A new image-based immersive tool for dementia diagnosis using pairwise ranking and learning
Abstract
Dementia disease is globally acknowledged as one of the most severe non-communicable diseases nowadays. Identifying different stages of dementia disease is significant in its later treatment for delaying the onset and progression of the disease. Among diverse types of tools utilized in dementia disease diagnosis, brain scanning is generally accepted as an effective and affordable way at present. There are several kinds of medical images incorporated in contemporary dementia studies, and magnetic resonance images receives vast popularity. In this study, arterial spin labeling, an emerging perfusion functional-magnetic resonance imaging technique, is adopted in a newly proposed image-based immersive tool for dementia disease diagnosis. Novel pairwise ranking and learning techniques based on a new continuous and differentiable surrogated Kendall-Tau rank correlation coefficient is proposed to realize the immersive tool. Extensive experiments based on a database composed of images acquired from 350 demented patients are carried out with several popular pattern recognition diagnosis tools being compared. Their results undergo rigorous and comprehensive statistical analysis, and the superiority of the newly proposed image-based immersive tool in dementia disease diagnosis has been demonstrated.
Keywords
Image-based immersive tool Dementia disease Pairwise ranking Learning1 Introduction
Dementia disease is widely acknowledged as a broad category of brain functions degeneration, which may result in gradual decrease of normal capabilities of thinking, memory, language, motivation, etc, for ordinary people in a long term. There are various forms of dementia disease, including vascular dementia, lewy body dementia, frontotemporal dementia, etc [29]. Among them, Alzheimer’s Disease (AD) is generally regarded as the most common form. According to statistics provided by the World Health Organization, AD is often diagnosed worldwide in patients over 60 years old, and is now considered as one of the five most severe non-communicable diseases in the whole world (i.e. others include cardiovascular disease, cancer, diabetes and chronic lung disease) [29]. According to another population study conducted by the United Nations, there are more than 26.6 million AD patients diagnosed globally [28], and 1 in 85 worldwide people is predicted to be suffering from AD by the year 2050 [3]. Thus, dementia disease becomes an actual threat in many countries of aging societies nowadays. Accurate diagnosis and timely treatment is essential to delay the onset and progression of dementia disease [3].
Identifying the progression of dementia disease into various stages accurately is often of great importance to understand mechanisms of the disease, making correct treatments to corresponding symptoms of the disease possible at a later stage [3]. Thus, in order to perceive the progression of dementia disease accurately in clinical diagnosis, a variety of methods have been proposed and utilized to date. Popular diagnosis methods include pathography analysis, cognitive examination, brain scanning, etc. Pathography is helpful to predict curable symptoms of demented patients who may usually suffer from other forms of diseases (e.g., stroke, heart disease, renal failure, etc) at the same time [20]. Cognitive examination evaluates the progression of demented patients through a series of cognition tests based on diverse cognitive capabilities of patients, including short-memory, long-memory, logic analysis, etc [8, 22]. Popular cognitive examinations include Mini-Mental State Examination (MMSE) [8] and Addenbrooke’s Cognitive Examination (ACE) [22]. Although these cognitive exams require few trainings for clinicians and are relatively easy to be carried out by them, outcomes of those exams could be highly biased by patients specialities. For example, patients of high-level education suffering from dementia disease are more likely to outperform ordinary patients of low-level education without dementia disease in those cognitive exams. For brain scanning, it is accepted as an effective and affordable way in dementia diagnosis nowadays. There are several imaging tools incorporated for dementia diagnosis, including Computed Tomography (CT), Positron Emission Tomography (PET), Magnetic Resonance Imaging (MRI), etc. Among them, MRI receives vast popularity, because of its prominent capability in both generating high-resolution images of brain tissues and free of ionizing radiation exposure, compared with other scanning tools such as CT and PET. Most contemporary MRI scanning techniques can be categorized into structural MRI (sMRI) and functional MRI (fMRI), and both of them have already been adopted in various dementia studies nowadays [21, 23].
