fMRI Based Cerebral Instantaneous Parameters for Automatic Alzheimers, Mild Cognitive Impairment and Healthy Subject Classification

April 17, 2019 0:43 WSPC/INSTR UCTION FILE ws-jin Journal of In tegrative Neuroscience c  Imperial College Press fMRI Based Cerebral Instan taneous P arameters for Automatic Alzheimer’s, Mild Cognitiv e Impairmen t and Health y Sub ject Classification Esmaeil Sera j* Scho ol of Ele ctric al and Computer Engine ering, Ge or gia Institute of T e chnolo gy Atlanta, GA, Unite d States eser aj3@gate ch.e du Mehran Y azdi* Dep artment of Communic ations and Ele ctr onics Engine ering, Scho ol of Ele ctric al and Computer Engine ering, Shir az University Shir az, Ir an yazdi@shir azu.ac.ir Nastaran Shahparian Dep artment of Computer Science & Engine ering and Information T e chnology, Scho ol of Ele ctric al and Computer Engine ering, Shir az University Shir az, Ir an nastar an.shahp arian@gmail.c om * Corr esp onding Authors: School of Electrical and Computer Engineering, Mollasadra Street, Shiraz Univ ersity , Shiraz, Iran Receiv ed 15 April 2019 Revised : Man uscript Submitted to b e Considered By Journal of In tegrative Neuroscience Automatic iden tification and categorization of Alzheimer’s patients and the ability to distinguish betw een different levels of this disease can b e very helpful to the researc h comm unity in this field, since other non-automatic approac hes are very time-consuming and are highly dep enden t on exp erts’ exp erience. Herein, we propose the utility of cerebral instan taneous phase and en v elop e information in order to discriminate b etw een Alzheimer’s patien ts, MCI sub jects and healthy normal individuals from functional magnetic resonance imaging (fMRI) data. T o this end, after p erforming the region-of-interest (ROI) analysis on fMRI data, differen t features cov ering p ow er, entrop y and coherency aspects of data are deriv ed from instantaneous phase and env elop e sequences of ROI signals. V arious sets of features are calculated and fed to a sequential forw ard floating feature selection (SFFFS) to choose the most discriminative and informativ e sets of features. A Student’s t-test has b een used to select the most relev ant features from c hosen sets. Finally , a K-NN classifier is used to distinguish betw een classes in a three-class categorization problem. The reported p erformance in ov erall accuracy using fMRI data of 111 combined sub jects, is 80.1% with 80.0% Sensitivit y to both Alzheimer’s and Normal categories distinction and is comparable to the state-of-the-art approaches recently prop osed in this regard. The significance of obtained results was statistically confirmed by ev aluating through standard classification p erformance indicators. The obtained results illustrate that in tro duced analytic phase and en velope feature indexes derived from the ROI signals are significantly discriminative in 1 April 17, 2019 0:43 WSPC/INSTR UCTION FILE ws-jin 2 distinguishing b et ween Alzheimer’s patien ts and Normal healthy sub ject. Keywor ds : Alzheimer’s; fMRI; R OI Analysis; Cerebral Signal Phase and Env elop e; PL V; Coherency; B rain Connectivity 1. In tro duction Alzheimer is a chronic neuro degenerativ e disease that causes one’s mental abilities suc h as memory and cognitiv e skills gradually decline, o v er the years. This o ccurs b ecause of the reduction of health y neurons in v olv ed in cognitiv e skills and as a result the atroph y of the brain. P eople generally are divided into three cases regarding to Alzheimer’s disease, namely health y sub jects, Mild Cognitiv e Impairmen t (MCI) patien ts, and Alzheimer patien ts. MCI is a middle stage and a patient in this stage is at an increased risk of developing Alzheimer’s or another dementia (Alzheimers, 2015). F unctional magnetic resonance imaging (fMRI) is a functional neuroimaging pro- cedure using MRI technology which measures brain activity b y detecting c hanges asso ciated with blo o d oxygenated level dep enden t (BOLD) signal. There are tw o main approac hes in studying fMRI: task-related fMRI, and resting state fMRI in whic h patien ts lying on the scanner with open ey es. fMRI scans should b e considered as a function of time, i.e. treat them as a time series(each time p oint representing one