SPECT image classification using random forests

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SPECT image classification using random forests
  SPECT image classification using randomforests J. Ramı´rez, J.M. Go´rriz, R. Chaves, M. Lo´pez,D. Salas-Gonzalez, I. A´lvarez and F. Segovia A novel computer aided diagnosis system for the early diagnosis of Alzheimer’s disease (AD) is presented. The system consists of voxel- based normalised mean square error feature extraction, a  t  -test withfeature correlation weighting for feature selection and random forest image classification. The proposed method yields an up to 96% classi-fication accuracy, thus outperforming recent developed methods for early AD diagnosis.  Introduction:  Alzheimer’s disease (AD) is the most common cause of dementia in the elderly and affects approximately 30 million individualsworldwide. Its prevalence is expected to triple over the next 50 yearsowing to growth of the older population. To date there is no singletest or biomarker that can predict whether a particular person willdevelop the disease. With the advent of several effective treatments of AD symptoms, current consensus statements have emphasised theneed for early recognition.Single photon emission computed tomography (SPECT) is a non-invasive, 3-D functional imaging modality that can be used to analysethe regional cerebral blood flow (rCBF) in patients. A SPECT rCBFstudy is frequently used as a complementary AD diagnostic tool inaddition to clinical findings. However, conventional evaluation of SPECT images is subjective and often relies on manual reorientation,visual reading of tomographic slices and semi-quantitative analysis of certain regions of interest (ROI). Moreover, the minimal changes inthe images in early AD make visual diagnosis a challenging problemthat requires experienced practioners [1]. Even with this problem stillunsolved, the potentials of novel machine learning techniques havenot been explored in depth for computer aided diagnosis (CAD). ThisLetter presents the design of a CAD system to detect early AD bymeans of random forests [2].  Random forests:  Variousensemble classification methods have beenpro- posed in recent years for improved classification accuracy. In ensembleclassification, several classifiers are trained and their results are combined through a voting process. Perhaps the most widely used of such methodsare boosting and bagging. Boosting is based on sample reweighting but  bagging uses bootstrapping. The random forest classifier  [2] uses bagging, or bootstrap aggregating, to form an ensemble of classificationand regression tree (CART)-like classifiers  h ð x ; T  k  Þ ; k   ¼  1 ;  . . . , where T  k   are the bootstrapreplicaobtainedbyrandomlyselecting  N   observationsout of   N   with replacement, where  N   is the dataset size, and   x  is an input  pattern [2]. For classification, each tree in the random forest casts a unit vote for the most popular class at input   x . The output of the classifier isdetermined by a majority vote of the trees. This method is not sensitiveto noise or overtraining, as the resampling is not based on weighting.Furthermore, it is computationally more efficient than methods based on boosting and somewhat better than simple bagging.  Materials and methods:  Each patient is injected with a gamma emittingtechnetium-99m labelled ethyl cysteinate dimer ( 99 m Tc-ECD) radiophar-maceutical and the SPECT scan is acquired by means of a three-head gamma camera Picker Prism 3000. Brain perfusion images are recon-structed from projection data using the filtered backprojection (FBP)in combination with a Butterworth noise filter. SPECT images requirespatial normalisation [3] in order to ensure that a given voxel in different images refers to the same anatomical position. This process was per-formed by using statistical parametric mapping (SPM) [4] yielding69    95    79 normalised SPECT images. Finally, intensity level is nor-malised to the maximum intensity as in [1]. The images were initiallylabelled by experienced clinicians of the Virgen de las NievesHospital (Granada, Spain) as normal (NOR) for subjects without anysymptoms of the disease and ATD to refer to possible, probable or certain AD patients. In total, the database consists of 79 patients: 41 NOR and 38 ATD.  