Feature extraction in sensor plant disease datasets using reformed membership functions independent of class variables

Abstract

Sensor-based datasets often have limited features because continuous sensor deployment is expensive and complex. This study aims to develop a Membership Function-based Feature Extraction (MFFE) technique that operates without dependency on class variables to enhance small-sized sensor-based plant datasets. The research utilizes two sensor-based tomato disease datasets - TomEBD and TPMD, which have been collected in real-time. To address the dataset imbalance, the KMeans-SMOTE technique is applied. Feature extraction is performed using reformed triangular and gaussian membership functions, where all parameters are computed solely from the training data to prevent information leakage and biased evaluation. The enhanced datasets are classified using two optimized models: Optimized Kernel Extreme Learning Machine (OKELM) and Optimized Radial Basis Function Neural Network (ORBFNN), both tuned using the Optuna framework. The proposed technique is further validated on eight benchmarking non-plant-based datasets. Among all models, the TMF-ORBFNN achieved the highest accuracy across both plant-disease and benchmark datasets. Further, statistical analysis using the Friedman test and post-hoc Bonferroni-Dunn test showed that TMF-ORBFNN performed significantly differently from its counterparts. The time complexity of the proposed approach has also been analysed. The proposed MFFE technique provides effective feature extraction in small, sensor-based datasets without class-variable dependency. Enhancing and classifying plant-disease datasets using the proposed TMF-ORBFNN model will help farmers take timely actions to prevent crop diseases and reduce pesticide use.

Introduction

Farming and agriculture are fundamental to a country’s economy, supplying food, raw materials, and employment. During the Covid-19 pandemic, agriculture significantly contributed to making India a $5 trillion economy by bolstering the national GDP through crops, livestock, forestry, and more.¹. However, various crops suffer from diseases: potato plants are prone to late blight and surface diseases, tomato plants to early blight and powdery mildew, and gooseberry and wheat plants to rust diseases. These diseases result in substantial global yield losses: 21.5% in wheat, 30% in rice, 22.5% in maize, 17.2% in potato, and 21.4% in soybean². Besides diseases, climate change also severely impacts crop yields, influenced by weather parameters such as temperature, humidity, wind speed, leaf wetness, and rainfall. The release of greenhouse gases like carbon dioxide () and methane () is expected to raise global temperatures by 2.5 to by the end of the 21st century³. This temperature rise could decrease yields of paddy by , maize by , and wheat by , leading to higher market prices³. On average, the global agricultural productivity growth has been impacted by in European regions, in Asian regions and nearly in African regions⁴ due to changes in climatic conditions. Additionally, it affects insect physiology, increasing pest populations and causing more crop damage and yield losses⁵. The global population is increasing at an alarming rate and is projected to reach nine billion by 2050, demanding a 70-100% increase in food production and a focus on reducing food losses⁶.

Tomato is a widely produced and consumed crop worldwide, with over 187 million tonnes produced in 2020, making India the second-largest producer⁷. The tomato industry is growing at a compound annual rate of from 2022 to 2027⁸. However, tomato plants may suffer from harmful diseases such as early blight and powdery mildew. Early blight is caused by the pathogens Alternaria tomatophila and Alternaria solani in the form of dark spots on leaves⁹ and powdery mildew is caused by the fungus Oidium neolycopersici in the form of powdery fungus growth on the leaves¹⁰. These diseases may lead to substantial yield losses in tomato fruit - to by early blight¹¹ and up to by powdery mildew¹².

Although pesticides and fungicides are used to control these diseases, their excessive use can degrade crop quality and exacerbate disease severity. For instance, overuse of fungicides in tomato plants can promote the growth of pathogens like Leveillula taurica and Alternaria solani, worsening the disease¹³. Additionally, agricultural experts are needed to guide farmers on proper fungicide use, which can be expensive and not always accessible. Therefore, developing a timely spray prediction model is crucial. This model would enable the precise application of fungicides on diseased plants only on conducive days, avoiding over-spraying on healthy plants, preserving crop quality, and reducing costs.

Recently, numerous researchers have employed Machine Learning (ML) and Deep Learning (DL) techniques to predict crop plant diseases³⁰. Table 1 lists various studies, detailing the plants under investigation and the learning techniques used. The table shows that a range of datasets, such as RGB images, hyperspectral images, sensor-based data, and plant attribute data, have been utilized for disease prediction. Several studies have also focused on feature extraction techniques to enhance the performance of ML and DL models.

Table 1.

Literature on disease prediction in plants.