In this study, a novel fMRI-based immersive tool based on new raking techniques is introduced for dementia diagnosis for the first time. Generally speaking, the purpose of ranking is to sort a list of items according to a system of rating or a record of performance, and most ranking approaches can be categorized into pointwise ranking approaches and pairwise ranking approaches. For pointwise ranking, provided an image list d = {d_{1}, d_{2}, … , d_{n}}, pointwise ranking aims to assign each image a discrete category: {(d_{1}, c_{1}),(d_{2}, c_{2}), … , (d_{n}, c_{n})}, in which {c_{1}, c_{2}, … , c_{n}} ∈ C; C = {c_{1} ≻ c_{2} ≻ … c_{m}} is a set of m (where m ≥ n) ordered categories, in which ≻ denotes an order between various categories. Since elements in C are ordered discrete values, pointwise ranking is also known as ordinal regression, which is between regression (outputs: real values that can be ordered) and classification (outputs: non-ordered discrete values) [5, 13]. Representative pointwise ranking approaches include constrained ordinal regression [5], Pranking [6], OAP-BPM [12], ranking with large margin principals [26], etc. Although pointwise approaches are convenient to implement due to their close resemblance to both regression and classification, their drawbacks are obvious: they can only deal with judgements in the form of absolute values. Non-absolute preference, such as pairwise preference and partial/full list orders, cannot be handled by those pointwise ranking approaches. For pairwise ranking, however, it focuses on data “pairs”, instead. Take images for illustration purposes, in the learning stage of pairwise ranking approaches, image pairs (d_{α}, d_{β}) (α, β ∈ {1, 2, … , n}, α ≠ β) are collected from an image list d = {d_{1}, d_{2}, … , d_{n}}. For each pair, a label r ∈ {+1, −1} is assigned indicating the order of two images (d_{α}, d_{β}): +1 shows d_{α} should be ranked before d_{β}, while −1 to the contrary. The main idea of pairwise ranking approaches is similar towards that of the well-known binary-class classification, and pairwise ranking approaches often formulate the ranking task as a classification problem accordingly [4, 9, 15]. Conventional classification methods, such as boosting, Support Vector Machine (SVM), and Artificial Neural Network (ANN), have been incorporated leading to corresponding pairwise ranking methods, such as RankBoost [9], RankingSVM [15], and RankNet [4], respectively. There are several advantages with pairwise ranking approaches compared with pointwise ranking approaches. First, existing classification methodologies can be conveniently adopted in pairwise ranking approaches [4, 9, 15]. Second, pairwise preference, rather than absolute relevance, is relatively easy to obtain under certain circumstances [15], making pairwise approaches more adaptive to be utilized in practical applications.
In this paper, a novel pairwise ranking technique and it associated learning method will be investigated in the newly proposed fMRI-based immersive tool for dementia diagnosis. Main contributions of this paper can be revealed as follows: 1) Technically, new pairwise ranking and learning techniques are introduced in this paper for the first time; 2) It is also the first attempt to perform dementia disease diagnosis from the new perspective of pairwise ranking, rather than conventional classification or clustering perspectives. The organization of this paper is described as follows. First, the conventional position-based ranking evaluation measure, Kendall-Tau rank correlation coefficient, is introduced in Section 2. The Kendall-Tau coefficient forms the theoretical basis of the new pairwise ranking technique introduced in this study. The learning of ranking functions in the pairwise ranking procedure is to be realized via an optimization process based on the Kendall-Tau coefficient, which is, however, neither continuous nor differentiable with respect to its discrete pair-counting terms. Hence, a new continuous and differentiable surrogate Kendall-Tau coefficient is proposed and its corresponding ranking functions learning method based on the new surrogate coefficient is introduced therein. All the above novel techniques and essential derivations are explicitly elaborated in Section 2. In Section 3, extensive experiments are conducted to evaluate the performance of the newly introduced image-based immersive tool for dementia diagnosis. fMRIs acquired from 350 real patients of different dementia disease progressions are utilized to construct a database for performance evaluation. The newly proposed tool has been compared with several other tools based on well-established pattern recognition techniques, and all experimental results of all compared methods are evaluated from the statistical point of view. Finally, the conclusion of this study is drawn in Section 4.
