GPCB: A Hybrid GA-PSO and Transformer-guided CNN-BiLSTM Framework for Cardiovascular Disease Prediction

Cardiovascular disease is still the leading cause of death in the world, accounting for an estimated 18.6 million deaths annually, and substantial burden on health economies across the globe. The Global Burden of Disease (GBD) study reports that the burden of CVD and CVD-related risk factors has increased steadily over the past thirty years, among high-income and low-income populations alike [1]. There are a number of clinical diagnostics currently available, even with clinical advances, much remain limited as their capacities still rely on discrete risk factor measures and linear scoring models that do not integrate clinical and behavioral data [2, 3]. To improve upon these deficiencies, artificial intelligence (AI) and machine learning (ML) methods have progressively been adopted for CVD risk prediction and early diagnosis [4, 5]. In particular, hybrid models show more accurate prediction as they capture complex non-linear patterns of patient data [6]. A number of studies have also successfully distinguished heart disease with ML algorithms such as Support Vector Machines (SVM), Random Forests (RF), and Artificial Neural Networks (ANN) a number of studies cannot generalize results due to data heterogeneity and or selecting the best features, etc.

Zhou et al. [7] conducted an extensive review of the literature and retrieved a collection of hybrid CNN-LSTM models that showed they were more prevalent and more effective than classical methods for arrhythmia detection and myocardial infarction classification. Deep learning (DL) models have gained traction as a favorable choice for modeling high-dimensional, time-series medical data. For instance, CNNs have been used to classify spatial patterns extracted from ECG signals and electronic health data. Long short-term memory networks (LSTMs) and bidirectional LSTMs (BiLSTMs) have successfully been used to capture temporal data dependencies [8-10].

A further problem associated with CVD prediction is the presence of features that are irrelevant, redundant, or noisy. Irrelevant and noisy features can undermine model interpretability and exacerbate overfitting issues [11]. Metaheuristic approaches such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and hybrid algorithms based on swarm intelligence are features selection methods that perform well at minimizing input dimensionality and improving accuracy [12]. Amal et al. [9] and Wang et al. [8] recommended that multimodal (clinical parameters, lifestyle, and behavioral) data be included in an attempt to develop patient specific system for risk assessment. Likewise, some studies that combine CNNs with BiLSTMs or transformer-based mechanisms ([13-16]) report superior predictive performance.

Recent research has proposed both unique optimization approaches as well as explainable AI-approaches to build trust and transparency in the medical decision-making process [17]. However, most prior research has focused on either feature engineering or optimized deep learning architectures in isolation. There is a research gap in optimized deep learning pipeline encompassing an integrated framework that simultaneously optimizes features and provides reliable temporal modeling in CVD prediction tasks.

In order to address these research gaps, the aim of this paper is to propose a two-phase hybrid framework that leverages multi-feature optimization using genetic algorithm (GA) and Particle Swarm Optimization (PSO) with the time-series data feature processing capabilities of a Transformer-guided Convolutional neural network and bidirectional Long short-term memory (T-CBLSTM) deep learning model as the final predictive tool for heart disease with interpretability. The framework was trained and validated using three diverse real-world datasets, namely UCI Heart, Framingham, and MIMIC-III datasets, and utilized clinical and lifestyle data within the datasets. As will be shown, the proposed framework improves performance based on accuracy, precision, recall, F1, and AUC-ROC, compared with existing benchmark models.

The UCI Heart Disease data set contains 303 samples with 76 clinical attributes (often later reduced to 13 for many prediction tasks), the Framingham Heart Study data set contains 4,240 records, with 15 attributes, and MIMIC-III clinical data set has 7,000 patient records with 25 selected features. The model's high precision, recall and generalizability across 3 datasets improves its utility as a decision-support tool for early identification and risk stratification of cardiovascular diseases. In addition, the feature reduction work in Phase I adds to the interpretability of the model by identifying the most pertinent clinical and lifestyle factors to the individual, which is paramount in healthcare expectations for transparency and precision.

This research presents a comprehensive and unified framework that addresses critical challenges in cardiovascular disease (CVD) detection and health risk assessment by integrating multi-objective feature optimization with a hybrid deep learning model. The main contributions of this work are summarized as follows:

• Designed a novel architecture called GPCB, integrates a GA–PSO feature selector (Phase I) with a T-CBLSTM deep learning classifier (Phase II).
• Designed fitness function directs GAs–PSO meta-heuristic to simultaneously maximize classification accuracy and minimize feature redundancy.
• The T-CBLSTM model has CNN layers learning the spatial representation, learning long-range dependencies and contextual relationships.
• Models are evaluated using the UCI Heart Disease, Framingham and MIMIC-III datasets, along with a combined dataset with the results showing excellent accuracy and AUC.

