A Novel Approach for Fmri Data Analysis Based on the Combination of Sparse Approximation and Afﬁnity Propagation Clustering

Magnetic Resonance Imaging 32 (2014) 736–746

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Magnetic Resonance Imaging

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A novel approach for fMRI data analysis based on the combination of sparse approximation and afﬁnity propagation clustering

Tianlong Ren, Weiming Zeng ⁎, Nizhuan Wang, Lei Chen, Chenglin Wang

Digital Image and Intelligent computation Laboratory, College of Information Engineering, Shanghai Maritime University, Shanghai 201306, China

article info abstract

Article history: Clustering analysis has been widely used to detect the functional connectivity from functional magnetic Received 24 August 2013 resonance imaging (fMRI) data. However, it has some limitations such as enormous computer memory Revised 16 February 2014 requirement, and difficulty in estimating the number of clusters. In this study, in order to effectually Accepted 17 February 2014 resolve the deficiencies mentioned above, we have proposed a novel approach (SAAPC) for fMRI data analysis, which combines sparsity, an effective assumption for analyzing fMRI signal, with affinity Keywords: propagation clustering (APC). Sparse approximation fi fMRI The SAAPC method is composed of three parts: to obtain the sparse approximation coef cients set through Affinity propagation clustering wavelet packet decomposition and sparsity measuring and selection, which contributes a lot in the brain APC functional connectivity detection accuracy; to implement a split APC algorithm, which is put forward in this paper to overcome the computer memory shortage problem and to reduce the time cost in basic APC; to reconstruct the source signal by unmixing the mixed fMRI data using the time courses which are derived from the ultimate exemplars. In the task-related experiments, we can see that SAAPC is more accurate to detect the functional networks than basic APC, and it significantly reduces the time cost relative to basic APC. In addition, in the resting- state data experiments, the SAAPC method can successfully identify typical resting-state networks from the resting-state data set, while this performance is seldom reported by the classical cluster method and the basic APC method. This proposed clustering analysis method is expected to have wide applicability. © 2014 Elsevier Inc. All rights reserved.

1. Introduction independent components (ICA), but the meaningful decomposed components are hard to choose. Fuzzy clustering analysis (FCA) The blood oxygenation level dependent (BOLD) based function [18], k-centers clustering analysis [19,20] and hierarchical clus- magnetic resonance imaging (fMRI) is a powerful modality in the tering analysis (HCA) [21] are based on clustering analysis, and study of detecting the brain functional connectivity which is defined as their main drawback is that their reliability can only be established the “temporal correlations between spatially remote neurophysiolog- with repeated runs. ical events” [1,2]. Many researchers have already studied this kind of Recently, a novel data-driven method called affinity propagation connectivity through experimental approaches [3–7]. As the fMRI clustering (APC) has been proposed [22]. This algorithm simulta- technology draws attention from researchers in the field of computer neously considers all data points as potential exemplars, and science recently, more and more numerical methods and models from exchanges messages between data points until a good set of statistics, pattern recognition and signal processing, have been exemplars and clusters emerge. APC algorithm has been found to successfully applied to fMRI data analysis. perform well in clustering images of faces, identifying representative Data-driven methods [8] for detecting the brain functional sentences, and detecting genes. In addition, unlike the k-centers connectivity include two kinds: decomposition technique based clustering which is sensitive to the initial selection of exemplars methods and clustering based methods. The decomposition technique [19,20], in APC algorithm, the number of clusters (NC) need not be based methods, like principal component analysis (PCA) [9,10], pre-specified because of the influence of the input preference values. singular value decomposition (SVD) [11] and independent component Zhang et al. [23,24] has successfully applied APC algorithm to analysis (ICA) [12–17], try to express the original fMRI dataset as a detecting functional connectivity on task-related fMRI data. How- linear combination of basis vectors (PCA/SVD) or statistically ever, the intrinsic functional connectivity has not yet been revealed using the basic APC algorithm. ⁎ Corresponding author. Tel.: + 86 21 3828 2873; fax: +86 21 3828 2873. The assumption of sparisity has demonstrated that it can E-mail address: [email protected] (W. Zeng). significantly enhance signal separation accuracy and computation