scan). This is b ecause the BOLD signal will tend to b e correlated across succes- siv e scans, meaning that they can no longer b e treated as indep endent samples. The main reason for this correlation is the fast acquisition time (TR) for fMRI relative to the duration of the BOLD resp onse. Studies sho w ed that neuro degenerative diseases suc h as P arkinson, Multiple Scle- rosis (MS) and Alzheimer’s can b e observ ed the most significan t on Default Mo de Net w ork (DMN) of the brain. By applying stim ulations, energy consumption of brain increases appro ximately 5% (Prvulo vic et al. , 2011), and hereby , the rs-fMRI has b een increasingly used in recen t y ears as a noninv asive metho d in neuroimaging. In general, Alzheimer identification metho ds are divided in to tw o main groups: mo del based metho ds, and mo del-free methods. In the former, the goal is calculation of functional connectivit y betw een anatomical or functional regions, F or instance, Ko c h (Ko ch et al. , 2012) and Challis (Challis et al. , 2015) applied seed based method in which time series correlations b etw een a sp ecific region and others are calculated. Although it is an easy metho d to b e applied, finding the primary region is critical in reac hing prop er (V an Den Heuvel and Pol, 2010). In the mo del-free methods w e try to estimate time series of v oxels based on a reduced set of basis. Among these metho ds PCA and ICA are the most p opular ones. In PCA, the goal is finding the correlated regions of vo xels (Zhang et al. , 2015), while in ICA the goal is finding the indep enden t sources. Since in PCA an optimal result o ccurs when the data ha ve the normal probabilit y density function (pdf ), where fMRI data ha v e not, the b est usage of PCA is limited in filtering the noise in fMRI April 17, 2019 0:43 WSPC/INSTR UCTION FILE ws-jin 3 data (Ashb y, 2011). On the other hand, the most imp ortant challenge in applying these t wo methods is finding the prop er n umber of comp onen ts (Binnewijzend et al. , 2012), for instance ICA finds the spatially indep endent comp onent, blindly and at the end, hundreds of comp onen ts migh t b e found while only a couple of them are related to the study . Graph analysis is another mo del-free metho d in analyzing fMRI data. In this metho d, no des are defined by anatomical or functional atlases and the w eight of the edges are calculated by considering different criteria. A critical c hallenge here is defining the nodes and calculation of the w eights of the edges, since differen t algorithms in calculating these t w o, can lead to different results (Bahrami and Hossein-Zadeh, 2015; W ang et al. , 2010). Another metho d of analyzing is clustering metho d, during which the data are divided in to subgroups having the most inter-group similarity and least intra-group similarit y . V arious kinds of clustering hav e b een applied on fMRI data, for instance, Chen (Chen et al. , 2012) applied a hierarchical clustering metho d to define the difference in functional connectivit y betw een MCI patien ts and health y sub jects. Their rep ort show ed that the distribution of clusters and their functionally discon- nected regions are resembled to the altered memory netw ork regions identified in task of fMRI studies. Clustering is easy to apply but it is time consuming for large databases such as fMRI. Moreov er, defining the n umber of cen ters, determining a suitable distance criterion and p erforming an optimization strategy are so critical in this metho d. As recent endeav ors to leverage fMRI data to inv estigate Alzheimer’s and un- derstanding the underlaying neuro-dynamics Zh u and W ang (Zh u and W ang, 2018) prop osed a sup ervised structure learning metho d to explore laten t structures of rest- ing state fMRI data b elonging to different groups. The results rep orted a ’TREE’ structure iden tified as the p otential path for the progression of the Alzheimer’s disease. In other studies such as (Golbabaei et al. , 2016b; Khazaee et al. , 2014; Gol- babaei et al. , 2016a; Lee and Y e, 2012) differen t machine learning and dictionary learning approaches are in tro duced and discussed to discriminate AD and MCI sub- jects. Nev ertheless, these studies ha v e used differen t net w ork construction metho ds and are time-consuming