The rest of this paper is organized in the following way: Section 2 provides a thorough overview of the state-of-the-art literature covering machine learning and deep learning models for cardiovascular disease prediction, with a special emphasis on feature selection and hybrid models. Section 3 describes the datasets used, containing clinical and lifestyle features while also discussing the data preprocessing and normalization methods. Section 4 explains the GPCB framework including the GA-PSO based feature optimization step and the CNN-BiLSTM deep learning model guided by the Transformer (T-CBLSTM). Section 5 details the experimentation setup, including hyperparameter tuning and evaluation metrics. It also explains the results of the ablation studies and the conclusions drawn by comparing the model with existing models as well as the performance in individual datasets. Finally, Section 6 concludes the paper and outlines future research directions followed by references.

The GPCB (Genetic Algorithm-Particle Swarm Optimization + Transformer-guided CNN-BiLSTM) framework we are proposing is a two-phase intelligent system for an accurate CVD prediction tool using combined clinical and lifestyle information. This model is motivated by the imperative to address significant limitations of existing systems, such as dealing with high-dimensional input space, lack of personalization, and poorer quality feature learning for sequential patient data. The framework combines advanced feature selection with hybrid deep learning to ensure both high precision and generalizability across datasets. The two-phases implemented in the proposed cardiovascular disease prediction framework are:

• Phase I: Genetic Algorithm-Particle Swarm Optimization (GA-PSO)
• Phase II: Transformer-guided CNN-BiLSTM

3.1 Multi-objective feature optimization using GA–PSO

This is the phase I of the proposed model, it is designed as a multi-objective feature optimization framework. Just as in clinical and life-style datasets not all features contribute meaningfully to a CVD prediction. Some features will be irrelevant to CVD prediction, redundant, and noise or correlations, etc. Using all features will additionally just add complexity to the model, potentially make the model overfit worse, and also will add to computational costs especially with deep learning models. Thus, a means of feature selection is essential. Here, we are using a hybrid GA-PSO feature selection strategy that utilizes the global search ability of the GA while using the local refinement and fast local convergence and refinement of the PSO to find a small number of features with maximum predictive performance and reduced dimensionality.

In real world healthcare datasets, the dataset will most likely have features that are irrelevant, redundant, or noisy. Because of this, we propose the use of a hybrid GA-PSO based wrapper method for selecting an optimal subset of features that maximize classification accuracy and minimize model complexity. The overall design diagram of the phase I GA-PSO is provided as Figure 1.

image003.png

Figure 1. GA-PSO design diagram

In Phase I of the GPCB framework, let the input dataset $D=\left\{ \left( {{x}^{i}},{{y}^{i}} \right) \right\}_{i=1}^{N},~{{x}^{i}}\in {{R}^{d}},{{y}^{i}}\in \left\{ 0,1 \right\},$ employ a Genetic Algorithm–Particle Swarm Optimization (GA– PSO) hybrid approach to select the most important features from the high-dimensional clinical and lifestyle data. Each solution (i.e., a Vn of features) is encoded as a chromosome, a binary vector.

$c=~\left[ {{c}_{1}},~{{c}_{2}},~\ldots ,~{{c}_{d}} \right],~~{{c}_{j}}\in \left\{ 0,1 \right\}$                         (1)

Eq. (1) shows the chromosome representation in binary format, a gene ${{c}_{j}}=~1$ implies the jth feature is selected.

The first objective function outlined in this Eq. (2) is the multi-objective GA-PSO optimization process during the feature selection phase. The goal is to minimize the classification error of the set of features represented as chromosome c.

$Minimize:~{{f}_{1}}\left( c \right)=1-Accuracy\left( c \right)$                      (2)

This Eq. (3) establishes the second objective of the multi-objective optimization in Phase I (Feature Selection using GA–PSO) with the goal of minimizing the proportion of selected features in the final feature subset.

In short, it penalizes the selection of too many features and facilitates simplicity within the model promoting generalizability and a decrease likelihood of overfitting.

