3.1 Dataset description

The model’s performance was evaluated using tomato plant leaves images dataset was obtained from the open-access repository that can be found at www.PlantVillage.org. It contains a collection of more than 50,000 images of leaves. Images of tomato leaves were specifically extracted for the purposes of our research. An overview of our dataset is given in Fig 1, which provides a summary of the data. Our dataset contains eight thousand images, which are organized into nine different diseases and healthy images [39]. To ensure fair model performance across all categories and avoid potential performance biases due to imbalanced sample distribution, data augmentation techniques were applied. These techniques were specifically used on images showing both healthy and diseased leaves. The dataset is extensive and covers both single disease and multiple disease instances on tomato leaves, primarily caused by biotic stress factors [40]. To facilitate training and testing, the dataset was segregated into separate subsets, maintaining a ratio of 20% for testing data and 80% for training data. The training set of the dataset consists of 8000 images, while the test set contains 2000 images.

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Fig 1. Sample images of tomato leaf disease dataset.

(a) Bacterial spot, (b) Early blight, (c) Late blight, (d) Leaf Mold, (e) Septoria Leaf spot, (f) Spider mites, (g) Target Spot, (h) Mosaic virus, (i) Yellow Curl Virus, (j) Healthy.

https://doi.org/10.1371/journal.pone.0315031.g001

This dataset covers a wide range of tomato plant conditions, encompassing both healthy and diseased states, with annotations provided by field experts [41]. This study’s major goal is to assess and classify tomato plant leaves according to their health, with a focus on differentiating between diseases like yellow leaf curl virus (TYLCV), bacterial spot (Xanthomonas campestris), early blight (Alternaria solani), late blight (Phytophthora infestans), leaf mold (Passalora fulva), septoria leaf spot (Septoria lycopersici), spider mites (Tetranychus urticae), and target spot (Corynespora cassiicola), mosaic virus (ToMV) in addition to a category indicating ’healthy’ plants.

3.2 Data preprocessing

Pre-processing is an essential step in improving the quality of input images, specifically in the context of classifying plant diseases. Plant sample images are gathered in the early stages and subsequently transferred to the pre-processing phase. In this instance, a Gaussian filter is applied to the image to effectively eliminate noise, resulting in more distinct and informative images of the plant leaves. Furthermore, to ensure consistency in input dimensions and optimize compatibility with subsequent processing stages in our classification model, the image size is standardized to 224×224. This method combines deep learning techniques for preliminary feature extraction and optimizes the selection process through an EHO-inspired optimization mechanism.

The analysis was conducted using TensorFlow, Keras, and scikit-learn. TensorFlow and Keras were utilized for model development, while scikit-learn assisted with feature evaluation and optimization.

3.3 Convolutional neural network

To effectively evaluate susceptibility to diseases in various regions of tomato leaves is essential to discern unique characteristics within these leaf sections. Improving the model’s efficiency relies on extracting pertinent features from leaf images, is illustrated in Fig 2. This process entails feeding the images into convolutional neural network and choosing specific intermediate layers to extract features. These extracted features are later flattened to create a feature vector for each image, enabling thorough analysis.

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Fig 2. Input image and extracted features maps.

https://doi.org/10.1371/journal.pone.0315031.g002

Utilizing convolutional neural networks (CNNs) proves to be a potent technique for feature extraction. The CNN architecture predominantly comprises initial convolutional layers combined with pooling layers, working together to acquire significant features from the input target images. Selected features are subsequently derived from chosen intermediate layers, resulting in the creation of a feature vector by flattening the extracted features. The CNN architecture for the extraction of features from tomato leaf images is devised as follows Inception begins with an initial convolutional layer, comprising 16 filters of dimensions 5x5, generating 16 feature maps, each with dimensions 128x128. Following this, a pooling layer employs a 2x2 window to generate 16 characteristic maps, each measuring 64x64. Subsequent to this stage, another convolutional layer, armed with 32 filters, processes these maps, followed by a pooling layer, which yields feature maps of dimensions 32x32x32. The progression continues with an additional convolutional layer featuring 64 filters, further processing these maps, leading to a pooling layer that generates feature maps measuring 16x16x64. Final convolutional layer with feature maps measuring 16x16x64 will generate feature vectors with the following number of components. The spatial dimensions of this layer are 224 x 224, and it has three channels (RGB). As a result, the final convolutional layer will extract 16,384 features. The flattening layer will flatten these features into a one-dimensional array before passing them along to the fully connected layers for further processing. To abstract the features further, fully interconnected layers are used, and the flattening layer eventually generates the ultimate output label probabilities by applying a softmax activation function. The extracted features are then passed to the classification layer for the purpose of classification.