http://dx.doi.org/10.1016/j.mri.2014.02.023 0730-725X/© 2014 Elsevier Inc. All rights reserved. T. Ren et al. / Magnetic Resonance Imaging 32 (2014) 736–746 737 efficiency of existing ICA methods on MEG data [25]. In terms of fMRI (3) And the availabilities are computed using the rules: data, the sparse property is also a general assumption, and many 8 9 scholars have researched on it to help decode the functional < X = ; ← ; ; ; 0; connectivity among the cortical regions of the human brain. It has aiðÞk min: 0 rkðÞþk max 0 ri k ; ð3Þ 0 : : 0∉ ; been demonstrated that the optimal sparse representation is i s t i fgi k significantly beneficial to the de-noising of fMRI time courses [26]. X ; ← ; 0; Flandin and Penny [27] have proposed a kind of Bayesian fMRI data akðÞk max 0 ri k ð4Þ 0 : : 0≠ analysis with sparse spatial basis functions, which firstly projected i s t i k the original to wavelet space, followed by threshing the small (4) Finally, assignments are made: coefficients to make the projected-back data sparser. Sparse component analysis (SCA) introduced by Georgiev et al. [28] can ← ; ; ci arg maxfgriðÞk þ aiðÞk ð5Þ reveal a stronger potential ability of dependent fMRI sources k separation compared with ICA. Ye et al. [29] have put forward a data-driven sparse geo-statistical analysis in clustering method and In the basic APC, another important parameter, damping factor gained better performance compared with GLM analysis. Sparse λ ∈ (0,1), is designed to avoid numerical oscillations that arise in approximation technique is based on the sparse property of source some circumstances. During the iterations, the responsibility and signal, which can be used to obtain a dataset with less redundancy availability are updated with the value produced in the and improve the separation accuracy of source signal. Wang et al. previous iteration: [30] have introduced an effective sparse approximation coefficient- based ICA (SACICA) model which performed better than FastICA. All −λ λ ri ¼ ðÞ1 ri þ ri−1 the studies mentioned above demonstrated that the sparsity of the −λ λ ð6Þ ai ¼ ðÞ1 ai þ ai−1 fMRI signal is a useful feature for source separation. In this study, a novel approach for fMRI data analysis based on the The whole procedure of basic APC may be terminated after a fixed fi combination of sparse approximation and af nity propagation clustering number of iterations, after changes in the messages fall below a (SAAPC)isproposed.Theremainder of this paper is organized as threshold, or after the local decisions stay constant for some number fi follows: rstly, the theory and method associated with SAAPC will be of iterations. presented; and then, the task-related data experiments on testing the However, the basic APC has two limitations: oscillations cannot performance of SAAPC will be showed, followed by the resting-state be eliminated automatically when they occur, and it is hard to fi network detection experiment on resting-state data set; nally, some estimate the value of parameter p which will influence the producing discussions related to the advantages and limitations of this new method of optimal clustering outcomes. An adaptive APC proposed by Wang on analyzing fMRI data will be presented. et al. [31] which assumes λstep and pstep are the adaptive factors, has the ability to well overcome these limitations. The values of adaptive 2. Theory and method factors can be determined empirically. Assuming that Num(i) is the number of clusters during the iterations and Num is the expected fi min 2.1. Af nity propagation clustering (APC) minimal number of clusters. Then, the steps of adaptive APC are presented as follows: The specific framework of basic APC [22] is presented in the following: consider Y ={y1,y2,⋯,yN} as the set of data points to be (1) Execute basic APC procedure and get Num(i); λ ← λ λ clustered into different types. The basic APC takes as input a (2) If there exists numerical oscillations, then + step, else collection of real-valued similarities between data points of Y, where execute basic APC continually; ≤ ← ← the similarity s(i, k)isdefined as a negative value. (3) If Num(i) Num(i + 1), then p p + pstep, and s(i, i) p; ≤ Note that, when k = i, the s(k, k), which is referred to as (4) If i = max iteration or Num(i) Nummin, then the algorithm “preference (denoted as p)”, is often set as a constant by hand. The terminates. Else, go to step (2). preferences p are important parameters in basic APC, which influence The value ofpNumffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffimin can be determined empirically, and pstep is the final number of clusters. When p are larger, the number of set to 0:1×p = KiðÞþ50; where p denotes the median of the fi m m identi ed exemplars is increased, otherwise, it is decreased. input similarities. There are two kinds of message transmitted between data “ ” points: one is called responsibility (r(i, k)), which is sent from 2.2. Sparse approximation data point i to candidate exemplar point k,andreflects the accumulated evidence for how well-suited point k is to serve as the According to the recent study of Wang et al. [30], detecting the “ ” exemplar for point i; and the other is called availability (a(i, k)), functional connectivity of the human brain activities which is under fl which is sent from candidate exemplar point k to i,andre ects the the assumption that there exists a functional integration of activity in accumulated evidence for how appropriate it would be for point i multiple macroscopic loci or distinct brain systems, has been to choose point k as its exemplar. The procedure of basic APC is modeled as a kind of blind source separation (BSS) problem, and presented as follows: the details of the sparse approximation of the BSS problem have been given as follows: (1) To start the basic APC algorithm, the availabilities are In order to retrieve the underlying sources which is denoted in initialized to zero: T N vector notation as S =(s1,s2,…,sN) ∈ R , assuming a zero mean T P from observed mixtures, X =(x1, x2,…,xN) ∈ R , the BSS problem ai; k 0; for all i; k 1 ðÞ¼ ð Þ can be written as a formula:

(2) Then, the responsibilities are updated with the formula: X ¼ AS ð7Þ

N P 0 0 where A is a mixing matrix with the size of P × N from R to R . The riðÞ; k ←siðÞ; k − max ai; k þ si; k ð2Þ k0s:t:k0≠k basic assumption underlying for all sparse separation methods is 738 T. Ren et al. / Magnetic Resonance Imaging 32 (2014) 736–746 that each source can be approximately represented by a linear formation, clustering analysis using split APC and source signal combination of a few elementary signals φk, known as atoms that are reconstruction. The details of these three procedures will be often assumed to be unit energy. These atoms φk are called a described in the next sub-sections. complete dictionary Φ if these atoms can be used to reconstruct any M signal Si ϵ R . Specifically, it is assumed that each (unknown) source 2.3.1. Sparse approximation coefficients set formation signal can be written as: In order to obtain the sparse approximation coefficients of the mixture discussed in Section 2.2, the sparse approximation coeffi- XK cients set formation procedure is involved. It mainly consists of two s ¼ c ðÞk φ ð8Þ i i k parts: 1D wavelet packet decomposition, sparsity measuring and k¼1 selection of the optimal sparse wavelet packet tree nodes [30]. where only few entries c (k) of vector C are significant, and most of The 1D wavelet packet library is particularly composed of the i si them are negligible. Unofficially, a set of coefficients ci(k) are triple-indexed family of functions: considered sparse when most of the coefficients are zero or very small and only a few of them are significant. In terms of statistical, φ j=2φ j − ; ; ∈ ∈ jmkðÞ¼t 2 m 2 t k j k Z and m M ð13Þ coefficients ci(k) are said to have a sparse or super-Gaussian distribution if their histogram has a strong peak at the origin with where j denotes the scale parameter, k denotes the shift parameter, heavy tails. Thus, the sparse model of source Si can be written in a matrix form: and m is the frequency parameter related to the number of oscillations of a particular generating function φm(t). The function φ s ¼ C Φ ð9Þ set, jm(t), forms a (j, m) wavelet packet, and it can also be split into i si two parts at a coarser scale, φj + 1,2m(t) and φj + 1,2m +1(t), from where C ¼ ðÞc ðÞk K is a row vector of K coefficients. If the selected which will result an orthonormal basis of the subspace that spans si i k¼1 dictionary Φ is a basis with K = M, then there exists a one-to-one {φjm(t)}. Then, a family of wavelet packet functions on a binary tree correspondence between the source signal Si and its coefficients could be formed. The nodes of this tree are numbered by two indices: − C ¼ s Φ 1 (C ¼ s ΦH for an orthonormal basis). This is the specific the depth of the level j = 0,1,⋯,J-1,J and the number of nodes m = si i si i case for a dictionary corresponding to an orthogonal basis of discrete 0,1,2,⋯2j-1 at the specific level [10,32]. In addition, for the wavelets, or the orthogonal discrete Fourier basis [32]. Furthermore, decomposition coefficients