AD-HOLDER: Alzheimer’s Disease Detection via Machine Learning based Histograms of Light GBM Classifier using MRI and PET Images

In this study, the OASIS dataset [26] consists of MRI and PET images from a longitudinal collection of 150 subjects aged 60 to 96 years. Each individual performed a total of 373 imaging sessions, with at least one year between visits. For each patient, three or four distinct T1-weighted MRI images were obtained in a single session. The subjects include both men and women, and all are right-handed. During this analysis, 72 research participants were categorized as non-demented. At the time of their first visits, 64 of the included subjects – 51 of whom had mild to moderate AD were classified as demented, and their condition remained that way for all future scans. A total of fourteen additional participants were initially diagnosed as non-demented but later developed mental health issues.

In this section, MRI and PET images are denoised using the Deep Image Prior (DIP) filter [27] to improve the quality of both MRI and PET images for efficient BS classification. A randomly initialized DIP filter takes random noise as input and reconstructs the corrupted image. Despite the corruption, the internal structure of the filter effectively adapts to fit the clear image. Let x₀ denote the corrupted image; DIP proposes the following optimization: (1) θ*=argminθx0−T(θ|z)22,x^=θ*|z {\theta ^*} = \arg \mathop {\min }\limits_\theta \left\| {{x_0} - T(\theta |z)} \right\|_2^2,\hat x = \left( {{\theta ^*}|z} \right)

Here, T represents the DIP filter, z is the random noise input, x̂ is the recovered (denoised) image, and θ^∗ represents the optimized filter parameters. This approach does not require conventional training data pairs. Instead, Stochastic Gradient Langevin Dynamics (SGLD) is used for posterior inference, improving denoising performance while avoiding early stopping. (2) x^=x+ε,ε=N0,σn2 \hat x = x + \varepsilon ,\varepsilon = N\left( {0,\sigma _n^2} \right) where x^∗ = ∫ρ(z,θ|x̂) T(z,θ) dz dθ generates the required image after a suitable prior ρ(z,θ) is added to the parameters. To ensure global optimality, Regularization by Denoising (RED) is applied. This framework allows integration of any image denoising filter and defines a regularization term as: (3) ρx=12xTx−fx \rho \left( x \right) = {1 \over 2}{x^T}\left( {x - f\left( x \right)} \right) where f(⋅) denotes the denoised version of the input image x. The gradient of the regularization function becomes: (4) ∇ρx=x−fx \nabla \rho \left( x \right) = x - f\left( x \right)

The MRI and PET image restoration process estimates and removes the noise component from the input image, thereby preserving the essential structure of the image. A DIP filter with 64 filters, a 3 × 3 kernel size, and ReLU activation functions was used in the denoising step. The Adam optimizer was used to optimize the filter for up to 200 epochs at a learning rate of 0.001, with early stopping implemented after 20 consecutive epochs if validation loss did not improve. This DIP configuration effectively reduced noise artifacts while preserving clinically relevant anatomical details, ensuring high-quality inputs for subsequent feature extraction. Filters produce a clear image output that reduces noisy distortions while maintaining the integrity of significant features, improving downstream tasks such as segmentation and classification. Data augmentation, including multi-angle rotation, adding Gaussian noise, improving and reducing brightness, and horizontal and vertical mirroring, was used to increase categorization ACC.

The features are extracted using the HOG method [28], which captures essential patterns and edges from the images. HOG was used to extract structural features such as edges, contours, and textures relevant for distinguishing normal from abnormal brain tissues. A cell size of 50×50 pixels was selected to balance local detail capture and computational efficiency. In medical imaging applications, larger cells provide improved robustness against intensity variations while retaining discriminative edge information with similar parameter settings. Experimental investigations showed that 50×50 cells offer the optimal balance between ACC and processing cost. We empirically evaluated different cell sizes (20×20, 30×30, and 50×50) and found that 50×50 yielded the highest classification ACC with reduced computational cost. HOGs represented each item as a single value vector by moving the window detector across the image, rather than computing a collection of feature vectors for different image areas. To obtain a HOG feature, the image’s scale is modified while the HOG descriptor is calculated for each location.

