2.1. Overview

This study was conducted using the data from the Epidemiology of Dementia in Singapore (EDIS) study. Participants, aged 60–90 years, were drawn from the Singapore Epidemiology of Eye Disease (SEED) study, a population-based study involving Chinese (Singapore Chinese Eye Study [SCES], [18]), Malays (Singapore Malay Eye Study [SiMES-2], [19]), and Indians (Singapore Indian Eye Study [SINDI-2], [20]). The dataset contains n = 864 subjects with p = 67 variables, including subject ID, diagnosis, demographic information, risk factors, neuroimaging markers and assessment scores used for evaluating cognitive impairment and dementia. Cognitive Impairment No Dementia (CIND) was defined as impairment in at least one domain of a neuropsychological test battery (NTB), which assesses seven domains, including five non-memory and two memory domains. CIND mild was diagnosed when no more than two domains were impaired, while CIND moderate was diagnosed when more than two domains were impaired. For more details, see [18] and [21]. Thus, the subjects can be categorized into four classes based on their diagnosis of cognitive impairment and dementia, namely, NCI, CIND mild, CIND moderate, and Dementia. Since the test scores were used for diagnosing cognitive impairment, they were excluded from the prediction models. As a result, we manually selected p = 25 variables for this study. Further, the observations were removed with missing values and potential outliers. For each class, values beyond three standard deviations from the mean were considered outliers, and observations containing outliers were removed. As a result, 78 observations were excluded from the dataset.

The cleaned dataset comprises n = 786 observations: n₁ = 238 with NCI, n₂ = 258 with CIND mild, n₃ = 263 with CIND moderate, and n₄ = 27 with Dementia. Due to the low number of dementia cases, as suggested by the clinicians, CIND moderate and Dementia were combined into a single category for classification analyses, referred to as the CIND moderate/Dementia group. The exploratory data analysis involved grouping the variables into three clusters, namely, basic demographic information, risk factors, and neuroimaging markers. For categorical variables, the contingency table was displayed, and Pearson’s chi-squared test was conducted to determine whether the distribution of counts for those diagnosed with and without cognitive impairment differs. For continues variables, we plotted boxplots and performed pairwise Student’s t-test [22] to assess whether the means for different groups are significantly different. The detailed results of the exploratory data analysis for these three clusters are presented in the following subsections. Note that the prevalence of any cognitive impairment was calculated as (n₂ + n₃ + n₄)/n, representing the proportion of subjects with either CIND mild, CIND moderate, or Dementia.

2.2. Basic Demographic Information

This subsection includes basic demographic information about the subjects, such as age, race, gender, and education level. For age, we categorized the continuous variable into three groups, namely, 60–69 years, 70–79 years, and 80 years and older. There are 396 individuals aged between 60–69, 315 aged between 70–79, and 75 aged 80 and above. The prevalence of any cognitive impairment (in %) for each feature is displayed in Table 1 below.

From Table 1, several conclusions can be drawn. Firstly, adults over 80 years of age have the highest prevalence of cognitive impairment at 97.33%, followed by those aged 70–79 years at 79.68%, and those aged 60–69 years at 56.57%. As age increases, the prevalence of any cognitive impairment increases. Secondly, the Chinese have the lowest prevalence of cognitive impairment at 57.20%, whereas the Malay have the highest prevalence, at 81.82%. Thirdly, females have a higher prevalence of cognitive impairment (76.37%) compared to males (62.13%). Finally, adults with tertiary education have the lowest prevalence for cognitive impairment at 40.24%, whereas those with no education (labelled as ‘Nil’) have a prevalence of 91.03%. As the level of education increases, the prevalence of cognitive impairment decreases: 72.49% for primary education, 60.95% for secondary education, and 40.24% for tertiary education. Notably, no participants with tertiary education were diagnosed with dementia. This suggests that a higher level of education is associated with a lower likelihood of being diagnosed with cognitive impairment.

