Computational protocol: Gaussian Mixture Models and Model Selection for [18F] Fluorodeoxyglucose Positron Emission Tomography Classification in Alzheimer’s Disease

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[…] Experiments were performed on two independent datasets. One is from the publicly available ADNI database (http://adni.loni.usc.edu/) and the other is an in-house dataset of patients and controls recruited at the memory outpatient unit of the Department of Psychiatry at Technische Universität München. The above datasets are in the following referred to as ADNI and TUM, respectively. ADNI has a large pool of PET (co-registered, averaged) images, which have been acquired on various scanners using different imaging parameters. To eliminate the bias of these factors, we selected images that have been obtained using the same scanner as well as the same parameters, such as the number of slices. The patient information and the PET scanner type are summarized in . Further details about the ADNI recruitment procedures are provided in the acknowledgments.Prior to their use for image analysis, PET images had to undergo two pre-processing steps: spatial normalization and smoothing (kernel size [8 8 8] mm), which were achieved by SPM5. The spatial normalization ensures that the processed image is of the size 91×109×91, which is in accordance with Anatomical Automatic Labeling (AAL) []. The final step is the intensity normalization that was done by dividing each voxel by the mean intensity value averaged over all brain voxels (grand mean normalization, the non-brain voxels surrounding the brain were excluded). The second intensity normalization method is called pSMC (primary sensorimotor cortex) and was reported to be advantageous in a study []. Anatomically, the “Precentral_L, Precentral_R, Postcentral_L and Postcentral_R” regions in the AAL brain template can be used as the primary sensorimotor cortex. [...] We employ a clustering method (GMM) to group brain voxels into small regions that exhibit both high similar intensity and geometric affinity. A PET image can be viewed as three dimensional (3D) spatial data along with one extra dimension that represents the intensity of each voxel. Thus, a voxel is denoted by a 4-tuple (x,y,z,I)∈ℜ4, where x,y,z are the spatial coordinates and I is the intensity value. We used NC PET images as reference images to obtain the clustering results and used these clusters to extract the features from the NC, MCI and AD groups. Note that the method is applied on the AAL (gray matter voxels of MNI space) defined voxels, which constitute the gray matter in the brain. The mean intensity and standard deviation of each cluster are subsequently defined as features. To ensure the clusters have similar intensity values and are geometrically connected, we first group the original voxels into a certain number (e.g., 100) of bins of equally sized intensity ranges, and then cluster each bin by the introduced methods based only on the spatial information, i.e., the x,y,z coordinates. A bin is a data interval that is described by a statistical histogram. The data falling into the same bin are from a certain value interval, such that the data within the same bin are similar in their values. Theoretically, it is hard to find the most appropriate number of bins in advance, thus we tested different numbers from 50 to 150 with step size 10, i.e., 50, 60, …, 150. The best one can be chosen by a cross-validation on the training data. In practice, cross-validation is repeated in a way that the division into sets is identical for the various bin sizes. Given the training data, we can further split them into sub-training and sub-test data, which are used to train and evaluate the model respectively. Evaluating the model using the sub-test data gives a predictive accuracy. The yielded highest accuracy of a certain bin corresponds to the most appropriate number of bins. Once the number of bins is determined in this way, the same training procedure can be applied to the whole training data to maximize the use of present training data. Therefore only the training data is used to set the optimal parameters in the experiments. The workflow of the proposed method is summarized in .If there are 1000 clusters formed using GMM+MS, then the image can be represented as a 2000 (1000μ and 1000σ) dimensional vector. Generally, not all of these features are informative, thus we applied a feature selection technique [] to choose the most discriminative ones for building the model. In this study, we empirically used the top-150 most informative features for learning the model. From of BIC, we observe that the classification accuracy increases in the beginning, but drops after selecting too many features. 150 features appear to provide sufficient classification relevant information, and more features may hamper the classifier's performance due to the well-known curse of dimensionality []. As for AIC, top-400 features were selected to perform the experimental comparison. AIC needs more features than BIC, which may be the reason why AIC divides voxels into more clusters so that the discriminative information are spread over many clusters. It should be pointed out that the feature selection [] and the model building steps only used information from the training set: no information from the test set is used at any point in time (in other words, no information leakage from the test set to the training set has occurred).A support vector machine (SVM) was used to build the final classification model, which is trained on the training data. The SVM has been shown to perform well in a variety of applications, thus it was chosen to be the classifier in this study. A tutorial [] offers a good introduction to the SVM. Apart from the SVM, other classification methods could be used, such as Random Forests, Naïve Bayes, and others. We do not attempt to compare the proposed method with SVMs, we rather use a SVM as a classifier in the method. The suggested method aims at extracting useful features from brain voxels, whereas SVMs are a classification method based on input features (voxels).In terms of running time, it costs roughly 15 hours to cluster the mean NC image from 50 bins to 150 bins. It takes only a few seconds to extract the features of a given PET scan after having the clusters. Therefore, the proposed approach is very efficient once the clusters are derived, since extracting features from new images is fast. The code is implemented in MATLAB and runs on a machine with Intel(R) Core i7-3632QM CPU @2.20 GHz, 8GB of memory. In addition, the LIBSVM [] package provides a fast classification, once the features are constructed. […]

Pipeline specifications

Software tools SPM, AAL, LIBSVM
Databases ADNI
Applications Miscellaneous, Magnetic resonance imaging
Organisms Homo sapiens
Diseases Alzheimer Disease
Chemicals Fluorodeoxyglucose F18