References	Disease	Plant	Dataset type	Classifier/technique
14	Multiple	Multiple	Categorical data	Hybridised IterativeImputer- Synthetic Minority Oversampling Technique for Nominal (SMOTEN)-OptimisedXtremeGradientBoosting (OXGB) with Ant Lion Optimiser (ALO)
15	Early blight	Tomato	Sensor data	Hybridised Kernel Extreme Learning Machine-KmeansSMOTE
16	Pest	Coffee	RGB images	Multi-layer hybrid vision graph neural networks
17	Late blight	Potato	Sensor data	Artificial neural network
18	Multiple	Potato	RGB images	EfficientNetV2B3 + Vision transformer
19	Fungal disease	Multiple	RGB images	Modified ResNeXt
20	Pest	Apple, guava	RGB images	SegLearner based on ResNet-50
21	Fungal diseases	Multiple	Sensor data	Multilayer perceptron
22	Charcoal rot	Soybean	Attribute data	RLogistic regression, Random forest (RF), Multilayer perceptron, Gradient tree boosting, Support vector machine
23	Powdery mildew	Tomato	Sensor data	Extreme Learning Machine
24	Weed	Multiple	RGB images	You only look once (YOLO) with particle swarm optimization (PSO)
25	Fungal, bacteria, viral	Multiple	RGB images	Radial basis function neural network
26	Multiple	Rice	Sensor data	Naive Bayes
27	Multiple	Coffee	RGB images	Convolutional neural network (CNN)
28	Blister blight	Tea	Sensor data	Multiple linear regression
29	Powdery mildew	Tomato	Sensor data	k-nearest neighbor (kNN), Decision tree, RF

Features are properties that influence the variable being predicted. For instance, predicting the severity of a plant disease on a given day may involve features like temperature, rainfall, relative humidity, wind speed, and sunshine hours. Feature extraction is crucial for improving the set of available features, which serve as independent variables in predicting the dependent variable. This enhancement is especially important for small datasets with limited features, leading to better prediction results and overall performance³¹. Table 2 lists studies that have focused on feature extraction techniques for plant disease-related datasets.

Table 2.

Literature on feature extraction in plant disease datasets.

References	Disease	Plant	Dataset type	Feature extraction technique
39	Rust	Aloe vera	RGB images	Quantum CNN
40	Multiple	Multiple	RGB images	Optimum restricted Boltzmann machine
41	Early blight, late blight	Potato, tomato	RGB images	Quantum image descriptors
42	Multiple	Cotton	RGB images	Gray Level Co-occurence Matrix (GLCM), Improved Local Binary Pattern (ILBP), Generalized Low Rank Model (GLRM) with Binary Guided Whale-Dipper Throated Optimizer for Feature Selection (FS)
43	Multiple	Multiple	RGB images	Ensemble of ResNet18 and LBP features optimized using Binary Dragonfly, Ant Colony and Moth Flame Optimization
44	Multiple	Watermelon, pear	RGB images	Color, GLCM, Histogram of Oriented Gradients (HOG)
45	Multiple	Mango	RGB images	CNN followed by Adaptive Squirrel-Grey Wolf Search Optimization for FS
37	Multiple	Multiple	RGB images	Ensemble of Swin Transformers and Residual CNN
46	Multiple	Multiple	RGB images	Morphological Opening, Fourier descriptors of Polar Fourier Transform (PFT), Canny Edge Detection, GLCM
47	Multiple	Multiple	RGB images	CNN
48	Meloidogyne luci	Potato	Hyperspectral images	Principal component analysis, Linear discriminant analysis, Partial least squares
49	Weed detection	General	RGB images	Simple Linear Iterative Clustering (SLIC), HOG
50	Early blight, powdery mildew	Tomato	Sensor data	Fractional Mega Trend Diffusion (FMTD) function with Genetic Algorithm (GA) for Optimization

Apart from plant-based datasets, a few studies have also explored feature extraction techniques in sensor datasets from other domains. A recent study³² utilised Long Short-Term Memory (LSTM) networks for feature extraction and KNN as a classifier for detecting cyberattacks from sequential sensor data. However, DL models like LSTM generally require large labeled datasets and high computational resources for training, making them less practical for small sensor-based datasets with limited features.