Feature extraction:  Similarity measures of the rCBF of each subject and the mean rCBF value associated to normal controls were used as features. First, the mean value of the voxel intensity of normalsubjects was computed by averaging the voxel intensities of all thenormal controls in the database. Only those voxels with a meanintensity above 50% of the maximum intensity and defining a 3-Dmask were considered. Then, the normalised mean square error (NMSE) of a block of   ð 2 v  þ  1 Þ  ð 2 v  þ  1 Þ  ð 2 v  þ  1 Þ  voxels centred at the point with co-ordinates (  x ,  y ,  z  ) is defined as:  NMSE   p ð  x ;  y ;  z  Þ ¼ P þ vl  ; m ; n ¼ v ½  f    ð  x  l  ;  y  m ;  z   n Þ   g   p ð  x  l  ;  y  m ;  z   n Þ 2 P þ vl  ; m ; n ¼ v ½  f    ð  x  l  ;  y  m ;  z   n Þ 2 ð 1 Þ where  f   (  x ,  y ,  z  ) and   g  (  x ,  y ,  z  ) are the mean voxel intensities of controlsand the  p  subject, respectively.  Feature selection:  Not all the NMSE features defined by (1) provide thesame discriminant value for detecting early AD. In fact, the posterior cingulate gyri and precunei, as well as the temporo-parietal region aretypically affected by hypo-perfusion in AD [5]. A feature selection process is carried out to find the region of interest (ROI) to train therandom forest. It is based on an absolute value two-sample  t  -test witha pooled variance estimate on the NMSE features: T  ð  x ;  y ;  z  Þ ¼ j m  1   m  0 j  ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  s  21  þ s  20 p   ð 2 Þ where  m  1  and   m  0  denote the ATD and NOR within the class means of the NMSE features, respectively, and   s  21  and   s  20  their variances.Fig. 1 a  shows a map of the value of   T   (discriminant value of thefeature) for each of the voxels within the mask and a voxel size  v ¼ 4.The feature selection also uses correlation information to outweigh the T   value of potential features using  T  ð 1   ar  Þ , where  r   is the averageof the absolute values of the cross-correlation coefficient between thecandidate feature and all previously selected features, and   a  is a weight-ing factor. A large value of  r  (close to 1) outweighs the significance stat-istic; this means that features that are highly correlated with the featuresalready picked are less likely to be included in the output list. Fig. 1shows the 100 most discriminant ROI co-ordinates that were found using this feature selection procedure with  a  ¼  0 : 95. 10200304050050100050 100 020406080 a b  Fig. 1  Magnitude of T for each voxel within mask and voxel size v ¼ 4, and 100 most discriminant ROI co-ordinates of AD after applying feature selec-tion based on t-test with feature correlation weighting  a  Magnitude of   T b  100 most discriminant ROI co-ordinates  Evaluation experiments:  Several experiments were conducted to tune arandom forest classifier. First of all, Fig. 2 shows the out-of-bag error rate that is used to analyse the convergence of the random forest and the selection of the optimum voxel size  v . In this analysis, the randomforest is trained with all the 100 most discriminant features obtained above. Note that the generalisation error for the forest converges to alimit as the number of trees in the forest becomes large. Moreover, thegeneralisation error depends on the strength of the individual trees inthe forest and the correlation between them. It can be concluded that (i) the random forest classifier converges for about 20 to 30 treesgrown, and (ii) increasing the voxel size up to  v ¼ 4 reduces the ELECTRONICS LETTERS 4th June 2009 Vol. 45 No. 12  Authorized licensed use limited to: UNIVERSIDAD DE GRANADA. Downloaded on June 16, 2009 at 14:06 from IEEE Xplore. Restrictions apply.  out-of-bag error rate. The importance of a feature variable for classifi-cation can be also estimated by randomly permuting all the values of the variable in the out-of-bag samples for each classifier (therebymissing the information provided by that feature). An increased out-of-bag error is an indication of the importance of that feature. Thus, it is not needed to supply test data for bagged ensembles because reliableestimates of the predictive power and feature importance are obtained inthe process of training, which is an attractive feature of bagging. 