3.4 Elephant herding optimization

This work describes the Elephant Herding Optimization (EHO) algorithm [42], a metaheuristic swarm-based approach to feature selection that improves the accuracy of classifying tomato plant leaf diseases. The EHO algorithm is employed following the initial step of training, which involves feature extraction using Convolutional Neural Networks. The suggested EHO-based feature selection method uses optimization concepts to identify features that minimize classification time while increasing accuracy. This novel approach highlights relevant features unique to datasets on tomato plant leaf diseases, making classification tasks easier. EHO uses cooperative behavior observed in elephant herds to select important features while continuously optimizing the feature space of tomato plant leaf datasets. The chosen features improve the accuracy and efficiency of disease classification and visual inspection of the leaves of tomato plants.

This algorithm derives its inspiration from the social structure observed within elephant groups. Elephants, in their natural habitat, exhibit complex social behaviors, with distinct roles for both female and male elephants. The foundation of elephant social organization rests on the formation of various clans, with the matriarch, the eldest female elephant, assuming the role of clan leader. Each clan comprises one female elephant along with other family members. Typically, female elephants maintain group cohesion, but as male elephants mature, they tend to depart from their family groups. The simulation of EHO incorporates operations akin to clan updating and clan separating, mirroring the real-world dynamics of elephant herding behavior [43]. In the process of selecting the feature, the goal is to pinpoint the optimal subset of features that enhance classification analysis outcomes. Within elephant groups, various clans emerge, each led by a matriarch and maintaining a consistent number of elephants. In every generation, a distinct group of male elephants resides apart from their herds, representing the minimum fitness value in maximization problems. In contrast, the matriarchs embody the maximum fitness value [44].

3.4.1 Fittest elephant’s position update using clan influence.

The positions of elephants within a clan are adjusted according to both the matriarch (the fittest elephant) and the elephant positioned at the centre of the clan. The matriarch’s position (the fittest elephant) is updated in relation to the elephant at the central position of the clan.

(1)

In this Eq 1, E is the current solution for the elephant, "E_next" is the next solution for the current elephant, the above equation combines the influences of the local best feature subset and the best subset of features at a global level ("") is the optimal subset of features found globally across all clans or iterations, using scaling factors "K" that determines how strongly the elephant’s solution is influenced by the best feature subset within its clan and "m" that determines how much influence the globally best feature subset has on the elephant’s solution.

(2)

This Eq 2 represents how the fittest elephant, often referred to as the matriarch, is updated position of the matriarch based on the variance from its present location and the location of the central elephant in the clan. The update is scaled by the factor "∅," which determines the strength of the influence of the center elephant on the matriarch’s position.

(3)

This Eq 3 calculates the centroid feature E_cenCi subset by taking the average of all the feature subsets N within the clan "ci." and represents sums up each feature across all subsets in the clan and then divides by the number of subsets to obtain the centroid.

3.4.2 Clan dispersal behavior.

As male elephants reach a certain age, they tend to exhibit a behavior where they depart from the clan and venture out independently. This phenomenon can be simulated within the optimization algorithm by considering elephants with lower fitness values as representative of this behavior. In this way, the departure of male elephants from the clan can be emulated through the algorithmic processes, influencing how certain individuals interact and contribute to the optimization process.