Research has also focused on crop detection using drone imagery^33–35. Furthermore, a few studies have explored blockchain-enabled learning systems to ensure secure and decentralized management of data³⁶, and deep vision-based frameworks that utilize convolutional or transformer architectures for visual plant disease detection³⁷. Similarly, cross-domain optimization techniques have been applied to improve the generalization of predictive models³⁸. However, as the blockchain grows, storing and validating every transaction becomes slower and requires more resources, limiting real-time processing and system scalability, which are essential for sensor-based disease prediction systems.

Research gap

As seen in Table 2, many studies have concentrated on image-based plant disease detection, where feature extraction methods use visual indicators such as texture, color, and shape to derive numeric features representing the disease symptoms. However, there has been limited work on feature extraction for sensor-based data. Sensor interfaces are quite expensive, often resulting in sensor data with fewer features.

The most relevant prior work by Bhatia and Chug⁵⁰ introduced a class-dependent feature extraction method for numeric data using a modified triangular fuzzy membership function. They utilized two tomato datasets - Tomato Powdery Mildew Dataset (TPMD) and Tomato Early Blight Dataset (TomEBD) to predict powdery mildew and early blight diseases in tomato leaves based on the parameters - leaf wetness, soil moisture, temperature, wind speed, dew point, relative humidity, and global radiation. The feature extraction process involved dividing the dataset based on the class variable and calculating parameters () necessary for the triangular membership function: lower limit (), upper limit (), mean (), the fraction of data points greater than mean (), and the fraction of data points less than mean (). These parameters were used to transform each predefined feature into c additional features, where c is the number of classes. Consequently, if there are initially n features, the total number of features after extraction becomes . After feature extraction, the dataset was divided into training and test sets and classified using the Optimized Kernel Extreme Learning Machine (OKELM), which is optimized using GA for hyperparameter tuning of the model parameters.

However, this technique has significant drawbacks:

• At the training level, it divides the dataset based on the class variable and then computes the transformed features. The class variable dependency renders the model ineffective for real-time disease prediction, as the class variable is not known at the time of model testing. Hence, features cannot be computed at the time of the application of the model in real time.

• The features are transformed using the parameters (), which are computed on the entire dataset, rather than separately on the training set, leading to biased results. For instance, the mean value of a feature should be computed only on the training set for extracting new features. This mean value should then be used during testing to extract features from the test data. This is because, in real-time scenarios, new data points are not included in the statistical value computations, so the values computed during training must be used for feature extraction on those new data points.

• The generalization capability of the feature extraction technique across diverse non-plant datasets has not been systematically evaluated.

Research objective and novel contributions

This study aims to enhance the existing feature extraction approach by eliminating class variable dependency and reducing statistical bias. The membership function parameters are computed solely on the training data, independent of class labels, making the method applicable to real-time scenarios where the class information is unavailable during predictions. The learned from the training data are then reused for transforming the features in the test data, for a fair evaluation of the feature extraction mechanism. The same two tomato disease datasets, TPMD and TomEBD, have been utilized and balanced using the KMeans-SMOTE (KM-SMOTE) technique. Features are then extracted using reformed triangular and Gaussian membership functions. The enhanced datasets are provided to two ML classifiers, OKELM and Optimized Radial Basis Function Neural Network (ORBFNN), for performance testing. The parameters of both classifiers are optimized using the Optuna framework based on Bayesian optimization, and k-fold cross-validation is employed for training and testing.

The choice of KM-SMOTE as the balancing technique and the use of OKELM and ORBFNN classifiers are based on some preliminary experiments explained later in the study. The proposed methodology is further validated on eight publicly available benchmark datasets: Breast Cancer Wisconsin Original (BCO)⁵¹, Glass Identification (GI)⁵², Pima Indians Diabetes (PID)⁵², Glioma Grading Clinical and Mutation Features (GGC)⁵³, Heart failure clinical records (HFC)⁵⁴, Differentiated Thyroid Cancer Recurrence (DTC)⁵⁵, Rice (Cammeo and Osmancik) (RCO)⁵⁶, and Speaker Accent Recognition (SAR)⁵⁷. Further, the performance difference between the classifiers is analysed using the Friedman test and post-hoc Bonferroni-Dunn test. The novel contributions of this study are outlined as follows:

1. Introduction of class-independent Membership Function-based Feature Extraction (MFFE) technique by reforming triangular and gaussian membership functions for enhancing datasets with a limited number of features.

2. Prevention of information leakage and biased evaluation by computing feature-transforming parameters solely on the training set.

3. Development of an optimized ML model for predicting powdery mildew and early blight diseases in tomato plants.

4. Hyperparameter optimization of OKELM and ORBFNN models using Optuna and analysis of hyperparameter importance for accuracy maximization.