2.3. Risk Factors

In this subsection, we examined risk factors including Body Mass Index (BMI), smoking history, stroke history, and diagnosis of diabetes, hyperlipidemia, or hypertension. We categorized the continuous BMI values into four groups: underweight (below 18.5), normal (18.5–24.9), overweight (25.0–29.9), and obese (30.0 and above). Table 2 displays the prevalence of cognitive impairment for each of these risk factors.

According to Table 2, most participants have a normal BMI. Adults who are underweight exhibit the most prevalence of cognitive impairment at 89.29%, followed by those who are obese 76.15%. Additionally, non-smokers have a slightly higher prevalence of cognitive impairment (70%) compared to smokers (68.93%).

Pearson’s chi-squared test was conducted to determine if there is a difference in the distribution of cognitive impairment diagnoses between non-smokers and smokers. The p-value is 0.8428 which is significantly larger than 0.05, indicating no significant difference in the prevalence of cognitive impairment between smokers and non-smokers. It is important to note that this result is based on the study conducted in Singapore, where high tobacco taxes and prices lead to fewer smokers. Additionally, adults with a history of stroke, diabetes, hyperlipidemia, or hypertension show a higher prevalence of cognitive impairment compared to those without these medical conditions.

2.4. Neuroimage Markers

The neuroimage markers in this dataset include the volumes (in mm) of total intracranial (ICV), total grey and white matter (GWM), total grey matter (GM), total white matter (WM), total white matter lesions (WML), left hippocampus (LH), and right hippocampus (RH). These measurements were obtained from MRI scans and assessed by radiologists in the EDIS study. Due to high correlations between GWM, GM, and WM, as well as between LH and RH, we present the distributions for ICV, GWM, WML, and LH here. Boxplots of these neuroimaging markers across different classes are shown in Figure 1 below.

The white dot in each boxplot represents the mean value. It is observed that, except for WML, the mean values of the neuroimaging markers decrease from NCI to CIND mild, then to CIND moderate, and finally to Dementia. Adults with dementia show significantly larger volumes of WML compared to the other groups.

To further investigate whether the mean values of the volumes of ICV, GWM, WML, and LH differ significantly among the four groups, we conducted six pairwise Student’s t-tests. We first performed Bartlett’s test [23] to assess the equality of variances between the groups. Based on the results, the appropriate Student’s t-test was applied, either assuming equal or unequal variances. The p-values of these tests are shown in Table 3. The results show that the mean ICV in the NCI group differs significantly from that in the other three groups, indicating that ICV volume decreases as cognitive impairment progresses. Similar conclusions can be drawn for the volume of GWM. The volumes of WML and LH show highly significant between groups, suggesting that they may be key measures for detecting cognitive impairment. A significant level of 0.05 was used, with p-values smaller than 0.05 highlighted in bold. The results show that the mean ICV in the NCI group differs significantly from that in the other three groups, indicating that ICV volume decreases as cognitive impairment progresses. Similar conclusions can be drawn for the volume of GWM. The volumes of WML and LH show highly significant between groups, suggesting that they may be key measures for detecting cognitive impairment.

In addition to the volumes, this dataset includes other neuroimaging markers, such as the number of lacunes, cortical cerebral microinfarcts (CMI) numbers, central atrophy rate, number of cortical infarcts, and number of stenosed artery. The analysis results are displayed in Table 4 below.

Adults with any of the following conditions—lacunes, CMI, or stenosed arteries—exhibit a higher prevalence of cognitive impairment compared to those without these conditions. Additionally, adults with severe central atrophy rates show the highest prevalence of cognitive impairment, while those with cortical infarcts also have a higher prevalence of cognitive impairment. Regarding the number of cortical infarcts, individuals with cortical infarcts are more likely to have cognitive impairment. However, due to class imbalance, it is not possible to conclusively determine this relationship without hypothesis testing. Therefore, we performed Pearson’s chi-squared test, and the p-value is 0.2077. This indicates that there is no significant difference in the prevalence of cognitive impairment between individuals with and without cortical infarcts.