To compute the HOG feature, the image’s gradients must be determined. Image gradients are defined as directed increases in pixel intensity along the x- and y-axes. A pixel’s gradient vector at position (y, x) is described by (5). (5) ∇fx,y=gxgy=∂f∂x∂f∂y=fx+1,y−fx−1,yfx,y+1−fx,y−1 \nabla f\left( {x,y} \right) = \left[ {\matrix{ {{g_x}} \cr {{g_y}} \cr } } \right] = \left[ {\matrix{ {{{\partial f} \over {\partial x}}} \cr {{{\partial f} \over {\partial y}}} \cr } } \right] = \left[ {\matrix{ {f\left( {x + 1,y} \right) - f\left( {x - 1,y} \right)} \cr {f\left( {x,y + 1} \right) - f\left( {x,y - 1} \right)} \cr } } \right]

Here, g_x and g_y are the gradients in the x and y directions, respectively, and f (x, y) is the pixel intensity at coordinates x and y. The gradient’s phase, θ(x, y), and magnitude, M(x, y), can then be determined using the following formulas. (6) Mx,y=gx2+gy2 M\left( {x,y} \right) = \sqrt {g_x^2 + g_y^2} (7) θx,y=arctangygx \theta \left( {x,y} \right) = {{\arctan}}{{{g_y}} \over {{g_x}}}

Here, g_x and g_y are the gradients in the x and y directions, respectively.

The LGBM classifier [29] is used to classify normal and abnormal cases using MRI and PET images. Ensemble learning includes techniques such as gradient boosting. Fig. 2 shows the architecture diagram of the HOG-based LGBM classifier. In the ensemble boosting strategy, models are constructed sequentially by continuously minimizing the error of previously trained models. When splitting and propagating a tree, it is important to select the leaf that minimizes the loss the most. LGBM uses a histogram-based method to find the best split candidates. It employs gradient-based one-side sampling (GOSS) to determine the importance of image occurrences for training, focusing more on data samples with larger gradients and less on those with smaller gradients.

Fig. 2.

Architecture diagram of the HOG-based LGBM model.

It is assumed that data with smaller gradients have previously undergone extensive training, as they contain fewer errors. GOSS proposes discarding these less-informative data points and using the remaining ones to determine information gain when establishing the best splits. However, this changes the original data distribution and creates a bias towards samples with larger gradients. To address this, GOSS retains all samples with large gradients and randomly samples data with small gradients. When computing information gain, GOSS applies a constant multiplier to the weights of data instances with moderate gradients, as the sample remains skewed toward data with strong gradients. Additionally, LGBM regulates dataset sparsity using Exclusive Feature Bundling, which combines features almost losslessly by removing incompatible aspects and retaining the most useful components.

Table 1 presents the hyperparameter settings of the LGBM classifier. The proposed AD-HOLDER model performance was evaluated using ACC, PRE, REC, SPE, and F1. To optimize performance, the number of estimators was set to 500, the learning rate to 0.05, and the maximum tree depth to 8. The feature fraction was set to 0.8 to reduce feature correlation and improve generalization. Regularization terms were incorporated through λ_L1 = 0.1 and λ_L2 = 0.2 to control model complexity and minimize overfitting. The OASIS dataset was split into 75 % for training and 25 % for testing, with cross-validation performed on the training set to ensure robustness and prevent overfitting. Cross-validation confirmed consistent results across folds, indicating strong generalization and minimal overfitting.

The abnormal region is segmented using the GBS model [30] to specifically detect the region for early diagnosis of AD. GBS is a technique for segmenting images to enhance their quality by using graphs. Here, E is the set of edges composed of two vertices (v_i, v_j), G = (V, E) is an undirected graph, and w_ij is edge weight. Edge weights in GBS indicate the degree of dissimilarity between two pixels in an image. (8) IntD=maxwe, e∈MSTD Int\left( D \right) = \max \left( {w\left( e \right)} \right),\;\;\;\;\;e \in MST\left( D \right) , (9) DifD1,D2=minwe,vi,vj∈e, vi∈D1,vj∈D2 \matrix{ {Dif\left( {{D_1},{D_2}} \right) = \min \left( {w\left( e \right)} \right),} \hfill \cr {\left| {{v_i},{v_j} \in e} \right.,\;\;\;\;\;{v_i} \in {D_1},{v_j} \in {D_2}} \hfill \cr }

The term min (w(e)) in (9) denotes the lowest possible edge weight that unites two separate components, D₁ and D₂, and is also known as “min (w(e)).” It is necessary to use the least edge weight because employing a quantile, such as the median, results in an NP-hard computational problem. (10) ED1,D2=True,DifD1,D2>MIntD1,D2False,otherwise E\left( {{D_1},{D_2}} \right) = \left\{ {\matrix{ {{\rm{True}},Dif\left( {{D_1},{D_2}} \right)} \hfill & { > MInt\left( {{D_1},{D_2}} \right)} \hfill \cr {{\rm{False}},} \hfill & {{\rm{otherwise}}} \hfill \cr } } \right.

The minimum internal difference, MInt(D₁, D₂) is defined as (11) MIntD1,D2=min IntD1+τD1,IntD2+τD2 MInt\left( {{D_1},{D_2}} \right) = \min \left( {Int\left( {{D_1}} \right) + \tau \left( {{D_1}} \right),Int\left( {{D_2}} \right) + \tau \left( {{D_2}} \right)} \right) where τ(D) is a threshold function that determines the minimum distance two components must have from each other for a border to exist between them. Fig. 3 shows visual examples of the segmented output.