$Minimize:~{{f}_{2}}\left( c \right)=\frac{1}{d}\underset{j=1}{\overset{d}{\mathop \sum }}\,{{c}_{j}}$                  (3)

Here,$~{{f}_{2}}\left( c \right)$ represents the second objective function, ${{c}_{j}}$ represents the binary value indicating the jth feature is selected or not and d is the total number of features in the dataset.

A starts as the optimization process of creating a population with binary chromosomes, each chromosome resulting in a different feature subset. The GA selects chromosomes to use as parents with a selection method based on round-robin selection or roulette wheel selection, placing a probability-based preference on parents with higher fitness. Crossover on the parents will recombine genetic information from two or more of the parents, which introduces some variability to allow any of the selected parents to create offspring in a new location in feature space. Mutation allows for small random changes (flips) of the chromosomes used to create the offspring. Mutation allows GA to move away from a local optimum, with a goal of fostering diversity in the parent population. Following are the GA operations:

Selection: either via roulette wheel or tournament selection to select parents.

Crossover: single-point crossover or uniform crossover to create offspring.

Mutation: bit flipping (0 → 1 or 1 → 0) with a low probability of mutation.

Let the initial population$~{{P}^{0}}$ for the hybrid GA–PSO method in Phase I of multi-objective feature selection. In nature-inspired metaheuristics, "population" refers to a set of candidate solutions referred to as individuals (or particles, or chromosomes). Each individual $c_{\mathbf{i}}^{0}$ is a binary chromosome representing a subset of features selected from the entire dataset for one solution in the initial generation (generation 0) as given in Eq. (4).

${{P}^{0}}=\left\{ c_{1}^{0},\ldots ,c_{n}^{0} \right\}$                             (4)

This Eq. (5) represents a single-point crossover operator for Genetic Algorithms (GA). Crossover involves the combining of some features (chromosomes) of each of two parent solutions to create a new offspring solution. The intent of crossover is to induce genetic diversity by mixing different genetic material (feature subsets) from different individuals.

$Crossover\left( {{c}_{1}},{{c}_{2}} \right)=\left[ {{c}_{1}}\left[ :k \right],{{c}_{2}}\left[ k: \right] \right]$                      (5)

Here, c₁, and c₂ represents first and second parent chromosomes, k is the randomly chosen crossover point, and $\left[ {{c}_{1}}\left[ :k \right],{{c}_{2}}\left[ k: \right] \right]$ represents genes of the chromosomes c₁ and c₂.

The mutation operation used here is

$\text{Mutation }\!\!~\!\!\text{ }\left( {{\text{c}}_{\text{j}}} \right)=\left\{ \begin{matrix}   1-{{\text{c}}_{\text{j}}}~~~~~with~probability~{{\text{p}}_{\text{m}}}  \\{{\text{c}}_{\text{j}}}~~~~~~~~~~~~~~~~~~~~~~~otherwise  \\ \end{matrix}\text{ }\!\!~\!\!\text{ } \right.$                        (6)

The following equation defines the mutation operation for a binary chromosome $c=\left[ {{c}_{1}},{{c}_{2}},\ldots \ldots ..{{c}_{d}} \right]$used in the GA part of the hybrid GA–PSO feature selection strategy. Mutation is a genetic operator that maintains diversity in the population and prevents premature convergence.

This equation describes how to convert a particle's velocity into a probabilistic value within the bounds of [0,1]. The sigmoid activation function does this. As shown in the Binary Particle Swarm Optimization (BPSO) algorithm, features are selected or not selected (0 or 1). While we cannot make continuous updates to the particle's position as in PSO, we can still update the particle's position probabilistically as shown in Eq. (7).

$v_{j}^{\left( t+1 \right)}=\omega v_{j}^{\left( t \right)}+{{c}_{1{{r}_{1}}}}\left( pbes{{t}_{j}}-x_{j}^{\left( t \right)} \right)+{{c}_{2{{r}_{2}}}}\left( gbes{{t}_{j}}-x_{j}^{\left( t \right)} \right)$                        (7)

Here, $v_{j}^{\left( t \right)}$​ $\omega $is the inertia weight, i.e. 0.4<$~\omega <0.9$,$~{{c}_{1}}$and ${{c}_{2~}}$cognitive acceleration and social acceleration coefficients, ${{r}_{1}}and~{{r}_{2}}$ are the random numbers.