(4)

In this Eq 4, the male elephants’ behaviour is implicitly represented by the balance between the centroid position and the current matriarch’s. Adjust the placement of the most robust elephant matriarch, E_cenCi is the centroid feature subset for the clan "ci", is the present position of the most robust elephant matriarch. The value of α can be adjusted between 0 and 1 to control the extent to which male elephants’ influence affects the matriarch’s position update. The centroid is given more weight when α is greater, whereas the matriarch’s current position is given more weight when α is lower.

Algorithm 1 provides the algorithm for the EHO based feature selection. Initialization of parameters including population size (N), maximal number of iterations (MaxIter), herd size (H), exploration rate (CR), and exploitation rate (MR) occurs at the outset of the algorithm. Subsequently, a population of feature subsets is generated at random to represent potential solutions. Each iteration involves elephants in the herd perturbing their current solutions in order to investigate the feature space, and subsequently assessing the fitness of the subsets that result. Optimal solutions are subsequently updated. Additionally, knowledge sharing among elephants is incorporated into the algorithm to increase search diversity. In conclusion, convergence is assessed and the optimal feature subset discovered is returned.

Algorithm 1.Working principle of EHO technique

1. INPUT:
2. Size of the population = N
3. Maximum number of iteration = MaxIter
4. Herd size = H
5. Rate of Exploration = CR
6. Rate of Exploitation = MR
7. PROCESS:
8. Initialize Population:
9. Create N randomly selected feature subsets.
10. Repeat for MaxIter iterations:
11. For each elephant in the herd:
12.  Explore:
13. NewSubset = Perturb(CurrentSubset, CR)
14. Exploit:
15. Fitness = EvaluateFitness(NewSubset)
16. BestSubset = UpdateBestSolution(BestSubset, NewSubset)
17.  Share knowledge:
18. AdjustPosition(ElephantPosition, MR)
19. Convergence Check:
20.  If MaxIter iterations are reached, stop the optimization process.
21. OUTPUT:
22. Return the best feature subset found during the optimization process.

3.5 Proposed architecture and workflow

The initial stage of the process starts with gathering tomato leaf images, including both healthy and diseased samples. The subsequent phase encompasses preprocessing tasks applied to these input images. Moving to the third stage, the approach concentrates on isolating the diseased portion within an input image. After segmentation, the segmented portion of the diseased plant’s leaf image is used to compute and extract texture features, which highlight certain characteristics of the individual pixels or textures. The outlined method is visualized in Fig 3, through a block diagram.

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Fig 3. Proposed CNN (EHO+HOBS-ELM) architecture.

https://doi.org/10.1371/journal.pone.0315031.g003

The features extracted play a pivotal role in the subsequent analysis. Subsequently, with the goal of decreasing redundancy, a feature selection process takes place to choose the most relevant features that accurately reflect the provided image. After that, the type of disease is determined using these selected characteristics. Using a classification algorithm, the final step of this strategy is to identify the specific disease impacting the input plant leaf image [45]. Further elaboration on each of these phases of the proposed approach is provided below.

The decision to commence pruning from the final CNN layer is rooted in empirical evidence demonstrating that its neuron connections exhibit a notably lower degree of correlation within each class when compared to the other layers, evaluated by Pearson’s correlation coefficient, a statistical metric that quantifies the linear association between two continuous variables. Pearson’s correlation coefficient ranges from -1 to +1, with -1 signifying a perfect negative correlation, +1 denoting a perfect positive correlation, and 0 representing the absence of correlation. This last layer, essentially the classification layer, also coincides with the role of ELM in serving as a means for dimensionality reduction. This reduction operates along the neuron directions, enabling the pruning of connections at this level. Rather than employing a "masking out" approach for smaller weights, direct pruning at the neuron level proves to be more efficient, resulting in significant savings in both space and time.

3.5.1 ELM basic principle.

The single-layer feed forward neural network (SLFN), known as ELM [46], is highly regarded for its outstanding capabilities in regression and multi-class classification applications. ELM’s theoretical underpinnings underscore the notion that the hidden neurons can be generated randomly. In contrast to the SLFN, where both input and output layer weights are initialized randomly and subsequently adjusted through the back-propagation algorithm, ELM adopts a different approach. Through setup and training, the hidden layer weights in ELM are fixed to a random value. Unlike SLFN, where both layers undergo adjustments, ELM concentrates solely on updating the output layer weights. This distinctive feature, where only one layer’s weights are modified in ELM, gives it a significant speed and efficiency advantage [47].