and often require training on large datasets. In particular, man y of these studies ha v e significan t differences in net work construction metho ds (i.e., weigh ted versus binary and differen t density thresholds). It has b een discussed b efore in (Reijneveld et al. , 2007) and (F ornito et al. , 2010; Bo ostani et al. , 2017) that these differences are highly likely to affect the ac hiev ed results. Recently W ang et al (W ang et al. , 2018) prop osed an approach to discriminate b et ween Alzheimer’s diseases (AD) patien ts and MCI sub jects under size limited fMRI data. The pro- p osed method emplo ys R OI analysis to deriv e correlation co efficient b etw een v arious R OIs and then uses a regularized linear discriminant analysis (LDA) alongside with AdaBo ost classifier to classify AD versus MCI sub jects. W e b enchmark this study against our prop osed pro cedure and present the discussion in the last section of this pap er. In general, our approac h leverages feature vectors and classification pro ce- April 17, 2019 0:43 WSPC/INSTR UCTION FILE ws-jin 4 dures that are more readily a v ailable and yet ac hieves comparable significan t results (Sameni and Sera j, 2017; Karimzadeh et al. , 2015). In order to p erform an efficien t and at the same time a simple analysis on the fMRI data, recently , the region-of-in terest (R OI) analysis has b een widely used (Pol- drac k, 2007). R OI analysis is a common approac h to analyze the fMRI data in whic h signals from sp ecified regions of interest (ROI’s) are extracted. R OIs can b e extracted either in terms of structural or functional features. Structural R OIs are mostly de- fined based on macro anatomy , suc h as gyrus anatomy; whereas functional ROIs are generally based on analysis of data from the same individual. One common approach is to use a separate lo calizer scan to identify v o xels that show a particular resp onse in a particular anatomical region and then these vo xels are explored to examine their resp onse to some other manipulation. When using single-sub ject atlases suc h as the AAL atlas or T alairac h atlas in order to extract ROIs, one should b e cautious ab out the inabilit y of spatial normalization to p erfectly matc h brains across individ- uals. Accordingly , the b est practice is to use ROIs based on probabilistic atlases of macroscopic anatom y or probabilistic atlases whic h are a v ailable as part of the SPM Anatom y T oolb ox or FSL (Poldrac k, 2007) In ROI analysis, b y considering fMRI data as time series, the summation of time series of all v o xels in specified anatomical or functional regions pro vide the ability of statistical analysis in signal processing terms. In this study phase and env elop e (amplitude) of ROI signals are used to presen t efficien t, comprehensiv e and discriminative feature sets for the application of iden- tifying Alzheimer’s patients. F or this purp ose, instantaneous phase and env elop e of R OI signals are estimated through analytic form represen tation for the sequences relating to eac h brain area. F or instantaneous parameters, i.e. phase, frequency and en v elop e, estimating a recently prop osed metho d named T ransfer F unction Per- turbation (TFP) is used (Sera j and Sameni, 2017). TFP improv es the quality of estimated instantaneous parameters b y employing a statistical Monte Carlo based approac h and removing the side-effects of previous con ven tional phase estimation metho ds (Sameni and Sera j, 2017). After calculating the phase and en velope for brain areas in R OI signals, three t yp es of features are in tro duced and estimated. P o w er, entrop y and coherency are the main categories of estimated feature sets for b oth phase and env elop e. Afterwards, a Sequen tial F orw ard Floating F eature Se- lection (SFFFS) algorithm is used to help c ho osing the most discriminativ e and informativ e sets of features among the introduced sets (Pudil et al. , 1994). Accord- ingly , Studen t’s t-test is used in order to select the most relev ant features. Even- tually , K-Nearest Neigh b ors (KNN) classifier is emplo y ed to discriminate b etw een three classes of (1) Alzheimer’s patients, (2) MCI sub jects and (3) Health y normal individuals. The rest of this study is structured as follo ws: within next section, first utilized dataset are introduced. Afterw ards, the presented approach for calculating differen t feature sets is detailed and eac h step is elab orated separately . Finally , the results April 17, 2019 0:43 WSPC/INSTR UCTION FILE ws-jin 5 are represen ted and discussed in last t w o sections. 