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Contents lists available at ScienceDirect

Neuroscience Letters

journa l homepage: www.e lsev ier .com/ locate /neule t

VM-based computer-aided diagnosis of the Alzheimer’s disease using t-testMSE feature selection with feature correlation weighting

. Chaves, J. Ramírez ∗, J.M. Górriz, M. López, D. Salas-Gonzalez, I. Álvarez, F. Segoviaepartment of Signal Theory, Networking and Communications, University of Granada, Spain

r t i c l e i n f o

rticle history:eceived 15 May 2009eceived in revised form 16 June 2009

a b s t r a c t

This letter shows a computer-aided diagnosis (CAD) technique for the early detection of the Alzheimer’sdisease (AD) based on single photon emission computed tomography (SPECT) image feature selection

ccepted 17 June 2009

eywords:PECT Brain Imaging Classificationomputer-aided diagnosis

and a statistical learning theory classifier. The challenge of the curse of dimensionality is addressedby reducing the large dimensionality of the input data and defining normalized mean squared errorfeatures over regions of interest (ROI) that are selected by a t-test feature selection with feature correlationweighting. Thus, normalized mean square error (NMSE) features of cubic blocks located in the temporo-parietal brain region yields peak accuracy values of 98.3% for almost linear kernel support vector machine(SVM) defined over the 20 most discriminative features extracted. This new method outperformed recent

arly A

lzheimer’s diseaseupport Vector machine developed methods for e

lzheimer’s disease (AD) is a progressive neurodegenerative disor-er first affecting memory functions and then gradually affectingll cognitive functions with behavioral impairments and eventu-lly causing death. According to the latest estimates, the globalrevalence of AD will quadruple to 100 million by 2050. To datehere is no single test or biomarker that can predict whether aarticular person will develop the disease. Its diagnosis is basedn the information provided by a careful clinical examination, ahorough interview of the patient and relatives, and a neuropsy-hological assessment. A regional cerebral blood flow (rCBF) studyy means of single photon emission computed tomography (SPECT)

s commonly used as a complimentary diagnostic tool in addition tohe clinical findings [7]. However, in late-onset AD there are min-mal perfusion alterations in the mild stages of the disease, andge-related changes, which are frequently seen in healthy agedeople, have to be discriminated from the minimal disease-specifichanges. These minimal changes in the images make visual diag-osis a difficult task that requires experienced explorers. Even withhis problem still unsolved, the potential of computer-aided diag-osis (CAD) has not been explored in depth [10,13,16,6].

Please cite this article in press as: R. Chaves, et al., SVM-based computer-aselection with feature correlation weighting, Neurosci. Lett. (2009), doi:10

Since their introduction in the late seventies, Support Vectorachines (SVMs) [17] marked the beginning of a new era in the

earning from examples paradigm. Recent developments in defin-ng and training statistical classifiers make it possible to build

∗ Corresponding author at: Dpto. Teoría de la Senal, Telemática y Comunicaciones,eriodista Daniel Saucedo Aranda 18071, Granada, Spain. Tel.: +34 958 240842;ax: +34 958240831.

E-mail address: javierrp@ugr.es (J. Ramírez).

304-3940/$ – see front matter © 2009 Elsevier Ireland Ltd. All rights reserved.oi:10.1016/j.neulet.2009.06.052

D diagnosis.© 2009 Elsevier Ireland Ltd. All rights reserved.

reliable classifiers in very small sample size problems [3] sincepattern recognition systems based on SVM circumvent the curseof dimensionality, and even may find nonlinear decision boundariesfor small training sets. This paper shows a new feature extractionand selection method for SVM-based classification of SPECT imagesand the design of an AD CAD system.

The SPECT image acquisition and preprocessing and the statis-tical methods used for feature extraction and feature selection ispresented in this article followed by the experiments that wereconducted in order to evaluate the proposed methods and the con-clusions. Finally, basic notions of SVM are explained in AppendixA.