In the scenarios of Extreme Learning Machines (ELM), the training dataset contains input vectors x_j and their corresponding output vectors t_j. A group of neurons defines the network’s hidden layer. Each characterized by weight vectors w_i, biases b_i, and an activation function g. These neurons within the hidden layers are coupled to those in the final layer through connections by specific weights expressed in the symbol as β_i.

The relationship among the hidden, output, and input layer can be stated as in Eq 5 (5)

Where, L denotes the hidden neurons count, and j signifies the input/output instance, and y_j is the output corresponding to input x_j. This relationship can be compactly represented as in Eq 6 (6)

Eq 7 represents the arrangement of matrices β and T in the context of the ELM model. Specifically, for m output nodes and L hidden neurons, the matrices β and T are structured as follows: (7)

Here, β is a matrix with the weights that link output neurons with hidden layer neurons, and T is the matrix containing all output values for the given inputs. The hidden layer’s output, as represented by Eq 8, is represented by the matrix H.

(8)

With the use of the generalized inverse of Moore-Penrose matrix H, represented as H⁺ in Eq 9, one may determine the ideal output layer weights β.

(9)

The computation of H⁺ can be done through methods like QR decomposition, singular value decomposition (SVD), orthogonalization, or orthogonal projection, enabling efficient learning without the need for extensive computational resources. ELMs are advantageous due to their ability to perform well with a large number of hidden neurons, reducing computational complexity. Moreover, ELMs simplify the network architecture by eliminating the need for determining optimal hidden layers and bypassing the challenges associated with back propagation. However, a notable challenge in ELMs is identifying the least important connections within the network.

3.5.2 HOBS- ELM pruning based classification process.

The core concept behind HOBS-ELM lies in the assessment of the relevance degree among hidden nodes, subsequently eliminating connections deemed irrelevant or of low relevance. This leads to the creation of more compact networks, all while preserving the network’s generalization capabilities. In this architecture, the strategy consists of regularizing methods to find and remove less important connections between the ELM’s hidden layer and output layer. Afterward, a pruning method is implemented to enhance the network’s structure by refining the chosen connections. The Hessian-based Optimal Brain Surgeon (HOBS) [48] algorithm serves as the pruning tool for hidden connections. HOBS leverages the Hessian matrix to gauge the sensitivity of the network’s output concerning the hidden layer connections, thereby excising connections with lower sensitivity values. Every step in our proposed approach, as outlined in Algorithm 2, is non-iterative. This model offers a systematic and automated approach for precise classification while effectively addressing computational efficiency concerns. Furthermore, through experimentation the optimum amount of hidden layers and neurons is chosen to improve the model’s convergence speed. The learning process of this proposed method can be executed via the workflow procedure illustrated in Fig 4.

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Fig 4. Working procedure of ELM classifier network.

https://doi.org/10.1371/journal.pone.0315031.g004

The first step is to start with an unpruned ELM neural network that links the hidden layer h to the input using random weights and biases (W,B). calculating the hidden layer H of output matrix requires knowledge of the input data matrix X, which has dimensions N x D, an activation function g, and N total amount of input feature mappings.

In step 2, analyze the sensitivity Sj for each hidden neuron j. For each input feature i calculate the absolute value of the weight connecting that feature to hidden neuron j is |W[i][j], Sum up these absolute weight values for all input features to get the total contribution of weights for neuron j is Σi|W[i][j]|.

In the next step, perform pruning using the Hessian Matrix H (j,k) this matrix elements are computed. This represents an element in the Hessian matrix corresponding to the interaction between hidden neurons j and k. Here Σi denotes the summation over all input samples(i). In the i_th input sample, H[i][j] represents the hidden layer activation value for hidden neuron j. In the input sample with index i_th,H[i][k] represents the hidden layer activation value of hidden neuron k.