2 Methodology
2.1 Kendall-Tau rank correlation coefficient
Generally speaking, the range of KT is within [−1, +1], and higher KT values indicate better ranking performance within the ranked list. In this study, KT is picked to evaluate the ranking performance, as the characteristics of data pairs is naturally inherited in this conventional position-based ranking evaluation measure, making it suitable for pairwise ranking. Based on KT, function learning can be carried out within an optimization process. However, the optimization cannot be executed directly on KT for ranking functions learning, because the original KT is neither continuous nor differentiable in terms of its discrete pair-counting terms P and Q. Hence, a new continuous and differentiable rank correlation measure is necessary for functions learning in the pairwise ranking.
2.2 Continuous and differentiable surrogate Kendall-Tau coefficient
Provided image x contains more severe dementia disease than image y, the disease severity in image x reflected by s_{(x)} = < a, ℜ_{x} > should be higher than that in image y (i.e. s_{(x)} > s_{(y)}). Meanwhile, the disease severity of image x annotated by clinicians should also be higher than that of image y (i.e. ℓ_{(x)} > ℓ_{(y)}). If the above conditions holds, (x, y) constitutes a concordant pair, P increases by 1 as indicated by (2) (i.e., s_{(x, y)} = s_{(x)} − s_{(y)} > 0 and ℓ_{(x, y)} = ℓ_{x} − ℓ_{y} > 0). The above explanation is also valid when x contains less severe disease than image y and (x, y) constructs a concordant pair in a ranked images list of an ascending order of disease severities. Otherwise, (x, y) forms a discordant pair, (3) holds, and Q increases by 1.
It can be easily observed that, the above SKT coefficient avoids discrete and non-differentiable problems inherited in the original KT coefficient, which makes direct optimizations feasible on SKT for the following functions learning.
2.3 Functions learning in pairwise ranking
An algorithm of functions learning based on SKT via pairwise ranking
Inputs | Images for training {x ∈ χ}; Images for validation {x_{v} ∈ χ_{v}}; |
Number of Iterations T; Learning rate η. | |
Training | |
T1. | Initialize the parameter a in function s_{(x)} as a_{0} |
T2. | For t = 1 to T |
T3. | Set a = a_{t−1} |
T4. | Feed {x ∈ χ} to (8) to calculate the gradient |
T5. | Update a via the gradient ascent: a = a+η⋅▽SKT(a) |
T6. | Set a_{t} = a |
T7. | End for T2 |
Validation | T learned functions s_{(x)} with T corresponding learned parameters a |
V1. | For j = 1 to T |
V2. | Feed j^{th} learned function s_{j}(x) to {x_{v} ∈ χ_{v}} for ranking validation images |
V3. | Calculate its corresponding SKT value using (6) |
V4. | End for V1 |
V5. | Determine a_{opt} and its corresponding function s_{opt}(x) with the highest SKT |
Outputs | Learned function: s_{opt}(x) |
In the above equation, a is the parameter to learn and there are several elements within it (i.e. the extracted feature vector R_{x} is 8-dimensional in this study, hence there are also 8 elements within a to be determined). Therefore, learning a in this study is actually solving a multi-dimensional optimization problem. It is commonly acknowledged that, sometimes high-dimensional problems can be really tricky to tackle, as it is often hard to find the global optimum. In many studies of computer vision, researchers try to look for a local minimum which is good enough for specific applications, instead. In Table 1, T iterations are executed in the training step and there are T learned parameters a obtained (i.e., from Steps T2 to T7 in Table 1). After that, an optimal a_{opt} with the highest SKT value evaluated based on the validation data is sorted out (i.e., from Steps V1 to V5 in Table 1). Learned function s_{opt}(x) with the optimal a_{opt} will be utilized in the next testing step for dementia disease diagnosis.