of the ith source signal si, the decompo- fi si the sparse representation model of the N sources S can be written in sition coef cients Cjmk, can be expressed as: matrix form as follow: DE Csi s ; φ 14 Φ 2 3 jmk ¼ i jmk ð Þ S ¼ Cs ð10Þ cS 6 1 7 6 cS 7 where the C satisfies C ¼ 2 ¼ ½C ðÞ1 ; C ðÞ2 ; ⋯; C ðÞK : s s 4 ⋯ 5 S S S Similarly, the decomposition coefficients of the ith mixture xi c could be expressed as: SN Both the estimation of the mixing matrix A and obtaining the DE xi ; φ source using blind source separation methods can be facilitated by Cjmk ¼ xi jmk ð15Þ sparse approximation of the observed mixture X. A sparse approximation of the mixture X takes the following form: Now, assume that there are N volumes of mixed fMRI data, and ≈ Φ each volume is analyzed by wavelet packet decomposition with X CX ð11Þ J levels, yielding L =2J +1-1 nodes, and thus producing N wavelet 2 3 packet trees. And then the node cells Node(1:N,1:L) can be formed, cx1 6 c 7 which is depicted in Fig. 1. In this study, the 1D wavelet packet where the P × K matrixC ¼ 6 x2 7 ¼ ½C ðÞ1 ; C ðÞ2 ; ⋯; C ðÞK is called X 4 ⋯ 5 X X X decomposition with three levels using db4 wavelet basis and

cxP Shannon entropy [33] is chosen to obtain the sparse approximation the sparse approximation coefficients subjected to the dictionary Φ coefficients from fMRI data. of the original X. By combining the formulation (7), (10) and (11), fi xi As the wavelet coef cients Cjmk of the mixture xi have different the resultant formula can be deduced below: sparsity degree levels, the wavelet coefficients with higher sparsity is selected, which will result in better separation performance [33]. ≈ CX ACs ð12Þ Here, we use the sparsity measuring machine and optimal sparse node selection machine proposed by Wang et al. [30] to obtain the when a proper dictionary Φ is selected. If Φ is an orthonormal basis, a ultimate wavelet coefficients Cxi with the highest sparsity, which unique representation exists for the mixture and the source, and can jmk can be summarized as follows: be calculated simply by inverse linear transform, necessarily satisfying CX ≈ ACS. According to the formula (12), the original BSS (1) Form the features' matrix Ml by extracting the lth equivalent problem of X is reduced to a separation problem of CX with a sparser nodes of the cell Node(:,l) to the corresponding rows of Ml; ' CS. Comparing the formula (7) with (12), the mixing matrix A is (2) Reshape the features' matrix Ml as a vector: Ml = Ml(:); unchanged if the approximation CX ≈ ACS is with sufficient accuracy (3) Form the sparsity quality Q(l) based on the Lp norm: Q(l)= (1/2)-(1/p) ' ' by a certain sparse approximation algorithm. Namely, the mixing n . ‖Ml‖p/‖Ml‖2,0b p b 1, where n denotes the ' matrix A can be estimated from the sparse approximation coeffi- element number of vector Ml (in this study, the value of p is cients CX. set to 0.5); (4) Repeat (1)-(3) for each l =1,…,L (L is equal to 15 with three- 2.3. Framework of SAAPC level 1D wavelet decomposition in this study);