The proposed CAD techniques were evaluated by means of aSPECT image database that was especially collected during a con-current study focussing on early AD diagnosis. Each patient wasinjected with a gamma emitting technetium-99m labeled ethyl cys-teinate dimer (99mTc-ECD) radiopharmaceutical and the SPECT scanwas acquired by means of a 3-head gamma camera Picker Prism3000. Brain perfusion images were reconstructed from projectiondata by filtered backprojection (FBP) in combination with a Butter-worth noise filter. SPECT images were spatially normalized [12] inorder to ensure that a given voxel in different images refers to thesame anatomical position. This process was done by using Statisti-cal Parametric Mapping (SPM) [5] yielding 69 × 95 × 79 normalizedSPECT images. The normalization method assumed a general affine

ided diagnosis of the Alzheimer’s disease using t-test NMSE feature.1016/j.neulet.2009.06.052

model with 12 parameters and a cost function which presentsan extreme value when the template and the image are matchedtogether. Once the image is normalized by means of an affine trans-formation, it is registered using a more complex non-rigid spatialtransformation model. Finally, intensity level is normalized to the

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aximum intensity following a procedure similar to that in [14,9].he images were initially labeled by experienced clinicians of theirgen de las Nieves Hospital (Granada, Spain) as normal (NOR)

or subjects without any symptoms of the disease and ATD to refero possible, probable or certain AD patients. In total, the databaseonsists of 79 patients: 41 NOR and 38 ATD.

Not all the brain regions provide the same discriminative valueor detecting the early AD. In fact, the posterior cingulate gyrind precunei, as well as the temporo-parietal region are typicallyffected by hypo-perfusion in the AD [8]. In a previous work, a studyas carried out in order to identify the most discriminating slices

f interest (SOI) [11]. The analysis showed the high discriminationbility of specific normalized mean square error (NMSE) featuresorresponding to coronal slices and defined to be:

MSEp =

M−1∑

m=0

N−1∑

n=0

[f (m, n) − gp (m, n)

]2

M−1∑

m=0

N−1∑

n=0

[f (m, n)]2

(1)

here f(m,n) defines the reference slice template (obtained by aver-ging the SPECT images of all the normal controls in the database)nd gp(m,n) the slice intensities of the p subject. Fig. 1 shows theifferences in rCBF provided by these SOI [11]. It shows three dif-

erent coronal slices of a template SPECT obtained by averaging theunctional SPECT of 41 controls (Fig. 1a) together with the corre-ponding coronal slices of a normal subject (Fig. 1b) and an ADatient (Fig. 1c). A SVM classifier was trained using only these SOIMSE features. Fig. 2 shows the 3D input space and the ability ofVM classifiers to separate the two classes (normal controls in cir-les vs. patients affected by ATD in squares) by means of linear

Please cite this article in press as: R. Chaves, et al., SVM-based computer-aselection with feature correlation weighting, Neurosci. Lett. (2009), doi:10

Fig. 2a), polynomial (Fig. 2b), quadratic (Fig. 2c) and RBF (Fig. 2d)ernels.

However, the method described above is far from being opti-um since not all the voxels in a given slice provide the same

iscriminative power [8]. In order to better delimitate the ROIs,

Fig. 1. Coronal slices of: (a) template, (b) normal subject, and (c) AD patient.

PRESStters xxx (2009) xxx–xxx

localized NMSE features were redefined in 3D voxel blocks. First,the mean value of the voxel intensity of normal subjects was com-puted by averaging the voxel intensities of all the normal controls inthe database. Only those voxels with a mean intensity above 50% themaximum intensity and defining a 3D mask were considered. Then,the NMSE of a block of (2v + 1) × (2v + 1) × (2v + 1) voxels centeredat the point with coordinates [x, y, z] is defined as

NMSEp(x, y, z)

=∑+v

l,m,n=−v[f (x − l, y − m, z − n) − gp(x − l, y − m, z − n)]2

∑+vl,m,n=−v[f (x − l, y − m, z − n)]2

(2)

where f(x, y, z) is the mean voxel intensity at (x, y, z), and gp(x, y, z)is the voxel intensity of the p patient.