3.1. Overview of the Methods Used

In this section, three classifiers, namely, multinomial logistic regression, XGBoost, and Autoencoder have been applied to a three-class classification task. The sample sizes for the three groups were 238, 258, and 290, respectively. The cleaned dataset was split into two parts: 80% was used for training and the remaining 20% was used for testing. The experiment was performed on Windows 10 Pro using Python (version 3.9.6) on a 2.3 GHz intel core i7, with 4 cores and 16 GB RAM. An overview of the research framework for our study is shown in Figure 2 below.

3.2. Multinominal Logistic Regression

The Logistic Regression (LR) is a powerful supervised machine learning algorithm used for binary classification problems. The Multinomial Logistic Regression (MLR) [24], also known as softmax regression, is a classification method that extends the Logistic Regression to handle multiclass problems. It estimates the probability of each category relative to a reference category by applying the softmax function to a set of linear predictors, resulting in probabilities that sum to one. The model calculates log-odds ratios for each category in comparison to the reference category, with coefficients estimated through maximum likelihood estimation.

Before building the MLR models, it is essential to ensure that the following two key assumptions have been satisfied:

(a) The independent variables should be independent of each other, meaning the model should have little or no multicollinearity.

(b) Only meaningful variables should be included in the model.

Therefore, we first removed variables that were highly correlated, defining high correlation as an absolute value greater than 0.7. For example, since the volumes of the LH and RH were highly correlated, we removed the RH volume from the dataset. After eliminating these highly correlated variables, we normalized the cleaned dataset. For numeric variables, we applied Z-score normalization, and for categorical variables, we used label encoding, which converts each category value into a numerical label. The numerical labels range from 0 to the number of categories minus one. We used the training dataset to build the MLR model, initially including all variables. The optimal MLR model was determined manually by sequentially removing variables until all remaining regression coefficients were significantly different from 0 at the chosen alpha level of 0.05. This MLR analysis was performed using the Python library Scikit-learn [25,26].

3.3. Extreme Gradient Boosting

Extreme Gradient Boosting (XGBoost) is a scalable, end-to-end tree boosting system introduced in [26], designed to implement gradient boosted decision trees with a focus on speed and performance. It has recently become a dominant method in applied machine learning methods for tabular data. Instead of fitting a single large tree, XGBoost uses an ensemble of smaller trees, each built sequentially based on the residuals of the previous trees. Specifically, after adding a new tree, XGBoost adjusts the residuals of the previous model to correct errors and improve performance in areas where the model previously struggled. This approach helps reduce overfitting by using an ensemble of shallow trees rather than relying on a single large tree, which also aids in better generalization. In addition to its strong predictive capabilities, XGBoost allows for the evaluation of input variable importance. We implemented the XGBoost algorithm using the Python libraries Scikit-learn [25] and xgboost. The parameters in our experiment were set as follows:

(a) Subsample ratio of columns when constructing each tree: between 0 and 0.3

(b) Minimum loss reduction required to make a further partition on a leaf node: between 0 and 0.5

(c) Boosting learning rate: between 0.01 and 0.05

(d) Maximum tree depth for base learners: integers between 1 and 4

(e) Number of boosting rounds: integers between 200 and 500

(f) Subsample ratio of the training instances: between 0.8 and 1

The hyperparameters were tuned using cross-validation. To prevent overfitting, early stopping was employed. The model stops if the score does not improve after 5 rounds.

3.4. Autoencoder

An autoencoder is an unsupervised ANN algorithm that aims to produce output identical to its input. As outlined in Section 1, the architecture of an autoencoder is structured to learn efficient representations of the input data. When used for anomaly detection, setting a threshold for the reconstruction error is crucial but can be challenging and subjective as well. Therefore, to address this issue in the multiclass classification problem, we trained k autoencoder models in this study, one for each class, rather than training a single autoencoder model solely on normal observations. For example, there are three classes in this study, that is, NCI, CIND mild, and CIND moderate/Dementia. We therefore train three separate autoencoder models, each using data from one of the three classes. For any new observation, we compute three reconstruction errors by inputting it into the three trained autoencoder models, respectively. The new observation is then assigned to the class with the smallest reconstruction error.