Algorithm 2. HOBS- Pruned ELM

1. Step 1: Unpruned ELM Network
2.  Multiply input data matrix with weight matrix add bias then apply activation function g to find the resultant matrix.
3.  H = g(XW+B)
4. Step 2: Calculate Sensitivity S_j
5. Dividing its total absolute weight contribution by the sum of total absolute weight contributions for all hidden neurons S_j = (Σ_i|W[i][j]/(Σ_kΣ_i|W[i][k])
6. Step 3: Compute Hessian Matrix H(j, k)
7. The average of the pairwise products of elements from columns j and k in matrix H, with the sum taken over all rows, divided by the number of rows (N) H(j,k) = Σ_i(H[i][j]*H[i][k])/N
8. Step 4: Apply Hessian based Optimal Brain Surgeon Pruning
9. Calculate the diagonal of the Hessian matrix D, sensitivity matrix S, saliency vector C, pruning threshold t is D = [H(1,1),H(2,2),….,H(h,h)], S = [S₁,S₂,…,S_h], C = D*S, t = α*max(C).
10. Step 5: Compact ELM Network
11. If C[j] < t prune the neuron by excluding its associated weight and bias, or else keep the neuron and its associated weight and bias.

Applying the HOBS pruning step involves calculating the importance of connections using the Hessian matrix and sensitivity values. The saliency vector C captures the combined importance of each connection, and the pruning threshold t is determined as a percentage of the maximum saliency value, where α is a hyper parameter. This threshold helps identify connections to prune, and create a more compact neural network while retaining its important components.

The HOBS algorithm effectively identifies and prunes less important hidden connections, leading to a more compact and efficient neural network with potentially improved generalization capabilities. The specific choice of pruning threshold (t) and the number of retained connections may require experimentation and validation to achieve the best performance on the given dataset and task. The connection pruning method relies solely on straightforward matrix calculations to implement.

4.1 Hyper parameter tuning for proposed model

To improve classification accuracy, the proposed model’s hyper parameters are fine-tuned during training. These hyper parameters have a substantial impact on the training process, which improves the model’s capacity to learn and generalize properly [49].

Learning rate: If the learning rate is below the optimal level, the model will need additional epochs (hundreds or even thousands) to reach the optimal state. Conversely, if the learning rate is much higher than optimal, the outcomes may exceed the optimal state, potentially leading to calculation divergence.

The number of epochs (training iterations): Train the model for 50 epochs, allowing it to iteratively learn from the training data and adjust its internal parameters to minimize loss. This iterative procedure ensures that the model converges to an optimal state while increasing classification accuracy.

Activation Functions: The input layer utilizes the Rectified Linear Units (ReLU) activation function. The ReLU activation function introduces non-linearity to the model, enhancing its ability to properly capture intricate correlations within the data. This function optimizes the process of extracting features and improves the model’s capacity to comprehend a wide range of patterns within the input data. The output layer utilizes the softmax activation function. Softmax function is used to normalize the output scores for different classes, resulting in a probability distribution over the classes. This ensures that the model’s classifications are understandable and accurately reflect the probability of each class being the correct label.

Selecting an Optimizer: AdaM optimizer is used in the training phase. It enables effective convergence and quicker training by combining the benefits of momentum and RMSprop optimization approaches. Through adaptively changing learning rates for specific model parameters, AdaM facilitates the study of complex error surfaces and increases the process of convergence towards the optimal respond. It aim to maximize the performance of our suggested model by carefully adjusting these hyper parameters, ensuring accuracy, efficiency, and adaptability in the classification of diseases affecting tomato plants.

4.2 Performance metrics

The present study uses a benchmark dataset of images of tomato plant leaves to evaluate the efficiency of the proposed approach. In the split of the data set, training took up 80% of the images, while testing used up the remaining 20%. Within this dataset, the diseased plant leaf images exhibit afflictions stemming from one of ten distinct diseases. The performance metric quantifies the proximity between the original diseased plant leaf and its corresponding classified counterpart. Error rate, Kappa coefficient, training time, and testing time were regarded as additional evaluation measures for our suggested technique in addition to accuracy. When dealing with multiple classes, the accuracy metric computes the mean of individual class accuracies.