2.4 Disease severity diagnosis
3 Experiments and analysis
3.1 Data description and pre-processings
In order to demonstrate the superiority of the new fMRI-based immersive tool for dementia diagnosis, clinical data obtained from 350 patients of different disease progressions, including 110 Alzheimer’s Disease (AD) patients, 120 Mild Cognitive Impairment (MCI) patients and 120 Non-Cognitive Impairment (NCI) patients acquired in the affiliated hospital of Nanchang University, is utilized. Informed consent was obtained from all patients for research purpose. The averaged age of these patients is 70.56 ± 7.20 years old. Arterial Spin Labeling (ASL) images, which is an emerging perfusion fMRI technique and a new indicator in contemporary dementia studies [21], are acquired using a SIEMENS 3T TIM Trio MR scanner for each single patient. Acquisition parameters of the ASL scanning include: labeling duration = 1500 ms, post-labeling delay = 1500ms, TR/TE = 4000/9.1ms, ASL voxel size = 3 × 3 × 5 mm^{3}.
When the acquisition of ASL images is accomplished, they need to be pre-processed before feeding into the fMRI-based immersive tool for dementia diagnosis. The reason is because that, ASL images often suffer from the Partial Volume Effects (PVE) problem, which is mainly caused by signal cross-contamination due to pixel heterogeneity and limited spatial resolution of ASL images [24]. Since PVE indicates the loss of apparent activity in small objects because of the limited resolution of an imaging system, ASL images with the PVE problem become more prone to under-estimate the measured perfusion, making the fMRI-based immersive tool inaccurate to reveal the actual brain atrophy of demented patients.
Therefore, PVE needs to be properly corrected in the pre-processing step of ASL images. In this study, the popular regression-based method proposed in [1] is incorporated for PVE correction. The main idea of this method can be described as follows. When correcting PVE on pixel i of an ASL image, its neighbors are necessary to be incorporated for adding up extra information to solve the PVE problem. For instance, given an adopted neighbor of size n × n, a regression matrix P of the size n^{2} × 3 can be formulated using P_{GM}, P_{WM}, and P_{CSF}, which include fractional Gray Matter (GM), While Matter (WM), and Cerebro-Spinal Fluid (CSF) tissue volume of all n^{2} neighbor pixels respectively as P’s three columns. Unknowns to be solved in the PVE correction task on pixel i can be obtained using \((P^{T}P)^{-1}P^{T}\hat {M}\), where \(\hat {M}\) depicts a matrix with magnetization on all n^{2} neighbor pixels as its elements obtained in the ASL scanning process; T and −1 represent the transpose and the inverse of a matrix, respectively. For probability maps P_{GM}, P_{WM}, and P_{CSF}, they are generated using the SPM toolbox [27] based on High-resolution Magnetization Prepared Rapid Acquisition Gradient Echo (MPRAGE) T1-weighted MRI images [2] acquired with ASL images simultaneously, in the ASL scanning protocol of this study. The above obtained maps are then co-registered towards their corresponding ASL images after motion correction for every patient using the FSL toolbox [7].
3.2 Experiments and analysis on dementia diagnosis
After all the above pre-processing steps are executed, ASL images can be utilized as fMRI in the new image-based immersive tool for dementia disease diagnosis. The pre-defined parameters in this novel immersive tool are set as: the number of iterations T = 100 and the learning rate η = 0.01 in Table 1, through trial-and-error for optimal performance. Mean ASL signal calculated from the segmented left & right hippocampus, the left & right parahippocampal gyrus, the left & right putamen, and the left & right thalamus (i.e. the above tissue segmentation is realized via the IBA-SPM toolbox [14]) from ASL images after PVE correction is utilized to construct a 8-dimensional feature vector ℜ_{(x)} for image x, following literatures in clinical dementia studies [10, 11, 19].