(5) Choose the features' matrix Ml with the highest sparsity The framework of SAAPC is shown in Fig. 1, which includes three quality as the sparse approximation coefﬁcients set of the main procedures such as sparse approximation coefﬁcients set mixed fMRI data. T. Ren et al. / Magnetic Resonance Imaging 32 (2014) 736–746 739

Fig. 1. The framework of SAAPC. 740 T. Ren et al. / Magnetic Resonance Imaging 32 (2014) 736–746

After the whole procedure of sparse approximation coefﬁcients set where Xi is denoted the original fMRI mixed data of subject i. Then formation, the sparse approximation coefﬁcients set of the mixed the average functional maps and TCs are obtained by averaging the fMRI data is obtained. source signal of each subject:

2.3.2. Clustering analysis using split APC As the fMRI data is in a 4-dimensional form, taking the resting-state XH S ¼ S : ð18Þ experiment for example, with approximately 91 × 109 × 91 voxels X Xi and 123 temporal points, thus results in a 902629 × 902629 similarity i¼1 matrix. But the basic APC has a problem in handling large scale data, because the tremendous similarity matrix derived from the large scale 3. Generation and preprocessing of experimental data data cannot be loaded in a typical personal computer (for example, with computer memory of less than 8Gb) at one time. To deal with All algorithms involved were performed on a workstation whose large scale data, Guha et al. [34] proposed a CURE algorithm which operation system platform was Windows 7 Unlimited Service Pack1, performed a second clustering on the partial clusters, to yield the with Intel® Xeon® E5-1620 3.60 GHz processor and 40GB RAM. All desired clusters. Contraposing the basic APC algorithm, Xia et al. [35] processing algorithms of basic APC, SAAPC, FastICA and SACICA were introduced a PAP algorithm to get the similarity matrix partitioned, run on the Matlab platform (Matlab 2012b, Mathworks Inc., Sherborn, but, in this method, the formation of whole similarity derived from the MA, USA), and all steps of preprocessing such as slice-timing, motion large scale fMRI data also need a heavy computation load. Based on the correction, spatial normalization and smoothing were performed on heuristic of the informed studies, an improved algorithm called split SPM12b [36]. As for the location and display of the resting-state APC is proposed in the following: networks detected by SAAPC, FastICA and SACICA, we used PickAtlas software toolbox [37,38] and MRIcro software [39]. (1) Split the dataset, D, into m sub-groups (1 b m b N/(4C), where N denotes the total number of data points and C is 3.1. Task-related data the expectant maximal number of clusters). For each sub- In the task-related experimental test, six subjects (4 males and group Di (i =1,2,…,m-1),thesizeisa = ⌊N/m⌋, which is 2 females) were informed of the purpose of this study and took part an integer less than or equal to N/m, and the size of Dm is N-a(m-1); in the visual task experiment. The designed visual paradigm was “ ” (2) Implement the adaptive APC [31] on each sub-group, OFF-ON-OFF-ON-OFF-ON in 40 seconds block. At the ON state, respectively, and then obtain the clustering center sets of visual stimulus was corresponding to a radial blue/yellow checker- “ ” every sub-group; board, reversing at 7Hz. While at the OFF state, the participants (3) Gather all the clustering center sets of each sub-group up as a were required to focus on the cross at the center of