(10)

The error rate is the complement of accuracy, representing the proportion of misclassified instances. It provides an alternative view of the model’s performance.

(11)

TPs (true positives) indicate the overall count of true instances accurately classified across all classes. TNs (true negatives) represents the total amount of instances that were accurately classified as not included within any category. FPs (false positives) stands for the total number of erroneously classified instances within a given category. FNs (false negatives) represent the total instances inaccurately classified as not belonging to any category.

Cohen’s Kappa is a statistical measure that evaluates the agreement between predicted and actual classifications while considering the possibility of chance agreement.

(12)

p_o (Observed Proportion of Agreement) is the relative observed agreement between the predicted and actual classifications. P_e (Expected Proportion of Agreement by Chance) is the proportion of agreement expected by random chance. These performance metrics offer a thorough assessment of the effectiveness, efficiency, and reliability of the EHO-based HOBS-ELM model in classifying diseases in tomato plants.

4.3 Correlation matrix for EHO feature selection

EHO stands as an optimization algorithm, drawing inspiration from the cooperative dynamics observed in the natural world among elephants. Regarding the particular topic of classifying tomato plant diseases, its leverage the EHO to pinpoint the dataset’s most pertinent attributes associated with tomato plants. Our approach involves the construction of a correlation matrix, facilitating an assessment of the interdependencies among various dataset features. The primary objective revolves around the identification of features that exhibit substantial correlations with distinct disease categories, such as bacterial spots, late blight, and early blight. The rationale here is to unearth those features that promise valuable information for the classification task.

C1 and C2 are two correlation variables that can be calculated using Pearson’s correlation coefficient, which is a common method for measuring linear relationships as shown in Eq 13.

(13)

Where C1, C2 are the variables being correlated. μ_c1,μ_c2 are the ‘means’ of C1 and C2 respectively. σ_c1,σ_c2 are the standard deviations of C1 and C2 respectively.

Fig 5, visually depict the correlation matrix, generate a heat map where each cell signifies the correlation between two distinct features. Elevated positive correlations are typically depicted using warmer shades, notably the colour red, while strong negative correlations are represented by cooler hues, such as blue. This heat map presents a visual synopsis of the interrelationships among various attributes, shedding light on their potential influence on the classification process.

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Fig 5. Correlation heat map for feature selection.

https://doi.org/10.1371/journal.pone.0315031.g005

The correlation matrix and heat map serve as vital tools in comprehending the intricate interplay among attributes and their impact on precise disease categorization. These tools assist in the identification of attributes that not only provide information but also take into account their mutual interactions and dependencies. Through the visualization of correlations, valuable insights emerge regarding which characteristics wield the most influence in distinguishing among distinct disease categories, thereby facilitating feature selection. The attributes chosen based on their correlations with disease classes can then be harnessed to construct a more efficient model for categorizing tomato plant diseases. This process deepens our comprehension of attribute interdependencies and their consequential importance, ultimately guiding informed decision-making during the feature selection phase.

The correlation heat map provides critical insights into the relationships between the selected features. Bacterial spot exhibits minimal correlation with other diseases, indicating that it can be classified as a distinct class. The characteristics of late blight and Mosaic virus exhibit a moderate positive correlation, suggesting that there may be some overlap. This could potentially impact the performance of classification. The correlation analysis shows that numerous features exhibit minimal correlations with one another. This implies that the selected features make a distinctive contribution to the classification of diseases. This is expected to lead to improved classification accuracy in the model, as a result of the reduced redundancy and the more distinct distinctions between disease categories.