0 10 20 30 40 500.05 0.100.15 0.200.25 0.300.35 0.40number of grown trees   m  e  a  n  o  u   t  −  o   f  −   b  a  g  c   l  a  s  s   i   f   i  c  a   t   i  o  n  e  r  r  o  r v   =   2 v   =   3 v   =   4 v   =   5 Fig. 2  Random forest mean out-of-bag error rate against number of growntrees for selection of optimum voxel size v The performance of the random forest CAD system was further eval-uated as a tool for the early detection of AD. The experiments con-sidered an increasing number of features for designing the classifier.Sensitivity, specificity and accuracy values were estimated by leave-one-out cross-validation The results are shown in Fig. 3. Performanceimproves with the number of features up to a maximum stable value.Moreover, peak values of sensitivity ¼ 94.7%, specificity ¼ 97.6%and accuracy ¼ 96.2% are obtained. As a conclusion, the proposed system outperforms recent developed AD CAD systems combining prin-cipal component analysis (PCA) [6] and Bayesian classification [1], and  the voxel-as-feature (VAF) approach [7] that yields just an 80% classifi-cation accuracy by considering the voxel intensities of the SPECTimages as input data for a support vector machine (SVM). 02468101214161820 0 20 40 60 80 100 number of features sensitivity specificity correct rate Fig. 3  Performance of random forest classifier against number of input  features Conclusion:  Random forests have been investigated for classification of SPECT images and the design of an AD CAD system. The proposed system is based on voxel-based normalised mean square error featureextraction, the  t  -test with feature correlation weighting for feature selec-tion and random forest image classification. It is shown that the gener-alisation error for the forest converges to a limit as the number of trees in the forest becomes large. Moreover, the generalisation error depends on the strength of the individual trees in the forest and the cor-relation between them. The proposed method yielded an up to 96.2%classification (sensitivity ¼ 94.7%, specificity ¼ 97.6%) accuracy and outperformed recent developed methods for early Alzheimer’s diseasediagnosis.  Acknowledgments:  This work was partly supported by the MICINNunder the PETRI DENCLASES (PET2006-0253), TEC2008-02113, NAPOLEON (TEC2007-68030-C02-01) and HD2008-0029 projectsand the Consejerı´a de Innovacio´n, Ciencia y Empresa (Junta deAndalucı´a, Spain) under the Excellence Project (TIC-02566). # The Institution of Engineering and Technology 2009 20 April 2009 doi: 10.1049/el.2009.1111J. Ramı´rez, J.M. Go´rriz, R. Chaves, M. Lo´pez, D. Salas-Gonzalez,I. A´lvarez and F. Segovia (  Department of Signal Theory, Networking and Communications, University of Granada, Spain )E-mail: javierrp@ugr.es References 1 Lo´pez, M., Ramı´rez, J., Go´rriz, J.M., Salas-Gonza´lez, D., A´lvarez, I.,Segovia, F., and Puntonet, C.G.: ‘Automatic tool for the Alzheimer’sdisease diagnosis using PCA and Bayesian classification rules’,  Electron. Lett. , 2009,  45 , (8), pp. 389–3912 Breiman, L.: ‘Random forests’,  Mach. Learn. , 2001,  45 , (1), pp. 5–323 Salas-Gonza´lez, D., Go´rriz, J.M., Ramı´rez, J., Lassl, A., and Puntonet,C.G.: ‘Improved Gauss-Newton optimisation methods in affineregistration of SPECT brain images’,  Electron. Lett. , 2008,  44 , (22), pp. 1291–12924 Friston, K.J., Ashburner, J., Kiebel, S.J., Nichols, T.E., and Penny, W.D.:‘Statistical parametric mapping: the analysis of functional brain images’(Academic Press, 2007)5 Kogure, D., Matsuda, H., Ohnishi, T., Asada, T., Uno, M., Kunihiro, T., Nakano, S., and Takasaki, M.: ‘Longitudinal evaluation of earlyAlzheimer disease using brain perfusion SPECT’,  J. Nucl. Med. , 2000, 41 , (7), pp. 1155–11626 A´ lvarez, I., Go´rriz, J.M., Ramı´rez, J., Salas-Gonza´lez, D., Lo´pez, M.,Puntonet, C.G., and Segovia, F.: ‘Alzheimer’s diagnosis usingeigenbrains and support vector machines’,  Electron. Lett. , 2009,  45 ,(7), pp. 342–3437 Fung, G., and Stoeckel, J.: ‘SVM feature selection for classification of SPECT images of Alzheimer’s disease using spatial information’,  Knowl. Inf. Syst. , 2007,  11 , (2), pp. 243–258 ELECTRONICS LETTERS 4th June 2009 Vol. 45 No. 12  Authorized licensed use limited to: UNIVERSIDAD DE GRANADA. Downloaded on June 16, 2009 at 14:06 from IEEE Xplore. Restrictions apply.
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