2. Metho dology 2.1. Dataset Rs-fMRI and high resolution T1-w eigh ted MRI images obtained from the Alzheimer’s disease neuroimaging initiativ e (ADNI) database (Jac k et al. , 2008) Data from 111 sub jects gained, in whic h 43 data b elong to healthy normal sub jects, 36 to MCI patients and 32 to Alzheimer patien ts. T able 1 shows the detailed in- formation of eac h group. F or each sub ject, 140 gradient echo planar imaging (EPI) v olumes were acquired by using 3T Phillips Scanner. The parameters of the scanner are TR = 3s, TE = 30ms, matrix size = 64 × 64, slice thic kness = 3mm, and n um b er of slices = 48. Normal MCI Alzheimer Num b er of sub jects 43 36 32 Male/F emale 17/26 14/22 15/17 Mean Age 75.30 72.75 72.34 Standard deviation Age 6.37 6.35 7.12 Mean Education 16.27 15.25 15.75 Standard deviation Education 2.1 2.54 2.75 2.2. Pr epr o c essing: Extr acting R OI Signals All pro cesses hav e b een carried out by using FSL (fMRIB’s Softw are LibraryUK), REST to olb o x (Dev elop ed b y Zhang et al . at Lab oratory of Cognitive Neuroscience and Learning, Beijing Normal Universit y , China), and MA TLAB programming envi- ronmen t. Here we bring the details of eac h step in the prepro cessing pro cedure. F or a b etter understanding, a complete elab oration of the pro cedure is also represen ted in Fig. 1. The applied prepro cessing steps can b e summarized as follo w: (1) Applying head mov ement correction. (2) Applying slice timing correction. (3) Applying a spatial filter b y using an 3D Gaussian k ernel with 4mm3 FWHM in order to increase accuracy of registered functional images to standard space and to ac hiev e b etter signal to noise ratio (SNR) (4) Applying high pass filter with 100s cut-off frequency to remov e low level noise (5) Registering functional images to T1-w eighted images and then registering to MNI152 space using the transformations calculated on corresp onding anatomical images. April 17, 2019 0:43 WSPC/INSTR UCTION FILE ws-jin 6 Fig. 1. Emplo yed pro cedure for R OI signal extraction from raw fMRI data. (6) Applying a band pass filter (0.01HZ - 0.1HZ), since resting state BOLD signal, whic h arises from neuronal activit y , is lo cated in this frequency band. (7) Filtering output data in the previous step by regressing out mov emen t vectors as suggested b y F riston et al (F riston et al. , 1996). (8) Filtering unw anted signals such as physiological noise which can b e conducted b y principle comp onent analysis as it men tioned b y Behzadi et al (Behzadi et al. , 2007). (9) Filtering the linear trend of gray matter time series which o ccurred due to the heat of scanner. (10) Obtaining time series of 112 anatomical regions for each sub ject based on Harv ard-o xford atlas in Extract R OI time courses tab in REST softw are. Harv ard-o xford is a probabilistic atlas co vering 48 cortical and 21 sub-cortical structural areas, derived from structural data and segmen tations pro vided b y the Harv ard Cen ter for Morphometric Analysis. In this atlas, T1-weigh ted images of 21 healthy male and 16 healthy female sub jects (ages 18-50) were individually seg- men ted using semi-automated to ols. The T1-weigh ted images were affine-registered to MNI152 space and the transforms are then applied to the individual lab els. Fi- nally , they were combined across sub jects to form p opulation probability maps for eac h lab el (Karimzadeh et al. , 2017). The summation of time series of these regions is reformed into a v ector of 112 × 1 for eac h sub ject and then by putting together these vectors for each group, a final matrix of 112 × 16 is obtained and finally feature extraction metho d is applied on these matrices. 