4.4 Classification analysis

A series of experiments were carried out using three different algorithms to assess the performance of our proposed approach. Deep convolutional extreme learning machine (DC-ELM), CNN, and HOBS-ELM. These experiments were performed on the widely used Plant Village dataset, a benchmark collection in the realm of agricultural image categorization. The dataset is divided into ten categories, each of which corresponds to a distinct tomato plant disease. Table 3 showcases the results of classification accuracy obtained from different network models when applied to individual tomato plant diseases within the Plant Village dataset. The experimental results demonstrate that the proposed model, which includes feature selection, consistently outperforms both the CNN and Deep Convolutional ELM models across a variety of tomato plant disease categories. This significant improvement in classification accuracy, as demonstrated in each disease class, underscores the efficacy of the proposed approach in enhancing model performance for precise disease classification.

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Table 3. Classification accuracy results for each class in the tomato plant disease dataset.

https://doi.org/10.1371/journal.pone.0315031.t003

Table 4, illustrates the outcomes of various network models applied to tomato plant leaf disease classification after retraining our model following HOBS pruning. The results clearly demonstrate the significant impact of model compression on reducing the model’s dimensions and computational burden while simultaneously elevating accuracy. In specific application scenarios, speed is a crucial performance metric. The pruning algorithm effectively compresses the model based on the designated pruning ratio, streamlining the network for optimal efficiency.

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Table 4. Performance analysis of various model on the tomato plant dataset.

https://doi.org/10.1371/journal.pone.0315031.t004

The connection between accuracy and the pruning rate within the framework of tomato plant disease classification using the HOBS-ELM is a crucial aspect to highlight because two pruned networks undergo a single retraining iteration, ensuring an equitable comparison. Furthermore, to maintain parity in this evaluation, the pruned ELM (Extreme Learning Machine) layers are deployed for the purpose of classifying the optimized feature subset. The main objective is to simplify the classification layer by preferring alternative, lighter classifiers. It’s important to clarify that the reported percentage of pruning exclusively pertains to the ELM layers. To guarantee consistency, all shared hyper parameters are configured identically for both approaches, with occasional fine-tuning of parameters introduced only when necessitated. It’s worth noting that periodic adjustments to the batch size may be warranted to steer clear of local minima.

As depicted in Fig 6, the approach consistently outperforms the alternative method across various pruning rates. Notably, in some instances, this approach even exhibits a marginal accuracy enhancement. This superior performance can be ascribed to the method’s inherent understanding of each neuron’s contribution to the ultimate discriminative power during the pruning process, taking into account interdependencies spanning all layers. In contrast, the alternative method relies solely on the length of a single layer’s dependencies, potentially leading to the exclusion of diminutive weights that, in reality, contribute to more informative neurons in the final layer. This arises because minor weights may possess cumulative effects across multiple layers or might be amplified by larger weights in other layers. Pruning these minor weights within a single layer effectively severs entire connections, starting from the raw pixel level and extending to the ultimate classification stage. While weight magnitude indeed serves as a valid pruning criterion, it should not serve as the sole determinant when evaluating the significance of a comprehensive bottom-to-top connection, especially within the context of HOBS-ELM; the result serves to classify tomato plant leaf diseases. While the classification module significantly enhances the model’s classification accuracy, it does so without introducing additional parameters and complexity. However, it is essential to understand that the existing parameters and complexity of the model can still pose challenges for deployment on edge devices with constrained computational resources. To address this issue and decrease the model’s parameters and complexity, the proposed HOBS pruning on the model specifically targets the enhanced ELM module.

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Fig 6. Accuracy change vs. ELM layers pruning rate.

https://doi.org/10.1371/journal.pone.0315031.g006

Table 5 presents the outcomes obtained through retraining the model following various levels of pruning. Model compression offers substantial reductions in model size and computational demands while simultaneously showcasing noteworthy improvements in accuracy. To gain a deeper understanding of our pruning technique’s nuances, Fig 7, and Table 5 furnish a comprehensive layer-wise examination of the speedup ratio. Fig 7, visually underscores that the bulk of parameters in the final ELM layers (ELM N5 to ELM N9) do not exert a significant influence on our designated task. Conversely, in contrast to the preceding layers, the last four layers exhibit relatively modest reduction rates. This observation aligns with the prevailing knowledge that earlier layers tend to encompass most common features like edge and color blob detectors, which hold the potential for utility across all classification categories.