screen. The BOLD whole dataset which is denoted as ‘full-group’; fMRI data were acquired on a Siemens 3.0 Tesla scanner using a (4) Run the adaptive APC on the full-group. multi-element receiver coil to allow partially parallel image acquisition, a signal-shot SENSE gradient echo EPI with 36 slices providing whole-brain coverage, a SENSE acceleration factor of 3.0, a After steps (1)-(4), the ultimate clustering center set is obtained. TR of 2.0 s and scan resolution of 64 × 64. The in-plane resolution Note that when the number of partition parts m can be properly was 3.75 mm × 3.75 mm; the slice thickness was 4 mm; and the chosen, every sub-group data will be processed easily in a typical slice gap was 1 mm. personal computer. As the final step is done at all partial cluster Because the fMRI data were very large, in order to increase centers from every sub-group, the ultimate result is similar to the analysis efficiency, only signals in the brain were processed in the result when putting all the data points together at the very task-related experiments. In the smoothing procedure, different beginning [35]. Gaussian kernel FWHMs ranging from 0 mm to 8 mm were used. By implementing procedure 1 which is presented in Fig. 1 on the In basic APC and SAAPC, the Euclidean distance was utilized as fMRI mixed data of subject i, we can obtain the corresponding the similarity measure between the data points. Considering the size approximation coefficient set (denoted as Ci , where i ranges from 1 X of every sub-group and the full-group in the split APC procedure to H), respectively. After that, the average of the approximation which is mentioned in Section 2.3.2, the size of each sub-group was coefficient sets of all H subjects is calculated by the formula below to set to 50 data points (in case there is a remainder, it should be taken obtain statistical information: as a sub-group). Since the ROC curve and ROC power analysis are both common 1 XH and effective tools for evaluating the performance among different C ¼ C ðÞi : ð16Þ X H X applied algorithms [40], we used them to assess the performance of i¼1 signal reconstruction ability corresponding to basic APC, SAAPC and FastICA. Each point determined by the true positive rate and false Then, the split APC procedure mentioned above on CX is positive rate of the ROC curve was calculated based on the real active performed until the ultimate cluster center set emerges. template and the variant z-thresh maps, where z-thresh values corresponding to z-score maps varied from 0.5 to 5 with a 0.225 step. 2.3.3. Source signal reconstruction The sizes of the real active templates corresponding to the visual We consider the ultimate cluster center set which is formed in stimulus were determined by GLM [41] using the SPM12b toolbox Section 2.3.2 as the mixing matrix A, and take A† (when A is singular, † (the p value for t-test was 0.025, and the extent threshold was 10). A represents the generalized inverse matrix; when A is nonsingular, Each ROC power value was the area surrounded by the ROC curve. A† = A-1, representing the inverse matrix) as the un-mixing matrix W, thus, the source signalS of subject i (l ≤ i ≤ H) can be calculated Xi 3.2. Resting-related data by the formula presented below: The resting–state dataset was downloaded from the public S ¼ X W ð17Þ Xi i neuroimaging database [42]. This dataset was released by Dr. James T. Ren et al. / Magnetic Resonance Imaging 32 (2014) 736–746 741

