers for the detection of early AD progression are designed to help scholars and clinical experts develop new therapies and monitor their effectiveness, which can effectively reduce the cost and time of clinical diagnosis. A large number of academic institutions and private companies have worked together to build the ADNI database and recruited subjects from over 50 sites in the USA and Canada [42]. For up-to-date information, please refer to www.adni-info.org.

The data exploited in the preparation of this paper is acquired from the ADNI Phase-2 (ADNI-2) database. There are 24 MCI patients and 23 normal controls (NCs) in our study, which contains two time points (baseline and year1) rs-fMRI data. Every subject is scanned using 3.0T Philips Achieva scanners with matched age and gender and the slice thickness is 3.3 mm. The Raw Digital Imaging and Communications in Medicine (DICOM) MRI scans are obtained from the public ADNI site (adni.loni.usc.edu). The quality of these scans is checked, the spatial distortion caused by B1 field inhomogeneity and gradient nonlinearity are automatically corrected.

2.3Image preprocessing and feature extraction

All subjects used the 3.0T Philips Achieva to scan at different centres with the following parameters: TR/TE = 3000/30 mm, rollover angle = 80∘, imaging matrix = 64 × 64, 48 slices,140 volumes, body thickness = 3.3 mm. The SPM8 software package is used for preprocessing the rs-fMRI data. Prior to any further processing, the first 4 rs-fMRI volumes of every subject are discarded to keep the magnetization equilibrium. The remaining volumes are then fixed for the interleaved order of the slices during the echo plane scan. This correction guarantees that the data on every slice corresponds to the same point. The interpolation time point is selected as the TR/2 time so that the relative error of every TR is minimized. After obtaining time delay correction, the slice timing to correct rs-fMRI time-series of every subject are realigned. The realignment utilizes a rigid body spatial transformation and a least squares approach. The first volume is used as a reference for entire subsequent volumes to be readjusted. This step discards the head movement illusion in the rs-fMRI time series. There is no significant group difference in the head movement of whole participants utilized in the study. After readjustment, the volumes are resliced so that they can match the first volume voxel-by-voxel. Rs-fMRI images are then normalized to the Montreal Neurological Institute (MNI) space with resolution of 3 × 3 × 3 mm3 [43].

The rs-fMRI is divided into 116 brain regions using the automatic anatomical labelling (AAL) template. FSL software is used for pre-processing in our experiment [44]. The average rs-fMRI time series of each brain region is also filtered by high pass filtering. In addition, we regressed out head movement parameters, mean BOLD time series of the white matter and the cerebrospinal fluid. The mean of BOLD signal in every region of interest (ROI) is used as features. Accordingly, the original rs-fMRI signal is denoted by 116 ROIs (i.e.,116 nodes) and connections between each pair of 116 ROIs (i.e., the edges connecting them). PC of two mean time series between a pair of ROIs is computed to measure the connection strength.

2.4Multitask fused sparse regression model

The dimension curse is always an issue in modelling rs-fMRI dataset. To address it, it is argued that group lasso is an effective way. A small number of features of specific groups can be identified by the group lasso to construct connectivity map using non-zero weights of all predictors. There are differences in the connection between MCI and NC as indicated in [27].

Assuming there are N subjects and each brain is divided into R ROIs using AAL template, a response vector with M length regional mean time series of the r-th ROI is represented as: 𝒚=[y1⁢r,y2⁢r,…,yM⁢r]∈ℝM, and the 𝒀=[𝒚1,𝒚2,…,𝒚R]∈ℝM×(R-1) represents a predictor data matrix of a subject. Arn=[y1⁢r1,…,y2⁢rn,…,yM⁢rn] is data matrix of r-th ROI (the whole BOLD time series except for r-th ROI), wrn∈ℝR-1 is weighting regression coefficient vector, Wr=[wr1,…,wrn,…,wrN]. Then the key step of constructing the BFCN for this subject is to estimate the FC matrix W∈ℝR×R, R nodes (i.e., 𝒙i, i=1,2,…,R) denote all ROIs. There are many researches to construct a sparse network to model the brain region connectivity, and the typical group lasso sparse learning network is formulated as below

where Rg⁢(Wr) is the group regularization. Specifically, the group regularization is defined as below

where λ1 is the group regularization parameter, wr⁢g represents the connectivity coefficients of g-th predictor. The utilization of ℓ2-norm on row vectors groups g-th feature in the whole time points by imposing the weights, and the further adoption of ℓ1-norm jointly selects features via the weights of R time points. The group lasso regularization is the traditional sparse regression network, which makes sure that all the regression models in different groups have the shared set of connections. The ℓ2-norm group penalty imposes every representation coefficient using the same weight. Namely, this ℓ2-norm treats each ROI in the same way to reconstruct a target ROI. Accordingly, SR model with this objective function is able to reconstruct the target ROI by the ROIs different from the target ROI. In addition, each ROI reconstruction is independent from others.