This equation binarized the probabilistic output from Eq. (8). A uniform random number $r\in \left[ 0,1 \right]$ is generated. If the output from the sigmoid exceeds this random level, then the feature is selected (1). If it is below the random level, it is not selected (0). This creates a stochastic manner of feature selection, and encourages exploration.

$x_{j}^{t+1}=\sigma \left( v_{j}^{\left( t+1 \right)} \right),\sigma \left( v \right)=\frac{1}{1+{{e}^{-v}}}$                   (8)

Here, $x_{j}^{t+1}$updated binary selection of the j^th feature$~\sigma \left( v \right)$probability from the sigmoid function, and r is the random number sampled from uniform distribution U(0,1).

$x_{j}^{t+1}=\left\{ \begin{matrix}   1~~~~~~~~~~~~~~~~~~if~\sigma \left( \text{v}_{\text{j}}^{t+1} \right)>r  \\   0~~~~~~~~~~~~~~~~~~~~~~~~otherwise  \\ \end{matrix} \right.$                            (9)

The performance of each feature subset is evaluated by a multi-objective fitness function on two competing goals. It improves the classification accuracy while minimizing the number of features. Accuracy is computed after a lightweight classifier is trained on the features we selected and measured with cross-validation to ensure robustness. The second term in the fitness function penalizes the number of features, promoting compactness. By tuning the weights α and β, we adjust the trade-off between model performance and feature sparse characteristics. The score given to candidate solutions will lead our selection process and evolutionary process for future improvements.

Eq. (10) calculates the "feature ratio," or the fraction of selected features (the selected features divided by the dataset's total features). Use this as one of the objective functions in the multi-objective fitness function for feature selection. The goal is to minimize the selected features but retain a suitable classification performance.

$FR=\frac{\mathop{\sum }_{j=1}^{d}{{c}_{j}}}{d}$                        (10)

Here, d is the total number of features in the dataset and ${{c}_{j}}$ is the binary indicator for the jth feature.

Each candidate feature subset is evaluated by a CNN or SVM classifier on training data. Accuracy was computed using cross-validation and was used to reduce bias.

$Fit\left( c \right)=\alpha \cdot Acc+\left( 1-\alpha  \right)\cdot \left( 1-FR \right)$                        (11)

This Eq. (11) outlines the fitness of a chromosome (or feature selection), and balances two competing objectives. Acc shows how well the features you selected classify. Feature Ratio is the proportion of the features selected. And the FR part ensures that smaller subsets are rewarded. In the first phase of the work, GA and PSO were integrated into a hybrid feature optimization algorithm. GA parameters were established as follows: size of population = 50, maximum number of iterations = 100, crossover probability = 0.8, and mutation rate = 0.05. The parameters for PSO consisted of a swarm size = 50, initial inertia weight (w) = 0.7, cognitive coefficient (c1) = 1.5, social coefficient (c2) = 1.5, and maximum number of iterations = 100. All parameters were chosen with respect to the findings from previous optimization studies and personal tuning and testing, in order to achieve an approximation between convergence speed and exploring distinct subsets of features.

The preference of GA–PSO as opposed to other metaheuristic search algorithms like Differential Evolution (DE) or Ant Colony Optimization (ACO) is based on the use of complementary properties of the two algorithms. Whereas GA maintains a higher degree of exploration through genetic crossover and mutation, PSO maintains a level of exploitation via velocity updates. Thus, GA–PSO offers a compromise - preventing GA from being too random (as sometimes seen in GA), and preventing PSO from converging prematurely (as is sometimes seen in PSO). Prior studies have shown that GA–PSO hybrids achieve better global optima on high-dimensional biomedical datasets than DE, ACO, or either algorithm in isolation, making it suitable for cardiovascular datasets, which use varied clinical features and lifestyle features.

3.2 Phase II: Hybrid Transformer-guided CNN–BiLSTM (T-CBLSTM) Model

In Phase 2 of the GPCB framework, the optimized features selected by the GA–PSO module are inputted into a new CNN–BiLSTM (T-CBLSTM) architecture guided by a Transformer to generate predictions of cardiovascular disease. This hybrid architecture is capable of accommodating spatial patterns, temporal dependencies, and global contextual relationships across clinical and lifestyle features. The pipeline starts with a CNN layer that extracts local features and short-range dependencies across input variables at a high level. These local extracted features are then passed onto a Transformer Encoder Block, a type of block that improves the contextual understanding of heterogeneous health indicators using self-attention mechanisms to model global relationships across feature dimensions. Figure 2 shows the proposed design architecture of the phase II.

