Histogram-Based Feature Extraction from Individual Gray Matter Similarity-Matrix for Alzheimer’s Disease Classification

Abstract

Automatic computer-aided diagnosis (CAD) systems have been widely used in classification of patients who suffer from Alzheimer’s disease (AD). This paper presents an automatic CAD system based on histogram feature extraction from single-subject gray matter similarity-matrix for classifying the AD patients from healthy controls (HC) using structural magnetic resonance imaging (MRI) data. The proposed CAD system is composed of five stages. In the first stage, segmentation is employed to perform pre-processing on the MRI images, and segment into gray matter, white matter, and cerebrospinal fluid using the voxel-based morphometric toolbox procedure. In the second stage, gray matter MRI scans are used to construct similarity-matrices. In the third stage, a novel statistical feature-generation process is proposed, utilizing the histogram of the individual similarity-matrix to represent statistical patterns of the respective similarity-matrices of different size and order into fixed-size feature-vectors. In the fourth stage, we propose to combine MRI measures with a neuropsychological test, the Functional Assessment Questionnaire (FAQ), to improve the classification accuracy. Finally, the classification is performed using a support vector machine and evaluated with the 10-fold cross-validation strategy. We evaluated the proposed method on 99 AD and 102 HC subjects from the J-ADNI. The proposed CAD system yields an 84.07% classification accuracy using MRI measures and 97.01% for combining MRI measures with FAQ scores, respectively. The experimental results indicate that the performance of the proposed system is competitive with respect to state-of-the-art techniques reported in the literature.

Keywords

Alzheimer’s disease Fisher criterion histogram individual gray matter similarity-matrix

INTRODUCTION

Alzheimer’s disease (AD), a progressive and neurodegenerative disorder, occurs most frequently in elderly people [1]. It is estimated that the number of AD patients will increase to double in the next two decades and this number is expected to increase by 13.8 million people by 2050 [1]. AD is one of the top 10 causes of death of American people that cannot be cured or prevented [1]. Recently, neuroimaging techniques, such as structural magnetic resonance imaging (sMRI) [2 –10], functional MRI [11 –13], diffusion tensor imaging [14 –16], positron emission tomography (PET), and single photon emission computed tomography (SPECT) [17 –20], have been widely used in accurate detection of AD. In this study, we use sMRI data in the proposed CAD system for classification of AD. sMRI data have been widely used for AD detection, because of its good tissue contrast and excellent spatial resolution [21]. Recently, many researchers have investigated sMRI feature extraction for AD classification using different methods such as voxel-based morphometry (VBM) of gray matter [5 , 9], volume measurement of the hippocampus and the medial temporal lobe [22 –28], and volume and cortical thickness features [6]. The aim of this study is to propose an automatic histogram-based feature extraction from an individual gray matter similarity-matrix for AD classification. The proposed CAD system is accomplished using several ideas of five stages. Figure 1 shows the pipeline of the proposed method. In the first stage, structural MRI scans are segmented into gray matter, white matter, and cerebrospinal fluid (CSF) through the VBM8 toolbox. In this study, we use gray matter images. In the second stage, the individual gray matter image is employed to construct a similarity-matrix from gray matter images. This method provides intracortical similarities which represent a robust statistical description of individual gray matter morphology [29, 30]. In the third stage, we propose a novel statistical feature-generation method based on the histogram from the similarity-matrices with different sizes to generate a fixed-size and lower-dimensional feature vectors. Histograms have been used for characterizing objects [29, 30]. The dimensionality of the histogram-based feature vector can be adjusted using an automatic approach based on the Fisher criterion. This approach adaptively determines the optimum number of the histogram’s bins in each training data-set instead of using a fixed one. In the fourth stage, we investigate the classification of AD by combining MRI measures with a neuropsychological test, the Functional Assessment Questionnaire (FAQ), to improve the performance. Finally, the performance of the proposed statistical histogram-based feature-generation technique is evaluated using a linear support vector machine (SVM) classifier with 10-fold cross-validation strategy. To the best of our knowledge, this study is the first to investigate a similarity-matrix from individual gray matter MRI scans and the impact of combining MRI measures with FAQ scores for AD detection. In summary, the aim of this research is to introduce a novel and automatic statistical feature extraction based on the histogram of individual gray matter similarity-matrices for AD detection. The dimensionality of the proposed histogram-based feature vectors can be adjusted by maximizing the Fisher criterion in the training data-set. The proposed histogram-based method not only generates a statistical pattern of individual similar-matrices but also embeds the similarity-matrices of different size and order into a fixed-size feature vectors.