2.3. Instantane ous Par ameters Estimation The conv entional approac h for instantaneous phase, frequency and env elop e estima- tion, i.e. narrowband frequency filtering follow ed by analytic or complex representa- April 17, 2019 0:43 WSPC/INSTR UCTION FILE ws-jin 7 tion, is prone to highly affect the estimates and yield am biguous v alues, esp ecially during low SNRs of background activity (Sera j and Sameni, 2017), (Sameni and Sera j, 2017). The background activity here is referred to the undesired comp onen ts of the frequency-sp ecific instantaneous measures. F or obtaining an accurate and unam biguous estimation of instantaneous phase (IP) and instan taneous en v elop e (IE), herein, we use a recently dev elop ed metho d in (Sera j and Sameni, 2017) and (Sameni and Sera j, 2017). The metho d which is referred to as T r ansfer F unction Perturb ation (TFP) is a statistical Monte Carlo based estimation sc heme in which infinitesimal p erturbations or dithers are added to the utilized filter or input signal in order to generate estimation ensembles (Sera j and Sameni, 2017). The applied p erturbations or dithers in TFP are suc h that they are physiologically irrelev an t and the filter’s sp ecifications do not change significan tly according to the estimation standards (Sameni and Sera j, 2017). The filtering pro cess in TFP is p erformed in a forward-bac kward zero-phase approac h in order to preven t any phase distortion. Ev en tually , the final IP and IE estimates are calculated through ensemble av erag- ing ov er all dithered and p erturb ed ensembles. The rationale b ehind the TFP is b ey ond the scope of the curren t study and one can find a detailed description in (Sameni and Sera j, 2017) and (Sera j and Sameni, 2017). T o date, TFP has b een successfully used in a v ariet y of applications such as BCI (Sera j and Sameni, 2017; Sera j and Karimzadeh, 2017), brain connectivit y and synchronization (Sameni and Sera j, 2017; Sera j, 2017) and sleep stage classification (Karimzadeh et al. , 2018). In this study , for b oth IP/IE estimation and also deriving relev an t phase and en- v elop e features, we use the c er ebr al signal phase analysis to olb ox pro vided by the authors of (Sera j and Sameni, 2017; Sameni and Sera j, 2017; Sera j, 2017) which is in tro duced in (Sera j, 2016a) and is av ailable online at (Sameni, 2014). Accordingly , the analytic represen tation for sequences relating to eac h brain area in R OI signals extracted from fMRI data is calculated as follo ws: Z i ( t ) = x i ( t ) + j H { x i ( t ) } (2.1) Where x i ( t ) is the sequence in i -th brain area of extracted ROI signal and H. represen ts the Hilb ert T ransform. Using the represented analytic form the instan- taneous phase ( I P i ) and env elop e ( I E i ) for each brain area ( i ) are estimated as follo ws: I P i ( t ) = arg { Z i ( t ) } = arctan  H{ x i ( t ) } x i ( t )  (2.2) I E i ( t ) = | Z i ( t ) | = p x i ( t ) 2 + H{ x i ( t ) } 2 (2.3) Due to the usage of arctan ( . ) function, the calculated phase signal migh t be wrapp ed in p oin ts where the v alues cross ± π . Accordingly , an unwrapping step is required after estimating the IP as a p ost-pro cessing level. Fig. 2 shows the estimated IP and IE for each brain area o v er time-p oin ts calculated for the ROI signal extracted from fMRI data of a sub ject in emplo y ed dataset. April 17, 2019 0:43 WSPC/INSTR UCTION FILE ws-jin 8 -0.05 0 0.05 IP(t)-t 100 Time-points 50 Brain Area 100 0 50 0 0 5000 10000 15000 IE Magnitude 100 Time-points 50 Brain Area 0 100 50 0 Fig. 2. Estimated IP and IE for each brain area o ver time-p oints calculated for the ROI signal extracted from fMRI data of an Alzheimer’s patient 2.4. F e atur e Estimation: Intr o ducing F e atur e Indexes The estimated phase and env elop e measures for ROI signals derived from fMRI data of eac h sub ject, i.e. Alzheimer, MCI and Normal, are then used to extract the feature sets. Three different categories of features as (1) p ow er, (2) entrop y and (3) coherency are calculated for IP and IE to cov er almost all asp ects of physiological data by using b oth lo cal-scale (relating to one sp ecific area of brain) and large-scale (b et w een t w o distant areas within brain) features. 