Fig. 3.

Visual examples of segmented regions.

The greatest edge weight in the MST is indicated by Int (D) in (12). According to the GBS algorithm, the default threshold function is specified as (12) τD=kd \tau \left( D \right) = {k \over {\left| d \right|}}

In the GBS model, k serves as a control-scale parameter that influences the preference for merging components. Specifically, this threshold determines the minimum dissimilarity required between two regions for a boundary to be established. A higher k value promotes the formation of larger and more coherent segments by allowing greater intra-region variation before splitting occurs. This technique is particularly important for accurately describing pathological regions in brain images, where preserving structural consistency is essential for reliable disease localization and diagnosis.

The effectiveness of the AD-HOLDER approach for categorizing instances of AD is evaluated using a set of assessment criteria, including SPE, PRE, REC, ACC, and F1. (13) SPE=NtrueNtrue+Pfalse SPE = {{{N_{{\rm{true}}}}} \over {{N_{{\rm{tru}}e}} + {P_{{\rm{false}}}}}} (14) PRE=PtruePtrue+Pfalse PRE = {{{P_{{\rm{true}}}}} \over {{P_{{\rm{true}}}} + {P_{{\rm{false}}}}}} (15) REC=PtruePtrue+Nfalse REC = {{{P_{{\rm{true}}}}} \over {{P_{{\rm{true}}}} + {N_{{\rm{false}}}}}} (16) ACC=Ptrue+NtrueTotal no. of samples ACC = {{{P_{{\rm{true}}}} + {N_{{\rm{true}}}}} \over {{\rm{Total}}\;{\rm{no.}}\;{\rm{of}}\;{\rm{samples}}}} (17) F1=2PRE⋅RECPRE+REC F1 = 2\left( {{{PRE \cdot REC} \over {PRE + REC}}} \right)

Here, N_true and N_false represent true-positives and true-negatives, while P_true and P_false denote false negatives and false positives for the MRI and CT images.

Table 2 presents the efficiency of the AD-HOLDER model using the specific parameters ACC, PRE, SPE, REC, and F1. As shown in Fig. 5, the performance of the classification for the normal and abnormal classes is illustrated across different evaluation metrics. The AD-HOLDER model achieved an ACC of 99.12 %, SPE of 97.79 %, PRE of 97.57 %, REC of 92.60 %, and F1 of 96.55 % in identifying the two types of Alzheimer’s. This model attains higher ACC in identifying the normal class than the abnormal class. The overall average ACC achieved by the proposed AD-HOLDER model is 99.12 % for AD classification based on the collected OASIS dataset.

Fig. 5.

Performance analysis for two-class classification.

The ACC curve (Fig. 6) and loss curve (Fig. 7) of the proposed model over 100 epochs show its performance in classifying AD cases. The training curve is slightly higher than the testing curve, indicating effective learning and a steady improvement in ACC over time. The proposed model consistently reduces classification errors, demonstrating its effectiveness. The testing and training curves are nearly aligned, indicating good generalization without overfitting. These results suggest that the proposed model is well-trained, with minimal loss and excellent ACC.

Fig. 6.

ACC curve for the proposed AD-HOLDER model.

Fig. 7.

Loss curve for the proposed AD-HOLDER model.

Fig. 8 shows the classification efficiency of the proposed AD-HOLDER model for AD detection across two stages: normal and abnormal. The confusion matrix (CM)provides clinically relevant insights into the model’s performance. A false positive occurs when a normal case is misclassified as abnormal, which may lead to unnecessary anxiety. A false negative (FN) occurs when an abnormal case is misclassified as normal, causing delays in diagnosis and intervention, potentially accelerating disease progression. Minimizing false positives is crucial for reducing unnecessary evaluations, but it is also vital for early and accurate detection of AD. The CM shows the model’s high ACC, correctly classifying 98.96 % of normal and 99.29 % of abnormal samples, with low misclassification rates of 1.04 % and 0.71 %, respectively.

Fig. 8.

CM for two-class classification.

Fig. 9 illustrates the ROC curve of the proposed AD-HOLDER framework across Alzheimer’s stages. According to the area under curve (AUC), each curve represents the difference between the true positive rates (TPR) and false positive rates (FPR) for a particular class. The model performs poorly for the normal class (AUC = 0.98) and best for the abnormal class (AUC = 0.99), as estimated with TPR and FPR parameters. The high AUC values indicate strong discrimination capacity at every level, with only slightly lower ACC under the collected dataset.

Fig. 9.

ROC curve of the proposed AD-HOLDER classification model.