Other popular pattern recognition tools widely utilized in conventional disease diagnosis studies, including Linear Regression (denoted as “LR”), Support Vector Regression (denoted as “SVR” as a non-linear regression tool) and Ranking-Support Vector Machine (denoted as “RankingSVM” as a popular ranking tool) are implemented in this experiment based on all patients data for dementia diagnosis performance evaluation. Since learning is incorporated in the newly proposed immersive tool (denoted as “Our Method”), parameters of other methods are also determined via learning for fair comparisons. For SVR and RankingSVM, Gaussian Radial Basis Function (RBF) are adopted as kernels; Gaussian widths are learned via the popular radius/margin bound algorithm [17], and SVM-light toolbox [16] is utilized for their implementations. For LR and Our Method, disease severities of different progressions of dementia, i.e., AD, MCI and NCI, are labeled as 3, 2 and 1 respectively. Regression coefficients in LR are determined via labels and regressors (i.e., the 8-dimensional feature vector) of the training data.
The constitution of all 20 trials in 5-fold cross validation
Trial | Training | Validation | Testing |
---|---|---|---|
I | 1,2,3 | 4 | 5 |
II | 1,2,3 | 5 | 4 |
III | 1,2,4 | 3 | 5 |
IV | 1,2,4 | 5 | 3 |
V | 1,2,5 | 3 | 4 |
VI | 1,2,5 | 4 | 3 |
VII | 1,3,4 | 2 | 5 |
VIII | 1,3,4 | 5 | 2 |
IX | 1,3,5 | 2 | 4 |
X | 1,3,5 | 4 | 2 |
XI | 1,4,5 | 2 | 3 |
XII | 1,4,5 | 3 | 2 |
XIII | 2,3,4 | 1 | 5 |
XIV | 2,3,4 | 5 | 1 |
XV | 2,3,5 | 1 | 4 |
XVI | 2,3,5 | 4 | 1 |
XVII | 2,4,5 | 1 | 3 |
XVIII | 2,4,5 | 3 | 1 |
XIX | 3,4,5 | 1 | 2 |
XX | 3,4,5 | 2 | 1 |
In order to clear the above doubt, a designated statistical analysis composed of one-way ANalysis Of VAriance (ANOVA) followed by a post-hoc multiple comparison test [25] is further conducted. ANOVA is a popular correction of models analyzing the difference between diverse group means and their associated variations in statistics [25]. To be specific, in one-way ANOVA, means of prediction errors from all methods are compared to test a hypothesis (H_{0}) that, all prediction error means of various methods could be equivalent, against the general alternative that at least one method is different. P-value is used here as an indicator to reveal whether H_{0} exists or not. In this study, p-values for cases of 5 × 5, 9 × 9, and 15 × 15 are all nearly 0, which strongly suggests that H_{0} is an invalid hypothesis for all cases. Hence, the next step is to do more detailed paired comparisons. The reason to conduct paired comparisons here is because that, the generative alternative against H_{0} is too general to reveal which method is superior from the statistical point of view. Therefore, a post-hoc multiple comparison test is adopted to investigate it.