MATERIAL AND METHODS

The MRI scans and data used in this study are obtained from the 1.5 Tesla scanner by Siemens, GE, and Philips of the Japanese-Alzheimer’s Disease Neuroimaging Initiative (J-ADNI) database (http://humandbs.biosciencedbc.jp/en/). The MRI scans are pre-processed with intensity inhomogeneity correction [31] and phantom-based distortion correction [32] to normalize variations between scanners.

Subjects

We selected a total of 102 people who suffer from AD and 99 healthy controls (HC) from the J-ADNI data-set. All subjects received standard dementia screening such as medical history, physical and neurological examination, and an MRI scan. Table 1 shows details of the demographics and clinical characteristics of the subjects used in study.

MRI pre-processing

The Pre-processing steps are performed using SPM8 software (http://fil.ion.ucl.ac.uk/spm) and the VBM8 toolbox (http://dbm.enuro.uni-jena.de/vbm). In the VBM8 toolbox, all 3D raw-MRI scans are corrected for bias field in homogeneities and then the corrected images are normalized, and segmented into gray matter, white matter, and CSF components. In the current study, only native-gray matter components are considered for constructing similarity-matrices.

Extraction of similarity-matrix from individual gray matter segmentation

The group brain network methods entail the fixed brain network size among subjects. On the other hand, all brain networks must have the same size using a common brain atlas across subjects [33]. In order to overcome this issue, the individual brain network analysis is proposed for more flexible spatial correspondence between subjects. Figure 2 shows a schematic overview of the extraction similarity-matrix method from individual gray matter scans. As described in [34], after segmentation using VBM analysis, the gray matter images in the native-space are divided into non-empty 3×3×3 voxel cubes. These cubes include the 3D structure of the cortex intact in addition to geometrical information and gray matter values in the voxels. In this study, the cube size 3×3×3 voxels, corresponding to 6×6×6 mm³ is considered. The similarity between all cubes is calculated using a correlation coefficient. Equation 1 shows the correlation coefficient r_jm between v_j and v_m cubes.

$r_{jm} = \frac{\sum_{i = 1}^{n} (v_{ji} - \bar{v_{j}}) (v_{mi} - \bar{v_{m}})}{\sqrt{\sum_{i = 1}^{n} (v_{ji} - \bar{v_{j}})^{2}} \sqrt{\sum_{i = 1}^{n} (v_{mi} - \bar{v_{m}})^{2}}}$ (1)

Where $\bar{v_{j}}$ and $\bar{v_{m}}$ are cube’s average values and r_jm is calculated based on sum over the product of differences between cubes values at each voxel location i = 1, 2, …, n for n voxels. Given that the cortex is curved object, two similar cubes could be located at an angle from each other, which could decrease their similarity value [34]. In this regard, each seed cube v_j is rotated by an angle θ with multiply of 45° and reflections over all axes to find maximum correlation value with target cube v_m as follow [34, 35]: $\begin{matrix} r_{jm}^{max} = \underset{θ}{arg max} \\ (\frac{\sum_{i = 1}^{n} (v_{ji} (θ) - \bar{v_{j}}) (v_{mi} - \bar{v_{m}})}{\sqrt{\sum_{i = 1}^{n} (v_{ji} (θ) - \bar{v_{j}})^{2}} \sqrt{\sum_{i = 1}^{n} (v_{mi} - \bar{v_{m}})^{2}}}) \end{matrix}$ (2)

Because the similarity-matrix ( $A \in ℝ^{N \times N}$ ) is symmetric, lexicographically ordered entries of the upper-triangular part of the each matrix is used as raw-feature vector. In this case the embedding is formed as: $φ (A) = (\dots, A (i, j), \dots)$ (3)

Where i, j ∈ (1, 2, …, N) , j > i. As drawback, this method leads to high-dimensional feature vector of size $\frac{(N^{2} - N)}{2}$ with unequal size vectors. To address these issues, we propose to use histogram of the individual raw-feature vectors to represent statistical pattern of the respective high-dimensional data into low-dimensional and fixed-size space.