The output of the transformer is combined with the original CNN features, then passed into a BiLSTM layer at a high level which is capable of modeling the temporal dependencies in both forward and backward directions. This component models temporal dependencies that help to capture latent chronological or progressive trends in the data collected from the patient over time and could be especially meaningful for longitudinal features such as age, blood pressure, or lifestyle change over time. Finally, the output from the BiLSTM is passed through a Feed-Forward Fully Connected Dense layer with a sigmoid activation for binary classification or Softmax activation for multiclass classification.

image004.png

Figure 2. Design architecture of Phase II

The first stage of the model accepts an input vector of selected features, which are derived after preprocessing and feature optimization via GA–PSO. These features include both clinical e.g., blood pressure, cholesterol, ECG results and lifestyle factors e.g., smoking, exercise, alcohol use. For the UCI and Framingham datasets, the input is a static feature vector per patient $x=\left[ {{x}_{1}},{{x}_{2}},\ldots ,{{x}_{d}} \right]\in {{R}^{d}}$. The model input a vector that has optimized features $x\in {{R}^{d}}$, where d is the number of selected features obtained via GA–PSO. For sequential data, the input is treated as a time-series matrix $X\in {{R}^{TXd}},$ where T is the time steps. The CNN will receive the input as a two-dimensional matrix, where T is defined as the temporal length of the sequence, and d as the number of features per time step. This two-dimensional matrix represents the clinical and lifestyle characteristics provided by the GA-PSO module as Eq. (12).

${{X}_{CNN}}\in {{R}^{m\times 1\times 1}}$                      (12)

Here,$~{{X}_{CNN}}$ is the input tensor to the CNN layer, m is the selected features from phase I, R represents the 3D tensor with feature. Next, a set of convolutional filters (also called kernels) are applied to the input. Each filter slides across the input sequentially taking dot products between the kernel weights and the input subsequence. Mathematically, for a filter size of k, at position the convolution operation will take the form of Eq. (13).

${{H}_{k}}=\sigma \left( {{W}_{k}}*{{X}_{CNN}}+{{b}_{k}} \right)$                     (13) 

Here, ${{H}_{k}}$ is the output feature map from the k^th convolutional filter in a CNN layer. $\theta(\cdot)$ is a non-linear activation function, applied to the result of the convolution. ${{W}_{k}}$ is the convolution kernel for the k^th feature extractor and H_CNN is the input tensor to the CNN layer and ${{b}_{k}}$ is the bias for the k^th filter. The T-CBLSTM deep learning pipeline has two stages, and the first stage utilizes a CNN to capture local spatial patterns from the series of optimized features extracted from the GA-PSO module as shown in Eq. (14).

${{H}_{CNN}}=Concat\left( {{h}_{1}},\ldots ,{{h}_{K}} \right)$                      (14)

Here, ${{h}_{k}}$ is the output features. The CNN layer processes the input to train complex, non-linear, and highly correlated relationships between features. The output from the CNN layer is a transformed tensor as shown in Eq. (15).

${{F}_{cnn}}=Fl\left( {{H}_{CNN}} \right)~$                       (15)

Here$,~{{H}_{CNN}}$ is feature map flattened into one dimensional vector$~{{F}_{CNN}}$. The feature maps preserve the local correlational structures between the clinical and behavioral variables while reducing spatial dimensionality, and serve to input into the transformer encoder block in the next stage of the T-CBLSTM pipeline. This structure ensures that relevant short-range interactions are captured before applying the attention and sequential modeling. Once the local features have undergone CNN-based extraction and been transformed to output tensors, the tensors can be passed to a Transformer Encoder. The module's task is to learn only global contextual relationships between features (it is possible that the context between features are not neighboring but are related in some meaningful way from a semantic or, for example, clinical perspective). Convolution layers are only capable of learning to contextualize their immediate neighborhoods, whereas Transformer layers use self-attention mechanisms to produce a distribution of dynamic weightings between all positions in each feature representation, while allowing the model to focus on the most salient proto- interactions in each input instance. Following Eq. (16) shows the CNN-based local feature extraction, the transformed output tensor $FCNN\in R\left( T-k+1 \right)\times f$.