Multiple comparison test of all compared methods based on disease severity prediction errors in the case of 5 × 5
Method I | Method II | Prediction Error Difference (I-II) | A 95 % Confidence Interval |
---|---|---|---|
Our Method | LR | −0.1905 | [−0.2353,−0.1457] |
Our Method | SVR | −0.1028 | [−0.1475,−0.0580] |
Our Method | RankingSVM | −0.0196 | [−0.0644,0.0252] |
LR | SVR | 0.0877 | [0.0429,0.1325] |
LR | RankingSVM | 0.1709 | [0.1261,0.2157] |
SVR | RankingSVM | 0.0832 | [0.0384,0.1280] |
Multiple comparison test of all compared methods based on disease severity prediction errors in the case of 9 × 9
Method I | Method II | Prediction Error Difference (I-II) | A 95 % Confidence Interval |
---|---|---|---|
Our Method | LR | −0.1283 | [−0.1773,−0.0794] |
Our Method | SVR | −0.0085 | [−0.0575,0.0404] |
Our Method | RankingSVM | −0.0024 | [−0.0514,0.0465] |
LR | SVR | 0.1198 | [0.0709,0.1687] |
LR | RankingSVM | 0.1259 | [0.0770,0.1748] |
SVR | RankingSVM | 0.0061 | [−0.0428,0.0550] |
Multiple comparison test of all compared methods based on disease severity prediction errors in the case of 15 × 15
Method I | Method II | Prediction Error Difference (I-II) | A 95 % Confidence Interval |
---|---|---|---|
Our Method | LR | −0.1266 | [−0.1733,−0.0800] |
Our Method | SVR | −0.0462 | [−0.0928,0.0005] |
Our Method | RankingSVM | −0.0133 | [−0.0599,0.0333] |
LR | SVR | 0.0805 | [0.0338,0.1271] |
LR | RankingSVM | 0.1133 | [0.0667,0.1600] |
SVR | RankingSVM | 0.0329 | [−0.0138,0.0795] |
3.3 Discussion
In this study, the linear ranking function s_{(x)} = < a, ℜ_{x} > is utilized for each image x, where ℜ_{x} denotes the extracted feature from image x and a represents the unknown parameter to learn. In this section, the choice of linear and non-linear ranking functions and their influence on dementia disease diagnosis performance is investigated and discussed. To be specific, an exponential form s_{(x)} = exp(< a, ℜ_{x} > ) is incorporated as the compared non-linear ranking function in this fMRI-based immersive tool for dementia disease diagnosis. To reveal its performance, the same 5-fold cross validation using the same combinations of training, validation and testing data is adopted, and the same statistical analysis is performed with this non-linear ranking function. It turns out that, prediction errors (i.e., means ± standard deviation) for cases of 5 × 5, 9 × 9 and 15 × 15 are 0.4331 ± 0.4425, 0.5089 ± 0.4758, and 0.4849 ± 0.4632, respectively when the non-linear ranking function is incorporated. The accuracies for the above three cases are 97.43 %, 95.29 %, and 96.86 %, respectively when taking diagnosis outcomes with the absolute prediction error less than 1 as accurate diagnosis results following the same strategy as that of the linear ranking function. After comparing the above outcomes with ones of the linear ranking function accordingly within the same immersive tool, it can be concluded that, the dementia disease diagnosis performance brought by both linear and non-linear ranking functions in this newly proposed fMRI-based immersive tool are comparable. Thus, both linear and non-linear ranking functions are applicable.
4 Conclusion
In this study, a novel image-based immersive tool for dementia disease diagnosis via new pairwise ranking and learning techniques is proposed for the first time. Arterial spin labeling is incorporated as images for diagnosis. Extensive experiments and their comprehensive statistical analysis demonstrate the superiority of the novel image-based immersive tool in dementia disease diagnosis. Main contributions of this study can be summarized as: 1) Technically, new pairwise ranking and learning techniques based on a new continuous and differentiable surrogated Kendall-Tau rank correlation coefficient are introduced in this paper; 2) It is also the first attempt to perform dementia disease diagnosis from the new perspective of pairwise ranking. Future efforts will be emphasized on investigating other types of image-based immersive tools with more sophisticated ranking models equipped for diverse disease diagnosis, based on different modalities of medical images.
Notes
Acknowledgments
The authors would like to acknowledge Grants 61403182 and 61363046 approved by the National Natural Science Foundation of China, Grant [2014]1685 approved by the Scientific Research Foundation for Returned Overseas Chinese Scholars, Ministry of Education, China, as well as the 2015 Provincial Young Scientist Program 20153BCB23029 approved by the Jiangxi Provincial Department of Science and Technology, China.
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