The main goal in brain disease diagnosis is to enhance the diagnostic performance between NC and MCI, but the group lasso regression model with penalty fails to consider the smooth properties of different time points in the framework. For this reason, we devise a novel framework to jointly learn shared functional brain networks of each subject by the group sparse regularization and fused smoothness information with the devised regularization terms as below:

where Rg⁢(Wr) is group regularization, and Rs⁢(Wr) denotes the smoothness regularization. Specifically, the smoothness regularization is defined as below

where λ2 and λ3 are the parameters of smoothness regularization. The first term, ∥wrn-wr-1n∥1, is the regularization penalty derived from fused LASSO [45, 46], which constrains the diversity between two consecutive weighting vectors from successive time points to be as small as possible. Because of ℓ1-norm used in this fused smoothness term, the sparsity of weighting vectors difference is encouraged since lots of zero components will occur in the imparity vectors of weighting. Namely, due to the regularization of the smoothness fusion, a large number of components from the adjacent weight vectors will be the same. The informative features will be selected due to non-zero weights in our classification task. In addition, the last term, ∥Arn⁢wrn-Ar-1n⁢wr-1n∥22, is the target smoothness, which encourages the difference of two consecutive models of continuous time points as small as possible. When the smoothness regularization parameters λ2 and λ3 are zero, the proposed method is the conventional group lasso method [47]. We smooth the connectivity coefficients of the subjects at different time points by introducing the fused smoothness terms. In addition, this learning framework imposes a high degree of constraints through regularization terms. We call this sparse learning model as multi-task fused sparse regression model (MFSR).

2.5Optimization algorithm

Our objective function simultaneously includes both group and smoothness regularizations, and the iterative projected gradient descent algorithm is used to minimize the objective function. Specifically, the objective function in Eq. (3) is divided into the smoothing term

and the non-smoothing term

In each iteration k, two steps are contained in the projected gradient descent. Let the gradient of s⁢(Wr) at Wrk denote as (Wrk), and the step size denote as γk and be determined via line search. The first step is denoted as

The second step is as follow

For the non-smooth term n⁢(Wr) in Eq. (8), we can calculate sequentially the proximal operator that related with the group Lasso constraints [47] and the fused Lasso constraints [45]. We use the techniques discussed in [48] to further accelerate the above gradient. We compute the search point Srk to perform gradient descent via Wrk

where αk is a pre-defined variable and Vrk is defined as

Finally, the new approximate solution is obtained.

3.1Experimental setting

In our experiment, our proposed method is implemented using Matlab 2015a software. The sparse regression and classification are implemented by SLEP and LibSVM toolboxes [49], respectively. As our data size is small, we adopt the leave-one-out cross validation (LOOCV) scheme to evaluate the proposed method. The hyper parameters in each method are empirically set by the greedy search strategy to select the optimal parameters. For example, we obtain the optimal values of λ1, λ2 and λ3 through the exhaustive search strategy from 10-5 to 105. In order to evaluate the performance of various methods, we use the following evaluation metrics: accuracy (ACC), area under receiver operating characteristic (ROC) curve (AUC), sensitivity (SEN), specificity (SPEC), Youden’s Index (Youden), F1-score (F1), and balanced accuracy (BAC). We compare the proposed MFSR network with the related networks such as Baseline PC network, Baseline SR network, Baseline MFSR network, Year 1 PC network, Year 1 SR network and Year 1 MFSR network.

Figure 2.

ROC curves of various methods.

Figure 3.

Classification results via various metrics.

Figure 4.

Sampled MCI and NC connectivity networks of the base line and year 1 data.

Figure 5.

The selected most discriminative brain regions.

3.2Classification results

In order to assess the efficacy of our proposed MFSR method, we compare our method with the typical methods including PC and SR. Moreover, we conduct two groups of experiments on the multiple time points data of the ADNI-2 database, i.e., baseline and year 1 classification. The experimental results are displayed in Figs 2, 3 and Table 1, respectively. The proposed network achieves the best classification performance with an accuracy of 95.74% for baseline and 93.64% for year 1 data. We can see that our proposed network outperforms other competing networks in terms of classification results. The reason of our proposed brain network achieves better classification results is that it can overcome the previous network’s drawbacks. It is clear that multi-task learning is better than each individual task because it can uncover the potential relationships among multiple time points rather than the simple averaging. By observing the relationship of successive ROIs, we can see that the MFSR model outperforms the traditional SR and PC models in both baseline and year 1 data, which confirms that multiple time-point constrained network is beneficial for MCI classification. Another encouraging phenomenon is that the impact of time changes on the classification performance is less sensitive. It can be seen that the results of year 1 are slightly worse than that of baseline. We can see that our proposed group sparse learning with smoothing constraints is quite effective.

Figure 6.

The selected most discriminative ROIs and their connections.

Figure 7.

Illustraction of selected ROIs of both baseline and year 1 data.

We randomly select MCI and NC patients from the database to compare the performance of different methods in terms of network. From Fig. 4, we can see that the conventional networks achieve similar results between MCI and NC. Our proposed MFSR network shows more block structures and clear layouts, which can reveal the differences between MCI and NC.

Figure 5a and b show the top 10 selected brain regions in the baseline and year 1 data, respectively. Different colors represent 10 different selected brain regions of the highest frequency for clear discrimination. The experimental results show that baseline and year 1 data select several common regions as important features for MCI classification. In addition, it is obvious that the frontal and temporal features are frequently identified. The selected brain regions including the temporal inferior frontal gyrus, supplementary motor area, insula, frontal middle gyrus, middle temporal gyrus, superior gyrus, can be used for potential clinical diagnosis. A group of brain regions in the temporal pole, medial orbitofrontal cortex, and bilateral fusiform play an important role in the MCI identification. The connection relationship of the 5 regions with the highest probability is clearly shown in Fig. 6, where different nodes denote ROIs, and edges represent the degree of association of different ROIs. The thicker the connection, the greater the association weight between the ROIs. The blue and yellow lines represent the connection of the 5 selected brain regions in the year 1 and baseline data, respectively. ROIs connection relationships are displayed in Fig. 7. We find that gyrus, and temporal gyrus regions are identified for MCI diagnosis, which are in line with the findings of the most selected regions in MCI in previous studies. Overall, the top selected most discriminative brain regions are closely related with MCI pathology and consistent with previous clinical findings as well [28, 29].