Statistical feature generation based on histogram

The histogram is a set of observation into a finite number of discrete units. On the other hand, histogram is a statistical description of the distribution of occurrence that can be considered as a mapping a high-dimensional vector into a lower-dimensional space. A histogram of a vector H is defined as follow: $H = [η_{1}, η_{2}, η_{3}, \dots, η_{q}]$ (4)

Where η_i, is the number of observation falling into the ith bin, q is the number of bins. In this work, the histogram of similarity-vector extracted from similarity-matrix is used in the representation of the training and testing data for AD classification. The number of bins determines the size of the histogram vector. In this work, the number of bins is varied from 2 to 512. In order to find the optimal number of bins instead of using a fixed one, we propose Fisher criterion with an automatic manner, given in Equation 5 [36, 37]: $J (w) = \frac{w^{T} S_{B} w}{w^{T} S_{W} w}$ (5)

Where S_B and S_W represent the between-class and within-class scatter matrixes, respectively, as follow: $S_{B} = (μ_{1} - μ_{2}) (μ_{1} - μ_{2})^{T}$ (6)

$\begin{matrix} S_{W} = \sum_{H_{i} \in C_{1}} (H_{i} - μ_{1}) (H_{i} - μ_{1})^{T} \\ + \sum_{H_{i} \in C_{2}} (H_{i} - μ_{2}) (H_{i} - μ_{2})^{T} \end{matrix}$ (7)

Where μ₁ and μ₂ are the mean of the histogram vectors in class 1 and class 2, and $w = S_{W}^{- 1} (μ_{1} - μ_{2})$ . The optimal number of bin is selected along with the number of bins (i.e., from 2 to 512), on training set in each iteration through the cross-validation process. The number of bins which maximized the Fisher value on training set is selected as optimum number of bin for that training set and respective test data-set.

Data fusion between MRI measures and FAQ

In this paper, we propose a data fusion between MRI measures and FAQ scores to improve the performance of the proposed AD detection. The data fusion provides aid to integrate data from different sources to achieve a higher performance. Recently, many researchers have used data fusion technique between brain imaging data and clinical data such as the Mini-Mental State Examination (MMSE) and CSF to improve the AD detection systems [4 , 39]. In this study, we combine the MRI features obtained from proposed method described in section 2.4 with FAQ scores as follow: $Fusion - Vector = [MRI - measuresFAQ - score]$ (8)

Since the value of FAQ scores are smaller than histogram values, we propose to multiple FAQ scores by a coefficient, K. In other to find the optimal, K, we use a gird search among candidate set {2⁰, 2¹, … , 2¹⁰ } in each training set. The K value maximizing the training-accuracy rate is used as optimum coefficient for that training set and respectivetest set.

Classifier and performance evaluation

The implementation of classifier is done by using a SVM algorithm. The SVM algorithm has been used successfully in a number of recent application machine learning studies [7 , 40–43]. In the present work, the implementation of SVM is done using LIBSVM (http://www.csie.ntu.edu.tw/ cjlin/libsvm/) with linear kernel. The linear SVM has a parameter C (soft margin parameter). For tuning this parameter (i.e., C) a grid search is used to find the optimal C among candidate set {2^-5, 2^-4, … , 0, …, 2¹⁹, 2²⁰ } in each training set. In order to achieve a reliable measurement, a 10-fold cross-validation is used, i.e., each iteration 90% of subjects are used to train SVM classifier and remaining 10% of subjects are used to test the classifier. This process is repeated 10 times to cover all subjects as a test. The classification performance is reported by averaging classification results among 10-fold cross-validation. The classification performance is evaluated by means of accuracy (ACC), sensitivity (SEN), specificity (SPE), and area under the curve (AUC) as a follow [44]: $ACC = \frac{(TP + TN)}{(TP + FP + FN + TN)}$ (9) $SEN = \frac{TP}{TP + FN}$ (10) $SPE = \frac{TN}{TN + FP}$ (11)

Where: TP, TN, FN, and FP stand for true positive (the number of patients with AD correctly identified as AD), true negative (the number of patients with HC correctly identified as HC), false negative (the number of patients with AD incorrectly identified as HC), and false positive (the number of patients with HC incorrectly identified as AD), respectively.