${{E}_{input}}={{f}_{cnn}}\cdot {{W}_{e}}+{{b}_{e}}~$                        (16)

Here, the flattened CNN features are then linearly transformed with a learnable weight matrix ${{W}_{e}}$, and bias ${{b}_{e}}~$to generate the input embeddings for the Transformer encoder. Positional encoding is as shown in Eqs. (17) and (18):

$P{{E}_{\left( pos,{{2}_{i}} \right)}}=sin\left( \frac{pos}{{{10000}^{\frac{2i}{{{d}_{model}}}}}} \right)$                          (17)

$\text{P}{{\text{E}}_{\left( \text{pos},{{2}_{\text{i}}}+1 \right)}}=\text{cod}\left( \frac{\text{pos}}{{{10000}^{\frac{2\text{i}}{{{\text{d}}_{\text{model}}}}}}} \right)$                       (18)

Here, pos is position index, i is dimension index, ${{d}_{model}}$ model is model dimension. Eq. (19) gives the input to transformer encoding.

Input to Transformer Encoder

${{\text{Z}}_{0}}={{\text{E}}_{\text{input}}}+\text{PE}$                       (19)

Here, ${{Z}_{0}}$ is the initial input for the transformer encoder. The key operation in the self-attention based Transformer is scaled dot-product attention, defined as Eqs. (20) and (21):

$\text{Attention}\left( \text{Q},\text{K},\text{V} \right)=\text{softmax}\left( \frac{\text{Q}{{\text{K}}^{\text{T}}}}{\sqrt{{{\text{d}}_{\text{k}}}}}\text{ }\!\!~\!\!\text{ } \right)\text{V}$                     (20)

$A=Attention\left( Q,K,V \right)\in {{R}^{n\times dk}}$                (21)

Here, the queries Q, keys K, and values V are derived by projecting the CNN output ${{F}_{CNN}}$ through learnable weight matrices ${{W}^{Q}}$, ${{W}^{K}}$, and ${{W}^{V}}$, respectively. Each position of the feature sequence has the ability to attend to each of the other positions, and can assign higher level of importance to the most relevant features based on similarity. The scaling factor $\sqrt{{{\text{d}}_{\text{k}}}}$ is required to avoid gradient vanishing throughout training, and serves to normalize the output of the dot-product. After computing the attention-weighted output the model applies a residual connection followed by layer normalisation to promote feature propagation and ratio of stability during training. The output of Multi-Head Attention is given as Eq. (22).

$MHA\left( X \right)=Concat\left( {{h}_{1}},\ldots ,{{h}_{H}} \right){{W}^{O}}~$                   (22)

Feedforward Network is given as Eq. (23).

$FFN\left( x \right)=ReLU\left( x{{W}_{1}}+{{b}_{1}} \right){{W}_{2}}+{{b}_{2}}$                 (23)

Transformer Layer Output is given as Eqs. (24) and (25).

${{Z}_{l}}=LayerNorm\left( MHA\left( {{Z}_{l-1}} \right)+{{Z}_{l-1}} \right)~$                    (24)

${{Z}_{l}}=LayerNorm\left( FFN\left( {{Z}_{l}} \right)+{{Z}_{l}} \right)~$                      (25)

Output of Transformer is given as Eqs. (26) and (27)

${{F}_{trans}}=MeanPooling\left( {{Z}_{L}} \right)~$                 (26)

${{F}_{Trans}}=LayerNorm\left( Attention\left( Q,K,V \right)+{{F}_{CNN}} \right)~$                   (27)

This resulting tensor ${{F}_{Trans}}\in {{R}^{T-k+1\times f}}$ accounts for non-local feature dependencies: for example, blood pressure may affect distant features like lifestyle habits or medical history. The attention mechanism also aids interpretability because it is easier to visualize what features are most important to the model for making predictions. The feature representations enhanced by the transformer and the original CNN data are concatenated and used as input to the BiLSTM module for sequential learning.

To achieve this fusion, the output feature vectors from both the CNN and Transformer at each time step are concatenated along the feature dimension. Formally, if ${{h}_{t}}\in {{R}^{f}}$ is the CNN output and ${{g}_{t}}\in {{R}^{dk}}$ is the Transformer output at time step t, the fused vector is defined as Eq. (28).