The architecture of the autoencoder is detailed as follows. The categorical variables were represented using one-hot encoding, and the entire dataset was normalized into range [−1, 1] using min-max normalization. The autoencoder models used in this study are structured with fully connected networks for both the encoder and decoder. Each autoencoder includes one fully connected hidden layer, with batch normalization [27]. The activation function of the decoder’s last layer is Tanh, while LeakyReLU [28] with a negative slope of 0.2 is used for the hidden layers. To prevent overfitting, dropout [29] is applied to each hidden layer. Mean Square Error (MSE) is used as the reconstruction error metric. The autoencoder was implemented using the Python deep learning library, PyTorch [30], and its detailed structure can be found in the source available online (31]. For all three autoencoders, the optimal models were configured with a hidden layer width of 24, an embedding space dimension of 12, and a batch size of 100. The learning rate is set to 0.005 for the NCI-autoencoder and CIND moderate/Dementia-autoencoder, while it is slightly higher at 0.008 for the CIND mild-autoencoder. The number of epochs is 700 for the NCI-autoencoder and CIND moderate/Dementia-autoencoder, and 600 for the CIND mild-autoencoder. The dropout rates for the three classifiers are set to 0.15, 0.1, and 0.2, respectively.

Understanding the feature importance by analyzing the latent space of the trained autoencoder model is also crucial. This study proposes an intuitive method for estimating the feature importance based on the latent space representations learned by the trained autoencoder. Let the input data be represented as [Math Processing Error] $\mathbf{x}={\left({\mathrm{x}}_1,\dots ,{\mathrm{x}}_{\mathrm{p}}\right)}^{\mathrm{T}}$ , where p is the number of input features, and let the corresponding latent space be represented as [Math Processing Error] $\mathbf{z}={\left({\mathrm{z}}_1,\dots {,\mathrm{z}}_{\mathrm{m}}\right)}^{\mathrm{T}}$ , where m is the dimensionality of the latent space and $\mathrm{m}<\mathrm{p}$ . The latent representation can be written $\mathbf{z}=\mathrm{f}\left(\mathbf{x}\right)$ , where $\mathrm{f}(·)$ is the function learned by the encoder part of the autoencoder, capturing the compressed, most informative features of the data.

To estimate feature importance, the following procedure is followed after training the autoencoder. Firstly, we normalize the identity matrix I_p using the min-max normalization, scaling the entries of the identity matrix to the range of [−1, 1], and input it into the trained encoder. The identity matrix has ones on the diagonal and zeros elsewhere, which effectively “activates” each feature individually. Each column of I_p corresponds to one input feature being set to 1, while all other features are set to 0. The resulting encoded data corresponds to the latent space representation ${\mathbf{z}}_{\mathbf{i}}$ for each feature i, $\mathrm{i}=1,\dots ,\mathrm{p}$ , and can be used to quantify the importance of each feature. To calculate the importance of each feature, we compute the mean absolute value of the corresponding elements in the latent representation z_i. Specifically, for each feature i, its importance is calculated as [Math Processing Error] ${\mathrm{m}}^{-1}\sum _{\mathrm{j}=1}^{\mathrm{m}}\left|{\mathrm{z}}_{\mathrm{i}\mathrm{j}}\right|$ , where ${\mathrm{z}}_{\mathrm{i}\mathrm{j}}$ represent the value of the j-th latent variable in the encoded representation for the i-th feature. The larger the absolute values of the elements in z_i, the more influential the corresponding feature is in determining the latent representation. Hence, features with larger mean absolute values in the latent space are considered more important for the model’s encoding process. For example, to access the importance of the first feature, we would input $\mathbf{x}={\left(\mathrm{1,0},\dots ,0\right)}^{\mathrm{T}}$ into the trained encoder, meaning only the first feature is “activated”. The resulting latent representation z₁ captures how this single feature influences the encoded space, and the mean absolute value of z₁ quantifies its importance.