A study was carried out in order to find the most discriminativeROIs defined by the values of [x, y, z] and the corresponding NMSEfeature to train a SVM classifier. It is based on an absolute valuetwo-sample t-test with pooled variance estimate on NMSE features:

T(x, y, z) =∣∣�1 − �0

∣∣√

�21 + �2

0

(3)

where �1, �0 are the ATD and NOR class means of the features,respectively and �2

1 , �20 are their variances. The feature selection

also uses correlation information to outweight the T value of poten-tial features by T(1 − ˛�), where � is the average of the absolutevalues of the cross-correlation coefficient between the candidatefeature and all previously selected features, and a is a scalar valuebetween [0,1] that provides the weighting factor. Note that when ais close to 1, features that are highly correlated with already selectedfeatures are less likely to be selected. In the experiments shown inthis work, a is 0.95. Fig. 3 shows a map of the value of T for eachof the voxels within the mask and a voxel size v = 2. Note that, thet-test feature selection defined above clearly identifies the typicalareas of hypo-perfusion in AD. Finally, Fig. 4 shows the 100 mostdiscriminative ROI coordinates that were found by using the pro-posed method and after introducing a weighting factor over T thatavoids selecting correlated NMSE features.

SVM classifiers (see Appendix A) were used to define the ADCAD system. The most discriminative 3D NMSE features identifiedby the proposed feature selection process were used as input datafor defining the decision rule. The performance of the SVM classi-fier was tested on a set of 79 real SPECT images (41 normals and 38AD). Since leave-one-out cross-validation can suffer from high vari-ability in estimating the classification accuracy, the .632+ bootstrapmethod [4] combining low variance with only a moderate bias wasused for the evaluation of the proposed methods.

The results using localized 3D NMSE and 2D slice NMSE featureswere compared. The shape of the decision rule strongly depends onthe classification method and its associated parameters as well asthe input features as shown in Fig. 2. Note that, linear and poly-nomial SVM classifiers defined using only the three NMSE featurescorresponding to the most significant 2D slices are the classifiersthat better separate the two classes as shown in Fig. 2a and b. Theseresults are in agreement with the fact that, in applications wherethe number of instances is lower than the number of features, andwhen the number of features increases, a mapping of the input datainto a high-dimension feature space using more complex kernels isunnecessary [10].

Similar results are obtained by considering 3D cubic NMSE fea-tures identified by the feature selection process described in this

ided diagnosis of the Alzheimer’s disease using t-test NMSE feature.1016/j.neulet.2009.06.052

work. Fig. 5 shows the accuracy of the system as a function of thenumber of input features for linear, quadratic, RBF and polynomialkernel SVM systems. The accuracy of the system tends to increasewith the number of features up to a maximum stable value. SVMclassifiers using linear and polynomial kernels defined over the

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input

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F

Fig. 2. Decision surfaces for a SVM classifier using SOI NMSE features as

Please cite this article in press as: R. Chaves, et al., SVM-based computer-aselection with feature correlation weighting, Neurosci. Lett. (2009), doi:10

0 most discriminative input features yield the best results withccuracy values of about 98%, thus outperforming recent developedD CAD systems based on Principal Component Analysis (PCA) [1]r the voxels-feature (VAF) approach [15] that yields just an 80%

ig. 3. Magnitude of T for each of the voxels within the mask and a voxel size v = 2.

features and (a) linear, (b) polynomial, (c) quadratic and (d) RBF kernels.

ided diagnosis of the Alzheimer’s disease using t-test NMSE feature.1016/j.neulet.2009.06.052

classification accuracy by combining the voxel intensities as inputfeatures and linear SVM.

An additional experiment was carried out for testing the pro-posed methods. The selection of the optimum voxel size v was

Fig. 4. Coordinates of the 100 most discriminative AD ROIs obtained by featureselection based on a t-test with feature correlation weighting.

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ig. 5. Accuracy of kernel-based SVM classifiers as a function of the number of inputeatures and v = 2.

tudied by evaluating the performance of a SVM-based classifiersing the .632+ bootstrap method [4]. Fig. 6 shows the accuracyf a linear kernel SVM system as a function of the number of fea-ures for different values of the voxel size v. Note that, reduced sizeubic NMSE features yield the best results with an accuracy value ofbout 98% for v = 2 that tends to be stable as the number of featuresncreases.

In order to fully evaluate the proposed system, sensitivity andpecificity values were also estimated. They provide complimentarynformation to accuracy and are statistical performance measuresf a binary classification test. Sensitivity measures the proportion ofctual positives which are correctly identified (e.g. the percentagef AD patients who are identified as having the condition); and thepecificity measures the proportion of negatives which are correctlydentified (e.g. the percentage of normal subjects who are identified

Please cite this article in press as: R. Chaves, et al., SVM-based computer-aselection with feature correlation weighting, Neurosci. Lett. (2009), doi:10

s not suffering AD). The proposed method yielded excellent resultsor these three measures, yielding peak accuracy value of 98.6%

ith a 97.3% sensitivity of and 100% specificity. As a conclusion,he proposed NMSE features defined over 3D voxel blocks togetherith an effective t-test for feature selection with feature correla-

ig. 6. Accuracy of a linear kernel SVM classifier as a function of the number of inputeatures for selection of the optimum voxel size v.