2.4.1. Power F e atur e Sets Energy of the calculated IPs and IEs ov er time-p oints for each brain area ( i ) is used as a measure of p ow er, indicating a lo cal-scale feature set. This feature is used to capture the in tensity of brain activit y in separate areas. Accordingly , different amoun t of activity recorded in eac h cerebral region could potentially b e discrimi- nativ e b et ween Alzheimer’s, MCI’s and Normal sub ject’s data. The Energy of ROI signals for each brain area ( i ) ov er a p erio d of T time-p oints can b e calculated as follo ws: I P P ow i = T X t =1 | I P i ( t ) | 2 (2.4) I E P ow i = T X t =1 | I E i ( t ) | 2 (2.5) The calculated energy v alues are stored in vectors of size N which represen ts the n um b er of brain areas. Ac cordingly , for eac h sub ject, tw o vectors of length 112 (N = 112) are computed as IP and IE p o w er feature sets. April 17, 2019 0:43 WSPC/INSTR UCTION FILE ws-jin 9 2.4.2. Entr opy F e atur e Sets En trop y indexes are directly related to the amoun t of information em b edded in a signal. Herein, for capturing irregularity and significance of v ariations of the brain activit y within differen t regions, Shannon Entr opy is used as another lo cal-scale fea- ture. Although v ariance and en tropy indexes b oth reveal the information regarding v ariations and temp oral irregularity of the patterns in a signal, the v ariance is sen- sitiv e to the amplitude v alues (Sab eti et al. , 2009). Accordingly , using the estimated IP and IE images as illustrated in Fig. 3, Shannon Entrop y can b e calculated for separate brain areas as follo ws: I P E nt i = − X k p k log b p k (2.6) I E E nt i = − X k l k log b l k (2.7) where k is the range of all discrete amplitude v alues of the signals. Also, p k and l k are the probabilit y of the I P i ( t )and I E i ( t )signals ha ving the k -th magnitude, resp ec- tiv ely . Histogram analysis is a prop er tec hnique to calculate the probabilities and the entrop y in case that the num b er of samples in different discretized m agnitudes are sufficient. Moreo ver, the ranges of IP and IE sequences are not equal, where consequen tly , the width of bins p k and l k are different and v aried from one feature to another. Similar to the first feature set, i.e. p ow er features, the calculated entropies are stored in v ectors of size N=112 represen ting the num b er of brain areas. Accordingly , for eac h sub ject in eac h of three classes, t wo vectors, i.e. for IP and IE, are computed as the second sets of features. 2.4.3. Coher ency F e atur e Sets Tw o differen t but inheren tly similar coherency indexes, namely Phase Lo c king v alue (PL V) and Magnitude Squared Coherence (MSC), are prop osed here in order to in v estigate the correlation and dep endence b etw een apart regions of brain and create large-scale feature sets. PL V and MSC feature sets are calculated for the IP and IE sequences extracted from R OI signals, resp ectiv ely . PL V is one of the most common measures used in phase analysis whic h describ es ho w muc h the difference b etw een phases of tw o signals is constant (Lachaux et al. , 1999). F or calculating PL V, after estimating the IP difference b etw een t wo signals, the lo cal stability of this IP difference hav e to b e quantified. Accordingly , the sta- bilit y of IP differences b etw een brain regions ( i ) and ( j ) can b e quantified as b elow (Lac haux et al. , 1999). P LV ij =      1 T T X t =1 e j [ I P j ( t ) − I P i ( t )]      (2.8) where T is the length of signals and the summation is tak en o v er time-p oints ( t ). April 17, 2019 0:43 WSPC/INSTR UCTION FILE ws-jin 10 20 40 60 80 100 20 40 60 80 100 MSC 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 Brain Area 20 40 60 80 100 PLV 20 40 60 80 100 Brain Area 20 40 60 80 100 20 40 60 80 100 Brain Area 20 40 60 80 100 Fig. 3. Sample pairwise PL V and MSC matrices calculated for IP and IE sequences, resp ectively . F rom left to righ t, illustrated matrices b elong to Alzheimer’s, MCI and Normal sub jects from utilized dataset. The IPs and IEs are extracted from ROI signals for all (i.e. N = 112) brain areas. The MSC is employ ed to inv estigate the b etw een-region coherency for estimated en v elop e (IE). The con v entional approach for measuring MSC is based on calculating the P o w er Sp ectral Densities (PSD) for tw o signals (Carter et al. , 1973). Assuming I E i and I E j to b e tw o randomly c hosen instan taneous env elop e signals from t wo distan t brain areas (i) and (j), the MSC can b e computed as b elow (Sera j, 2016b; Carter et al. , 1973): M S C ij = | P S D ij | 2 P S D ii P S D j j = E { I E i I E ∗ j } E {| I E i | 2 } E {| I E j | 2 |} (2.9) Where E { . } is the mathematical exp ectation and P S D ij is the cross-sp ectrum b et w een instantaneous en velope sequences estimated from ROI signals extracted for brain areas ( i ) and ( j ) (Sera j, 2016b). PL V and MSC are b oth widely used cerebral sync hron y indexes and their v alues v ary b et w een 0 and 1. A PL V or MSC equal to 1 indicates highly coherent and sync hronous signals and vice versa (Sera j, 2016b; Carter et al. , 1973). F or b oth PL V and MSC, the coherency is insp ected betw een all p ossible pairs of 112 brain areas, resulting in 112 × 112 feature matrices for I P i ( t ) and I E i ( t ) resp ectiv ely . Figure 3 illustrates sample PL V and MSC matrices calculated for IP and IE sequences of a sub ject in utilized dataset. In this wa y , the third category of features is formed as a large-scale feature, cov ering the coherency and synchron y b et w een the activities of differen t cerebral areas in fMRI data. April 17, 2019 0:43 WSPC/INSTR UCTION FILE ws-jin 11 2.5. F e atur e Sele ction and Classific ation In this step, first, a Se quential F orwar d Flo ating F e atur e Sele ction (SFFFS) algo- rithm is applied to identify the most informative and discriminative sets of features among all 6 feature sets (2 sets for IP and IE in eac h category). The feature vector for eac h class is formed by concatenating the features calculated from the corresp ond- ing IP and IE signals. In this step, eac h feature set is used solely is a classification pro cess in similar settings and the w eak est sets in accuracy are left out. The c hosen features and remaining sets from the former step are fed to Studen t’s t-test in order to select the most relev ant and discriminativ e features within feature- sets. Studen t’s t-test assumes a normal distribution for the features of each class with equal but unknown v ariances and examines the n ull h yp othesis of whether they ha v e equal means (Duda et al. , 1973). Accordingly , only features with p-v alues b elow a significance lev el equal to 0.05, indicating confidence lev el in the rejection of the n ull h yp othesis, are included in the classification stage. Ev en tually , the remaining features are gathered and concatenated for eac h of three classes and the corresp onding lab els are assigned. The Alzheimer’s patients, MCI sub jects and health y Normals are lab eled as 1, 2 and 3 resp ectively . The com- bination of all selected feature sets together is fed to a K-Nearest Neighbor (KNN) classifier with K=5 to p erform the final discrimination b et ween three classes. Al- though v arious other v alues of K ha v e b een tested, i.e. K=1,5,10 and 15, K=5 show ed the b est p erformance and w as chosen for all lev els of classification (i.e. in feature selection with SFFFS). F or the classification, a total of 30 sub jects’ data (i.e. 10 of each class) ha v e b een c hosen randomly for the test and the remaining 81 w ere used for training the classifier. Accordingly , the classifier is trained b y the en tire com bined sets of features with a single lab el and then returns a single v alue, i.e. 1, 2 or 3, as the result of lab el testing with test data. 3. Exp erimen tal Results In this section, the results of classifying b etw een Alzheimer’s, MCIs and Normal sub jects by the com bination of all c hosen features are ev aluated through calculating four standard classification performance indicators, namely accuracy (A C), precision (PR), sp ecificity (SP) and sensitivity (SE).First, it is noteworth y to review the results of feature selection through significance tests. The significance tests were p erformed for all three p ossible cases, i.e. Alzheimer’s vs. MCI, Alzheimer’s vs. Normal and MCI vs. Normal, and the results are elab orated in Fig. 4. The confidence lev el for the rejection of the null hypothesis, as men tioned, w as c hosen equal to 5% (p-v alue < 0.05). As it can b e seen, approximately betw een 80% to 90% of the calculated features w ere confirmed as statistically significan t and relev ant. The selected features were in v olv ed in classification stage. By using a 5-NN classifier as describ ed previously , we were able to correctly lab el 21 sub jects out of selected 30 for the test, resulting in a 80.1% ov erall