J. Pekar and Dr. Stewart H. Mostofsky. Twenty-three healthy subjects 96 × 96. The in-plane resolution was 2.67 mm × 2.67 mm, and the (8 males and 15 females) were involved in this study. The age of these slice thickness was 3 mm. subjects ranged from 20 to 40. BOLD fMRI data were acquired on a The Euclidean distance was utilized as the similarity measure Philips 3.0 Tesla scanner using a multi-element receiver coil that allows between the data points in SAAPC method, and the size of each sub- partial parallel image acquisition with signal-shot SENSE group was set to 250 data points (in case there is a remainder, it acceleration factor of 2.0, a TR of 2.5 s and scan resolution of should be taken as a sub-group).

Fig. 2. The spatial maps corresponding to the visual cortex generated by basic APC, SAAPC and GLM. 742 T. Ren et al. / Magnetic Resonance Imaging 32 (2014) 736–746

4. Experimental results

4.1. Results of task-related data experiments

All subjects' visual cortexes discovered by basic APC and SAAPC from task-related data were shown in Fig. 2, and all of them were compared with visual cortexes obtained by GLM. One of the subjects' ROC curve was presented in Fig. 3, and from it we could see that the true positive rates of SAAPC were always larger than the ones of basic APC when the false positive rate changed from 0 to 0.08. Take the area surrounded by the ROC curve of each subject as the value of ROC power, Fig. 4 could be obtained, and it made clear that the ROC power values of SAAPC were larger than that of basic APC on all subjects. The time cost of basic APC, SAAPC and FastICA were showed in Fig. 5. From it we could find that FastICA was the fastest of the three methods involved in this study. And it also could be figured out that SAAPC could run 20 times faster than basic APC, for the average time cost of basic APC was 10798 s, and SAAPC cost only 534 s averagely. The result of t-test on the time cost of basic APC and SAAPC (statistical significance level p = 0.05) showed that the two sets of time cost were significantly different from each other. To further study SAAPC's reconstruction ability of smoothed fMRI data with varied Gaussian kernel FWHMs ranging from 0 mm to 8 mm, we used the ROC power analysis and chose the FastICA as a Fig. 4. The ROC power of networks corresponding to basic APC and SAAPC on all subjects. comparison. One of the subjects' ROC power analysis result was presented in Fig. 6, which indicated that the areas surrounded by the ROC curve of proposed SAAPC were larger than those of FastICA and basic APC in most of the FWHMs. When FWHM was set to 6 mm, the presented in Figs. 8–10 (all the networks are projected to a standard ROC power of all subjects could be acquired, as shown in Fig. 7. The brain template, and the MNI coordinates (in mm) of these result of t-test on the ROC power values (FWHM = 6 mm) of basic functional networks are labeled in these figures). Some typical APC, SAAPC and FastICA (statistical significance level p = 0.05) RSNs [30,43–46] were discovered by SAAPC: VIN (predominantly showed that the three sets of ROC power values were not occipital network, A), DMN (default mode network, B), BGN significantly different from each other. (a network involving basal ganglia regions, C), AUN (auditory network, D), SMN (a network involving bilateral sensorimotor 4.2. Result of resting-state data experiments cortex, E), LWMN and RWMN (a network including the left hemisphere and right hemisphere regions known to be involving In this section, the resting-state network (RSN) evaluation in working memory, F and G), DPN1 and DPN2 (a network involving results obtained by using the SAAPC, FastICA and SACICA were dorsal parietal and prefrontal cortex, H and I).

Fig. 3. The ROC analysis of networks corresponding to basic APC and SAAPC. T. Ren et al. / Magnetic Resonance Imaging 32 (2014) 736–746 743

Fig. 5. The time cost of basic APC, SAAPC, and FastICA.

5. Discussion separation, and the sparse approximation is used to remove redundancy from the source data and can make the signal detection 5.1. Sparse approximation coefﬁcients analysis procedure in APC more accurate [30]. It could be clearly seen that our proposed SAAPC had better performance in detection accuracy than basic APC on all Traditional clustering analysis methods such as k-centers subjects (showed in Fig. 4). clustering and k-means clustering are quite sensitive to the initial selection of exemplars, thusthey need alarge number of runsto ﬁnd 5.2. Split APC and running time cost analysis a good result. However, in APC algorithm, it does not rely on the initialization of the cluster centers, and the optimal cluster set Traditional clustering analysis methods like k-centers clustering derives from message passing among a given data set. In addition, and k-means clustering, may normally take hundreds of hours of sparsity property is an effective assumption for fMRI signal computing time, but the basic APC requires less computing time than

Fig. 6. The ROC power of visual networks corresponding to basic APC, SAAPC and Fig. 7. The ROC power of visual networks corresponding to basic APC, SAAPC and FastICA in different FWHMs. FastICA on all subjects (FWHM = 6 mm). 744 T. Ren et al. / Magnetic Resonance Imaging 32 (2014) 736–746

Fig. 8. Nine typical RSNs are detected by the SAAPC.