RESULTS

In this section, the experimental results obtained through the preprocessing and construction similarity-matrix phases followed by proposed histogram-based feature generation are presented. The experimental data consisted of 201 subjects from J-ADNI data set. A 10-fold cross-validation with 90% subjects in the training and 10% subjects in the testing processes in each iteration is used to evaluate the proposed method. The ACC (%), SEN (%), SPE (%), and AUC performance metrics are used for the performance assessment.

Similarity-matrix on individual gray matter

As described above, the native-gray matter images obtained through segmentation using VBM8 toolbox are investigated to construct similarity-matrix for each subject. As an example, Fig. 3 shows similarity-matrix for an AD sample and HC sample. As can be seen from Fig. 3, the similarity-matrix for an AD sample is less than a HC sample. The reason for this may be that gray matter atrophy occurs in patients with AD. The raw-feature vectors are extracted from the upper-triangular part of each similarity-matrix. The length of obtained raw-feature-vectors varied from 13533003 to 32236435.

Performance of the proposed histogram-based method

The proposed histogram-based feature-generation is accomplished by engendering a statistical pattern of unequal raw-feature-vectors obtained from similarity-matrices. The generated statistical patterns are reduced to lower-dimensional feature vectors of up to 512 components. Figure 4 shows an example of histogram-patterns for an AD sample and an HC sample with 512 components. The classification results based on proposed method obtained with different number of bins (i.e., from 2 to 512) are shown in Fig. 5. By investigating Fig. 5, it is clear that the performance of the proposed method is dependent on bin size. For example, for 100 bins, the ACC performance is 80.59%, while for 300 bins, ACC performance is 82.58%. To address this issue, the Fisher criterion is employed to find the optimal bin size of the training data in each iteration through the cross-validation process. The Fisher values are computed for different number of bins (i.e., from 2 to 512) in each training dataset. The number of bins maximizing the Fisher criterion rate is used as optimum bin size for training the classifier and evaluating the performance on the respective test set. The optimal number of bins obtained from the proposed histogram-based feature generation and Fisher criterion varied from 310 to 505. Table 2 shows the average of the performances with the optimal number of bins obtained in each fold, through 10-fold cross-validation.

Performance of data fusion between MRI measures and FAQ scores

Table 3 shows the classification performance of proposed MRI measures, FAQ scores, and combination MRI measures with FAQ scores. Table 3 shows that combination of MRI measures with FAQ scores resulted in a classification accuracy of 97% compared to 84% for MRI measures alone and 85% for FAQ alone. It can be observed that with FAQ, the classification accuracy improved significantly with an accuracy increment of 15.4%. In order to evaluate the overall performance of proposed MRI measures, FAQ scores and combination of MRI measures with FAQ scores, the receiver operating characteristic (ROC) curve is illustrated in Fig. 6.

DISCUSSION

Many studies have investigated advanced machine learning methods with different data modalities for AD detection. For instance, in [45], a Mann-Whitney-Wilcoxon U-Test is proposed to select the significance voxels from PET and SPECT modalities. In addition, the authors employed the Factor Analysis and a linear SVM in the data reduction and calcification stages. In [46], an association rule mining is introduced as a novel voxel selection method using PET and SPECT data. The authors in [47] presented two feature extraction methods, namely Gaussian Mixture Model and Partial Least Squares (PLS) using PET images for AD detection. In one study [48], the researchers investigated a mask-based feature reduction method followed by a combination of component-based SVM classification and a pasting-votes method using SPECT data for AD detection. In [49], researchers proposed a combination of brain tissues (i.e., gray matter + white matter) followed by two feature extraction method, namely PLS and PCA using MRI images. One study [50] used a novel data fusion method between PET and MRI modalities based on a deep learning structure. They implemented two deep learning structures and four different voting schemes for the proposed AD detection system. Another study [51] presented sparse inverse covariance estimation methods in order to learn undirected graphs with PET and MRI modalities. In another study [5], the authors investigated a statistical feature-selection approach based on the probability distribution function of the gray matter atrophy regions. They employed Fisher criterion as a part of feature selection method to determine the optimal number of bin sizes. In the present study, we introduced a histogram based feature-extraction method of the individual gray matter similarity matrix of whole brain, which is able to represent statistical patterns a high-dimensional and unequal vectors into a lower-dimensional and fixed-sizes vectors. In the proposed method, the Fisher criterion is employed to determine the optimal number of histogram bins with maximum separation between two groups. The experimental results indicate that the proposed histogram-based approach is suitable for high-dimensional and unequal pattern recognition, especially for AD classification with individual patterns. In addition, we proposed a data fusion by combining the MRI measures with FAQ scores to improve the classificationperformance.