accuracy (av erage accuracy of April 17, 2019 0:43 WSPC/INSTR UCTION FILE ws-jin 12 75 77 79 81 83 85 87 89 91 Al z he i m er's v s. Nor mal Al z he i m er's v s. MCI M CI vs. Nor mal 6545 f ea t ur es 6203 f ea t ur es 6381 f ea t ur es P er cen t ag e of Sign ifi c an t F ea tur es (% ) Fig. 4. Amount of statistically significant features selected by Student’s t-test to b e inv olved in classification stage. all classes). The confusion matrix of this ev aluation is represented in T able 2. T ruth Data Precision Classifier Alzheimer’s MCI Normal Alzheimer’s 8 3 1 66.7% MCI 2 5 1 62.5% Normal 0 2 8 80.0% Recall (Sensitivit y) 80.0% 50.0% 80.0% Ov erall Accuracy = 80.1% Considering the result presented in T able 2, the accuracy , precision, sp ecificit y and sensitivit y of the prop osed features are illustrated in Fig. 5 b oth for each class and in o v erall. The A C, PR, SP and SE are calculated as b elow: AC = T P + T N T P + T N + F P + F N (3.10) P R = T P T P + F P (3.11) S P = T N T N + F P (3.12) S E = T P T P + F N (3.13) Accordingly , the ov erall accuracy , precision, sp ecificity and sensitivity are then computed as the a v erage A C, PR, SP and SE of all classes, resp ectively . April 17, 2019 0:43 WSPC/INSTR UCTION FILE ws-jin 13 30 40 50 60 70 80 90 Alz h eim er ' s M C I Norm al Overal l AC 80 73.4 86.7 80.1 PR 66.7 62.5 80 69.8 SP 80 85 90 85 SE 80 50 80 70 P e r ce n t ag e (%) Fig. 5. The obtained accuracy (AC), precision (PR), sp ecificity (SP) and sensitivity (SE) for eac h of three class and the ov erall case. As depicted in Fig. 5, the classes b elonging to the Alzheimer’s patients and health y Normal sub jects are sho wing great results, ho w ev er, one might discuss that this is not the case for the class of MCI sub jects. T able 2 states that 8 out of 9 o ccurred misclassifications are someho w related to MCI category . Moreov er, 3 of MCI cases hav e b een mistaken b y Alzheimer’s patients which shows close sp ecifications b et w een these t wo classes. As a consequen t, although 8 out of 10 Alzheimer’s sub jects ha v e b een iden tified correctly , SP and PR are not relatively high for this class (as compared to the Normal category). Generally sp eaking, the prop osed phase and en v elop e features are showing significant results; nevertheless, further strategies are required in order to impro v e the classification rate of MCI sub jects. 4. Discussion Detection of Alzheimer disease in its early stage is significantly imp ortant for medicines to apply prop er treatments. Therefore, new trends in this domain are to- w ard using more efficient algorithms to distinguish normal sub jects from Alzheimer patien ts. In this pap er, we dev elop ed an algorithm which can efficien tly classify sub- jects into normal and different stages of Alzheimer disease using fMRI data. T o do that, we use for the first time new features which are phase and env elop e sequences of ROI signals from fMRI data, and the selected ROI are based on Harv ard-Oxford atlas which is a probabilistic brain atlas. W e also selected most informativ e sets of these features using a sequential forward floating feature selection. Our observ ation sho w ed that this new set of features can efficiently represent the characteristics of fMRI data and discriminate very well different stages of Alzheimer disease. As it April 17, 2019 0:43 WSPC/INSTR UCTION FILE ws-jin 14 R efer enc es sho wn in figure 6, separating MCI patien ts has the least accuracy and the algo- rithm mostly mistak en them b y Alzheimer’s and that is b ecause of the v ariation of the brain in patien ts such as Aggregation of protein fragmen t b eta-amyloid outside the neurons and also abnormally accum ulation of protein tau (tau tangles) inside neurons, which is basically similar in MCI and Alzheimer patients rather than nor- mal ones. In general the obtained results by applying the proposed algorithm on real fMRI data show ed a go o d p erformance which can b e a promising approach for clinical applications. Ac kno wledgments This researc h has been supp orted by the Cognitive Sciences and T echnologies Coun- cil of Iran (COGC), under the gran t n um b er 2250. Conflict of in terest statement The authors declare no comp eting in terests. 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