Table 3 presents the AD-HOLDER model cross-validation results using 3-fold and 5-fold methods based on the OASIS dataset. For 3-fold cross-validation, the dataset was divided into three subsets, with 70 % used for training and 30 % for testing in each iteration to ensure every sample was evaluated. For 5-fold cross-validation, 80 % of the dataset was used for training and 20 % for testing, providing a robust estimate of generalization ability. Compared to the fixed 75 %-25 % split, cross-validation minimizes the risk of selection bias and yields more reliable performance evaluation. The consistent results across both 3-fold and 5-fold validation confirm the stability and robustness of the proposed model.

The efficacy of conventional models was evaluated to verify that the proposed AD-HOLDER model achieves a high level of ACC. The comparison of ML classifiers was conducted to assess whether the proposed model obtains better ACC. The comparative assessment was performed between the proposed model and four ML networks: KNN, Naive Bayes, Decision Tree, and RF. The performance assessment was carried out using ACC, SPE, PRE, REC, and F1 for each ML method. The ACC of the proposed AD-HOLDER model is 99.14 %, which is higher than that of the classical ML methods.

Table 4 presents a comparison of different denoising methods on MRI and PET images. Traditional filters such as Median, Gaussian, Bilateral, and Non-Local Mean (NLM) improve the peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) values compared to noisy inputs; however, they often fail to preserve fine structural details and edges in MRI and PET images. The proposed DIP method achieves the highest PSNR (31.82 dB) and SSIM (0.917), indicating superior noise suppression and structural preservation. These results confirm the effectiveness of DIP denoising for enhancing MRI and PET images prior to feature extraction.

Table 5 presents a comparative assessment of existing classification networks. The proposed LGBM achieves the highest ACC (99.12 %) and F1 (96.55 %), demonstrating its superior performance. Decision trees and Naive Bayes perform moderately, while KNN performs lowest on all criteria, indicating its comparatively low efficacy. LGBM outperforms the other architectures across all metrics, achieving the highest ACC (99.12 %), SPE (97.79 %), PRE (97.57 %), REC (92.60 %), and F1 (96.55 %). The LGBM network achieves better results compared to the other detection networks.

The comparison was conducted with different DL-based segmentation networks using several parameters, as shown in Table 6. The proposed GBS network increases the overall DI by 26.34 %, 11.39 %, 7.66 %, and 5.38 % compared to U-net, V-net, Nested V-net, and SegNet, respectively. The proposed GBS approach outperforms all compared methods, achieving the highest ACC (99.12 %), DI (90.74 %), and intersection over union (IoU) (82.7 %). Traditional segmentation DL-networks did not perform as well as the GBS network.

Fig. 10 displays the visualization outcomes of the different segmentation methods. In this evaluation, the GBS was compared with conventional networks such as V-Net and U-Net. GBS reduces processing complexity and yields better segmentation results than current segmentation techniques.

Fig. 10.

Comparison results of different segmentation techniques.

Table 7 presents a comparison of various existing methods with the proposed AD-HOLDER model using the collected OASIS dataset.

Battineni (2021) employed a Gradient Boosting Algorithm (GBA), achieving 97.58 % ACC. Odusami et al. (2023) used XAI, achieving 73.90 % ACC. Hamdi (2022) implemented a CNN, which attained a slightly lower accuracy (96 %). The proposed AD-HOLDER model increases the overall ACC by 1.55 %, 25.44 %, and 3.14 % for the GBA, XAI, and CNN, respectively. The reported p-values from paired t-tests are all below 0.05, indicating that the performance improvements of the AD-HOLDER model are statistically significant compared to existing approaches. The proposed AD-HOLDER model also increases the F1 by 6.85 %, 8.70 %, and 3.23 % for the GBA, XAI, and CNN, respectively. Based on this overall comparative analysis, the proposed AD-HOLDER model achieves better ACC and statistical significance.

Fig. 11 illustrates the process of detecting AD using the proposed AD-HOLDER model. A patient first visits a hospital, where MRI and PET images are collected in real time for diagnosis. These images are then processed by the AD-HOLDER model, which analyzes them to predict AD locations. In the hospital, prediction results assist the doctor in refining the patient’s diagnosis and recommending a treatment plan. This streamlined process enables real-time diagnosis, supporting timely and accurate diagnoses. The approach focuses on specific AD types, such as normal and abnormal, to simplify diagnosis and improve ACC. However, because it relies on a specific MRI and PET image dataset, the proposed model may not be generalizable to broader clinical settings and requires high-quality imaging for accurate classification. Moreover, while the proposed AD-HOLDER model categorizes AD into normal and abnormal cases, it does not distinguish between multiple disease stages, limiting its ability to provide a detailed analysis of disease progression.

Fig. 11.

Real-time clinical setting of the proposed AD-HOLDER model.