the traditional clustering methods. However, the basic APC algo- 5.4. Limitations of SAAPC and future works rithm cannot process the fMRI data in a typical personal computer (with computer memory of approximately 8 Gb), because the large- Fig. 6 shows that the performance of FastICA decreases with the scale data will require a huge memory resource and entail a heavy increasing of FWHM. It is perhaps because the decomposition based computational load. In the split procedure, we can control the size of FastICA method is more sensitive to the false positive area resulted the sub-group to allow the APC algorithm to be performed on typical from the smoothing process, and the larger FWHM, the more false personal computer. In addition, the SAAPC algorithm performs positive area, thus resulting to the lower ROC values by using significantly faster than the basic APC in fMRI data analysis (showed FastICA. The performances of clustering based basic APC and SAAPC in Fig. 5). The time complexity of basic APC is O(n2), and as the data are not sensitive to the smoothing process according to Fig. 6, are randomly distributed, it is reasonable to suppose that the time however, the performance of our SAAPC appears casual to some used for seeking maximum value of an array is in direct ratio to its extent when compared with basic APC and FastICA, and the split size [35]. In split APC mentioned in Section 2.3.2, as the size of each strategy may be the reason of this phenomenon. Since the split sub-group is about 1/m2 of the whole data set, the iteration of every strategy in SAAPC is just with the knowledge of experiences, to sub-group spends about 1/m2 of the time of the whole data set. further improve SAAPC, in the future, we will focus on developing a When the number of sub-groups is increased by some scale, the size better way to get dataset split. Besides, though our SAAPC, as a of every sub-group is decreased, therefore the time spent on clustering based method, has performance comparable to the computing the similarity matrices can be ignored. Hence the total FastICA in detection accuracy, it still cannot keep pace with classical time spent is significantly shortened. decomposition based FastICA in terms of computing time (showed in Fig. 5), therefore, developing a more effective accelerating strategy for APC is also one of the goals in our future work. 5.3. Resting-state functional connectivity 5.5. Conclusions More and more methods have been proposed to identify brain networks with spontaneous and coherent activity from resting- In this study, we have demonstrated a novel fMRI data analysis state fMRI data. However, traditional clustering analysis methods method based on the combination of sparse approximation and an have difficulty in finding resting-state networks form resting- improved affinity propagation clustering (SAAPC). This proposed state fMRI data sets. Though the basic APC algorithm does not need method mainly consists of three parts: obtaining the sparse prior information, and is useful for visualizing the relationships approximation coefficients set, implementing the split APC algo- between large numbers of regions [47,48], the resting-state rithm and reconstructing the source signal. In task-related experi- networks of human brain have also not be investigated by basic ments, our method presents much better performance for APC [24]. Our proposed SAAPC algorithm in this paper has identifying patterns of brain activation than basic APC algorithm, successfully identified nine typical resting-state networks which both in detecting accuracy and in computing speed. What’s more, were similar to the results derived from FastICA and SACICA our SAAPC can identify the typical RSNs in resting-state data (showed in Figs. 8–10). experiment, which is a breakthrough in fMRI data analysis using T. Ren et al. / Magnetic Resonance Imaging 32 (2014) 736–746 745

Fig. 9. Nine typical RSNs are detected by the FastICA. clustering method. The approach appears to be a powerful tool for constructive comments of the anonymous reviewers who have exploratory analysis of fMRI data. helped the authors to improve the manuscript. Research supported by the National Natural Science Foundation of Acknowledgments China (Grant No. 31170952), the Innovation Program of Shanghai Municipal Education Commission (Grant No. 11ZZ143), the Program The authors are highly grateful to Dr. Ide Magagi Mounkaila for for Professor of Special Appointment (Eastern Scholar) at Shanghai assisting in revising and polishing the phrasing and grammar of this Institutions of Higher Learning, the Project Sponsored by the Scientiﬁc paper. Besides, the authors greatly appreciate the insightful and Research Foundation for the Returned Overseas Chinese Scholars, State

Fig. 10. Nine typical RSNs are detected by the SACICA. 746 T. Ren et al. / Magnetic Resonance Imaging 32 (2014) 736–746

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