PRESStters xxx (2009) xxx–xxx

tion weighting and SVM classification is a very useful method fordefining a CAD system for the early detection of the AD. Moreover,the system automatically focuses on the temporo-parietal regions.These results agree with the fact that temporo-parietal region ispractical for the early detection of the disease in patients that areno longer characterized by specific cognitive impairment but bygeneral cognitive decline [8].

In this work, a new feature extraction and selection method wasproposed for SVM classification of SPECT images with the aim ofdesigning an AD CAD system. The proposed system is based onvoxel-based NMSE feature extraction, t-test feature selection withfeature correlation weighting and SVM image classification. Theproposed method yielded 98.6% classification accuracy (97.3% sen-sitivity of and 100% specificity) and outperformed recent developedmethods for early AD diagnosis. Slice NMSE features were redefinedas variable size 3D cubic blocks NMSE features with the aim of bet-ter analyzing and identifying the ROIs that are first affected by theearly AD. The most discriminative ROIs were found by means ofa t-test feature selection process with pooled variance estimatesand feature correlation weighting that makes that features that arehighly correlated with already selected features to be less likely tobe included in the output list. Finally, the optimum voxel size andthe kernel transformation were discussed. The performance of theSVM classifier was tested on a set of 79 SPECT images (41 normalsand 38 AD) by means of the .632+ bootstrap method that combineslow variance and moderate bias estimation of the error rate. Theproposed method yielded an accuracy value of up to 98.6% for alinear kernel SVM classifier defined over the 20 most discrimina-tive 5 × 5 × 5 NMSE features selected. Moreover, the proposed CADtechnique outperformed several recently developed methods forearly AD diagnosis.

Acknowledgments

This work was partly supported by the MICINN of Spainunder the PETRI DENCLASES (PET2006-0253), TEC2008-02113,NAPOLEON (TEC2007-68030-C02-01) and HD2008-0029 projectsand the Consejería de Innovación, Ciencia y Empresa (Junta deAndalucía, Spain) under the Excellence Project TIC-02566.

Appendix A. Support vector machines (SVM)

SVM [17,2] separate a set of binary-labeled training data bymeans of a hyperplane (called maximal margin hyperplane). Theobjective is to build a decision function f : RN → {±1} using train-ing data that is, N-dimensional patterns xi and class labels yi so thatf will correctly classify new unseen examples (x, y):

(x1, y1), (x2, y2), . . . , (xl, yl) ∈ RN{±1} (4)

Linear discriminant functions define decision hyperplanes in a mul-tidimensional feature space:

g(x) = wT x + w0 (5)

where w is the weight vector that is orthogonal to the decisionhyperplane and w0 is the threshold. The optimization task consistsof finding the unknown parameters wi, i = 1, . . . , N and w0 thatdefine the decision hyperplane. When no linear separation of thetraining data is possible, SVM can work effectively in combinationwith kernel techniques so that the hyperplane defining the SVMcorresponds to a non-linear decision boundary in the input space.

ided diagnosis of the Alzheimer’s disease using t-test NMSE feature.1016/j.neulet.2009.06.052

If the data is mapped to some other (possibly infinite dimensional)Euclidean space using a mapping �(x), the training algorithm onlydepends on the data through dot products in such an Euclideanspace, i.e. on functions of the form �(xi)·�(xj). If a “kernel function”K(xi,xj) is defined such that K(xi,xj) = �(xi)·�(xj), it is not neces-

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ary to know the � function during the training process. In theest phase, a SVM is evaluated for each input vector x by comput-ng dot products of the test point x with w, or more specifically byomputing the sign of:

(x) =NS∑

i=1

˛i · yi · ˚(si) · ˚(x) + ω0 =NS∑

i=1

˛i · yi · K(si, x) + ω0 (6)

here si are the support vectors, and the coefficients ˛i, and ω0 arebtained during a training process.

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