${{z}_{t}}=\left[ {{h}_{t}}\,\parallel \,{{g}_{t}} \right]\in {{R}^{f+dk\text{ }\!\!~\!\!\text{ }}}~$                   (28)

The result is a new sequence ${{F}_{fused}}\in {{R}^{n\times \left( f+dk \right)}}$ where n is the length of the sequence. The fused representation retains fine-grained spatial information, as well as coarse semantic information, and this improves the ability of the downstream BiLSTM to learn timed dynamics and supports improved classification of cardiovascular disease risk levels. So, the concatenation step represents an important architectural junction that merges multiple aspects of the patient data together into a richer, more holistic representation for final prediction.

The BiLSTM architecture consists of two LSTM layers: one that processes the input from left to right (forward pass) and another from right to left (backward pass). Each LSTM unit includes memory cells and gating mechanisms specifically the input gate, forget gate, and output gate that regulate the flow of information through time. These gates allow the model to retain relevant historical patterns while filtering out noise, making the network resistant to vanishing gradients and overfitting, which are common issues in temporal modeling.

Let ${{z}_{1}},{{z}_{2}},\ldots ,{{z}_{n}}\in {{R}^{f+dk}}$ denote the fused input sequence of length n, where each vector combines CNN and Transformer outputs. The BiLSTM processes this sequence in both directions as shown in Eq. (29).

${{X}_{lstm}}=\left[ {{f}_{cnn}},{{f}_{trans}} \right]~~$                     (29)

These representations are then usually pooled, followed by the attention layers or final dense layer. The BiLSTM's bidirectional architecture allows the model to reason across the entire sequence, improving its capability to recognize temporality like the progression of symptoms (e.g. physical activity over one year), the effects of long-term behaviour (e.g. banking wine to incur delays in sequencing of behaviour), and clinically relevant delayed interactions (e.g. a prescription written by a physician delayed to medication administration three days later) - all necessary for personalized and accurate CVD risk prediction.

At each time step t, an LSTM computes using the following Eqs. (30)-(35).

${{i}_{t}}=\sigma \left( {{W}_{i}}~{{f}_{t}}+{{U}_{i}}{{h}_{t}}-1+{{b}_{i}} \right)~$                  (30)

${{f}_{t}}=\sigma \left( {{W}_{f}}{{f}_{t}}+{{U}_{f}}{{h}_{t}}-1+{{b}_{f}} \right)~~$                        (31)

${{o}_{t}}=\sigma \left( {{W}_{o}}{{f}_{t}}+{{U}_{o}}{{h}_{t}}-1+{{b}_{o}} \right)~~~$                      (32)

$\widetilde{{{c}_{t}}}=\tanh \left( {{W}_{c}}{{f}_{t}}+{{U}_{c}}{{h}_{t}}-1+{{b}_{c}} \right)$                       (33)

${{c}_{t}}={{f}_{t}}\odot {{c}_{t}}-1+{{i}_{t}}\odot \widetilde{{{c}_{t}}}~$                  (34)

${{h}_{t}}={{o}_{t}}\odot tanh\left( {{c}_{t}} \right)~~$                         (35)

where, σ is a sigmoid activation, tanh is a hyperbolic tangent activation, $\odot$ is an element-wise multiplication, ${{h}_{t}}$ is hidden state at time t, ${{c}_{t}}$ is the cell state at time t, $W*\in {{R}^{h\times d}}$ is the trainable weight matrices, $b*\in {{R}^{h}}$ are the bias vectors, and h is the LSTM hidden size. The BiLSTM processes the input sequence in both forward and backward directions as shown in Eq. (36).

$\overrightarrow{{{h}_{t}}}=LST{{M}_{fwd}}\left( {{f}_{t}} \right),~~\overleftarrow{{{h}_{t}}}=LST{{M}_{bwd}}\left( {{f}_{t}} \right)$                     (36)

The final BiLSTM output at each time step is as shown in Eq. (37).

${{H}_{t{{b}_{i}}}}=\left[ \overrightarrow{{{h}_{t}}}\,\parallel \,\overleftarrow{{{h}_{t}}} \right]\in {{R}^{2h}}$                    (37)

Here, $\|$ denotes vector concatenation. To obtain a fixed-size representation from all time steps (e.g., for classification), we apply final feature concatenation as shown in Eq. (38):

${{f}_{final}}=Concat\left( {{f}_{cnn}},{{f}_{trans}},{{f}_{lstm}} \right)$                (38)

This is passed to a fully connected layer and the output layers are as shown in Eqs. (39) and (40).