Comparison to other works

Zhang et al. [2] used multimodal classification of AD based on the combination of MRI, CSF, and PET. They reported ACCs of 86.2%, 82.1%, and 86.5% in the classification of AD/HC by MRI, CSF, and PET imaging modalities, respectively. Also, they achieved a high accuracy performance (93.2%) by combining the MRI, CSF, and PET results. In [43], the authors investigated a multi-modality framework and reported an ACC of 87.6% for MRI + PET and an ACC of 92.4% when combining MRI, PET, CSF, APOE, and cognitive scores. Hinriches et al. [52] reported an ACC of 75.27% based on MRI data and improved it to 81% by combining MRI and FDG-PET. In [6], the authors reported ACC of 87% and 91.8% using MRI data and combining MRI data with CSF measures, respectively. Aguilar et al. [4] achieved an ACC of 84.9% with computing cortical thickness and volumetric measures from MRI data and of 88.1% by combining MRI data with educational and demographic data. Zhou et al. [38] investigated MRI data by calculating 55 volumetric variables with an ACC of 78%. They also reported an ACC of 92.4% by combining MRI data with the MMSE. In the present paper, the MRI modality and FAQ score with 201 subjects from the J-ADNI dataset are used in the AD and HC groups. Table 4 shows the detail parameters of classification performance with different methods for distinguishing AD from HC. As can been seen in Table 4, the performance of the proposed histogram-based feature extraction method and data fusion technique outperforms the alternative techniques. The performance of the proposed CAD system is highly competitive for the performance terms including ACC, SPE, SPE, and AUC when compared to the other systems reported in the literature.

Conclusion

In this study, we proposed an automatic CAD technique on a novel statistical feature-extraction process, using the mean of histogram of individual similarity matrices, for the detection of AD. The proposed feature-generation method compresses the statistical information of high-dimensional similarity-matrices with different sizes into a fixed-size and lower-dimensional vectors. The proposed histogram-based feature-generation method is employed for high-dimensional AD classification, especially for feature-extracted of gray matter similarity-matrix. Moreover, we proposed the use of Fisher criterion to find the optimal number of bins based on the training set in each iteration. The proposed histogram-based method not only extracts the selected statistical features for unequal high-dimensional data but also reduces the dimensionality of the input vectors to fixed-size feature vectors with acceptably low dimensions. Furthermore, we showed that combining MRI measures with FAQ score improves the accuracy of AD classification. The performance of the proposed CAD system is evaluated on 201 subjects (102 AD and 99 HC) from the J-ADNI dataset through 10-fold cross validation. The experimental results show that the performance of the proposed approach is highly competitive with the state-of-the-art techniques reported in theliterature.

Footnotes

ACKNOWLEDGMENTS

This work was partly carried out under the Brain Mapping by Integrated Neurotechnologies for Disease Studies (Brain/MINDS) project (grant number 16dm0207017h0003), funded by the Japan Agency for Medical Research and Development (AMED). The J-ADNI was supported by a Grant-in-Aid for Translational Research Promotion Project (Research Project for the Development of a Systematic Method for the Assessment of Alzheimer’s Disease) (grant number 20100000001577) from the New Energy and Industrial Technology Development Organization of Japan (NEDO), by Health Labour Sciences Research Grants (Research on Dementia) (grant numbers H19-Dementia Research-024, H22-Dementia Research-009) from the Japanese Ministry of Health, Labour and Welfare (MHLW), and by a Grant-in-Aid for Life Science Database Integration Project (Database Integration Coordination Program) from the Japan Science and Technology Agency (JST). This work has been also partially supported by Estonian Research Council Grant (PUT638) and the Estonian Centre of Excellence in IT (EXCITE) funded by the European Regional Development Fund.

Authors’ disclosures available online ().

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