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Fig 7. Layer wise structure complexity reduction.

https://doi.org/10.1371/journal.pone.0315031.g007

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Table 5. Comparative analysis of layer, parameters and speedup ratio for original CNN+FC and proposed HOBS-ELM models.

https://doi.org/10.1371/journal.pone.0315031.t005

Plant leaf disease classification methods are compared by computing efficiency and accuracy in the Table 6. The suggested method achieves 95.73% classification accuracy with little computing load. Adaptive feature selection with deep learning MBi-LSTM has reasonable computing efficiency and 94.20% accuracy. Efficient adaptive feature selection with deep learning model has low processing requirements and 94.80% accuracy. Finally, the Hybrid optimization method using RBFNN and ABC has modest computing efficiency and 92.50% accuracy. The hybrid approach presents a promising compromise between computing efficiency and classification accuracy compared to existing feature selection and optimization strategies.

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Table 6. Feature selection and pruning strategies comparison.

https://doi.org/10.1371/journal.pone.0315031.t006

4.4.1 Statistical analysis.

Overall accuracy is the proportion of examples each algorithm successfully classifies across all classes. To account for chance, Cohen’s Kappa coefficient compares predicted and actual classifications. In imbalanced datasets or where accuracy alone may be misleading, this gives a robust classification performance measure. The amount of floating-point operations needed to process one second of data is used to measure the model’s computational complexity during inference. Real-time or resource-constrained applications benefit from lower GFLOPs indicating computational efficiency. Fewer parameters reduce over fitting and computational load by showing the model’s complexity and ability to learn from training data. Compact models are better for resource-constrained devices and efficient storage since they use less memory to hold model parameters. Computing efficiency and scalability are shown by model training time on the dataset. Large datasets and iterative model development make shorter training times preferable.

Table 7, shows the performance, computational complexity, and efficiency of the CNN, DC-ELM, and (EHO+HOBS-ELM) algorithms are assessed through statistical analysis using these metrics. The evaluation involves identifying the most appropriate algorithm for specific application requirements by comparing the trade-offs between accuracy, model complexity, and training/inference efficiency.

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Table 7. Statistical summary of models performance metrics.

https://doi.org/10.1371/journal.pone.0315031.t007

5.1 Comparative analysis of proposed work with previous literature

Additionally, an experiment was conducted to assess the model’s performance in classifying diseases from tomato leaf images. Table 9 shows the comparison with other state-of-the-art DL-based approaches. However, it’s worth noting that this comparison may not be entirely direct due to differences in training and testing methodologies, computational resources, and data preprocessing techniques employed in the respective methods.

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Table 9. Comparative analysis of proposed approach versus baseline models.

https://doi.org/10.1371/journal.pone.0315031.t009

To assess the generalizability and robustness of our proposed model, we conducted ablation studies on two additional datasets: rice leaf disease and bean leaf disease. Employing the same model architecture (CNN with EHO+HOBS-ELM), we observed accuracy scores of 94.20% for the rice leaf disease dataset and 93.50% for the bean leaf disease dataset. These results demonstrate the efficacy of our proposed model across diverse plant disease datasets, showcasing its potential applicability beyond the specific context of tomato plant leaf disease. Performing cross-dataset experiments further validates the robustness and effectiveness of our model in plant disease classification tasks.

5.2 Limitation and future work

There are notable limitations associated with this retrospective, unifocal investigation that needs to be addressed. The dataset used here is a subset of the Plant Village database, focusing solely on tomato plant diseases, which might not cover the full spectrum of plant diseases. Consequently, the findings and model performance may have limited applicability beyond tomato plant disease classification. To improve generalizability, future studies will include a larger and more diverse dataset covering a wider range of plant diseases. Additionally, efforts will be made to develop a more robust system suitable for real-world scenarios, as the current reliance on laboratory-generated images poses a significant limitation. Future research will also focus on refining the disease classification process for various plant diseases and automating the recognition of different disease stages, potentially incorporating images from natural environments. Additionally, future endeavors will involve augmenting the dataset of plant leaf images and implementing alternative validation techniques like K-fold cross-validation to enhance accuracy.