$z={{f}_{final}}\cdot {{W}_{fc}}+{{b}_{fc}}~~$                     (39)

$\hat{y}=\sigma \left( z \right)~$                     (40)

where, $\hat{y}$ is an output prediction (binary or multi-class), σ is the sigmoid or softmax function, ${{W}_{o}}\in {{R}^{c\times 2h}}$ are an output weights, and c is the number of output classes.

After modeling both spatial and temporal relationships through the CNN, Transformer, and BiLSTM layers, the T-CBLSTM framework arrives at a compact, high-level feature representation of the input sequence, denoted as ${{h}_{final}}$. This vector captures both short-range and long-range dependencies among clinical and lifestyle features. To translate this abstract embedding into an interpretable decision, it is passed through a fully connected or dense layer. This layer applies a learned linear transformation, projecting the feature vector into a space whose dimensionality matches the number of output classes as shown in Eq. (41).

${{L}_{BCE}}=-\frac{1}{N}\underset{i=1}{\overset{N}{\mathop \sum }}\,\left[ ylog\left( \widehat{{{y}_{i}}} \right)+\left( 1-{{y}_{i}} \right)\log \left( 1-{{{\hat{y}}}_{i}} \right) \right]~$ (41)                            

Here, ${{y}_{i}}~is~the~$true label (ground truth), and $\left( {{{\hat{y}}}_{i}} \right)~$is the predicted probability. For binary classification tasks, a sigmoid function is applied to squash the output to a probability between 0 and 1, indicating the likelihood of disease presence. For multi-class classification tasks, a softmax function distributes the output across multiple classes, ensuring that the predicted probabilities sum to 1. During training, the model parameters are optimized by minimizing a suitable loss function binary or categorical cross-entropy which penalizes incorrect predictions and encourages the model to assign high probabilities to the correct class as shown in Eq. (42).

${{L}_{CCE}}=-\underset{i=1}{\overset{N}{\mathop \sum }}\,\underset{j=1}{\overset{C}{\mathop \sum }}\,{{y}_{ij}}\log \left( {{{\hat{y}}}_{ij}} \right)~$                 (42) 

Here, ${{y}_{ij}}~is~the~$true label (ground truth), and $\left( {{{\hat{y}}}_{ij}} \right)~$is the predicted probability.

This section explains how the proposed CNN–BiLSTM-based heart disease prediction model is trained and assessed to provide reliable, generalizable, and interpretable results. A few important areas of discussion are the training plan, the loss functions, and the metrics used to evaluate the model. To train the proposed hybrid CNN–BiLSTM model, a predefined training plan was in place to maximize the generalization and performance of the model across the individual cardiovascular datasets. Overall, the data was divided into training (70%), validation (15%), testing (15%). For time-series data (i.e. the MIMIC-III dataset), when conducting the split of the training, validation, and testing data, temporal locality was preserved so that data could not leak (i.e. for validation or testing data) forward/backward, from future to past.

The training was conducted with a batch size of size 32 over a maximum of 100 epochs. An early stopping plan was in place while the model was in training, where the validation loss was monitored at the end of training and if there were no improvements in the loss using some minimum number of epochs to define "no improvement" then the training would have stopped. In addition, the Adam optimizer was used due to its rapid convergence and adapting learning rate capability as shown in Eq. (43). Lastly, a learning rate scheduler was used to manage the learning rate during training; where if performance stalled the learning rate was reduced in a controlled manner, allowing fine-tuning during the latter epochs.

${{\Theta }_{t}}+1={{\theta }_{t}}-\eta ~.\frac{\widehat{{{m}_{t}}}}{\sqrt{\widehat{{{v}_{t}}}}+\epsilon }~$                 (43)

where, $\widehat{{{m}_{t}}}$ are bias-corrected moment estimates, and η is the learning rate. The transformer component was set to four encoder layers in total with 8 self-attention heads, 128 hidden dimension, 256 feedforward network layer size, and a dropout of 0.2 to minimize overfitting. The convolutional neural network in front of the Transformer consisted of 2 Conv2D layers with 64, 128 filters, and kernel size 3 × 3 with ReLU activation and maximum-pooling, followed by a flattening layer. The BiLSTM component consisted of two layers both 128 units to allow bidirectional temporal modeling. This selection of hyperparameters was based on empirical tuning and literature that showed their combination produced a trade-off between complexity and generalizability on medical datasets.