5. Validation of the proposed approach for generalisation capabilities on eight diverse benchmarking datasets.

6. Statistical significance testing of the performance difference between the models using the Friedman test and post-hoc Bonferroni-Dunn test.

7. Time complexity analysis of the proposed approach.

Enhanced classification results using the proposed technique will allow farmers to take appropriate preventive measures for disease control with limited use of fertilizers and pesticides only on conducive days. This will save money and protect crop quality.

Research outline

The rest of the sections are organized as follows: Section "Methodology" describes the materials and methods used. Section "Results and discussion" details the results, followed by a discussion. Section "Conclusion and future scope" concludes the study along with future directions.

Methodology

This section outlines the core elements of this study and is divided into seven subsections. Subsection "Data collection procedure" describes the two plant disease datasets and the eight benchmarking datasets. Subsection "Data resampling" discusses the resampling technique used. Subsection "Membership function based feature extraction (MFFE)" explains the proposed feature extraction approach. Subsection "ML classifiers" details the two ML classifiers, followed by hyperparameter tuning in Subsection "Hyperparameter optimization". Subsection "Preliminary experiments" presents the preliminary experiments that informed the experimental framework of the current study. Finally, Subsection "Research framework" presents the overall research framework.

Data collection procedure

This subsection briefly explains the two plant disease datasets and the eight benchmarking datasets utilized in this study.

1. TomEBD dataset represents a real-time early blight dataset for tomato plants. The tomato seedlings were sown at ICAR-Indian Agricultural Research Institute, Pusa Campus, New Delhi - 110012, in January 2021. To induce early blight disease, the pathogen Alternaria solani was introduced to some of the plants about a month later. The disease began to manifest around April 2021. For the meteorological data collection - Temperature (Temp) in , Relative Humidity (RelH) in %, Leaf Wetness (LWet) between 0 and 15, Soil Moisture (SMois) in volumetric water content (VMC), and Dew Point (DP) in , three sensors were used. Hence, there are five independent variables - Temp, RelH, SMois, LWet, and DP, and one dependent variable having two class labels - diseased and healthy. For Temp and RelH, WatchDog 1000 Series Model 1450 Temp + RH + 2 External Ports was used. For LWet, 3666 HSN 9015 was used. For SMois, WaterScout Soil Moisture 100 Sensor 6 ft was used. The DP was calculated⁵⁸ using the equation

   1

   The sensors were placed in both the healthy and diseased plants in March 2021. Images showing the placement of sensors in tomato plants are presented in Fig. 1a and b. The data from March 2021 to May 2021 was collected using the SpecWare 9 Pro Software. The entire data collection process is shown in Fig. 2. First, the data loggers are setup and the LWet and SMois sensors are connected. Further, the preferences are set for DP calculation and for adding the support for the loggers. The healthy and diseased stations are then created using the WatchDog Manager screen, and their properties are set using the WatchDog Properties. Finally, the data can be collected and downloaded using the book icon in the toolbar. SpecWare also provides Temp and DP graphs for analysis along with a real-time wather monitor screen. The collected dataset contained numerous duplicate records because the weather parameters did not change frequently. Additionally, some records had missing values due to noise and network issues. To address these issues, the data was pre-processed: records with missing values were removed, and similar records were averaged over 6 h intervals. The resulting dataset consists of 380 samples - 250 healthy and 130 diseased.

2. TPMD is another sensor-based tomato disease dataset for powdery mildew disease⁵⁹. It comprises five independent variables - Temp, LWet, RelH, Wind Speed (WSpd), and Global Radiation (GRad), and one dependent variable with two class labels - conducive and non-conducive, which indicate the environmental conditions as supportive or non-supportive for the powdery mildew disease growth. There are 217 non-conducive and 27 conducive samples - a total of 244 samples. The TPMD dataset is publicly available in the research article⁵⁹.

3. The eight benchmarking datasets for validating the proposed approach - BCO, GI, PID, GGC, HFC, DTC, RCO, and SAR are described in Table 3. The independent variables, class labels, and the number of samples present for each class are also mentioned in the table. Please note that a diverse set of datasets was selected to test the generalizability of the proposed method. Out of eight datasets, five - BCO, PID, GGC, HFC, and DTC, are based on medical patient records. One dataset, RCO, is used for plant variety classification, and two datasets, GI and SAR, are used for multi-class classification. For the GI dataset, the glass type VWFP represents Vehicle Window Float Processed, WFP represents Window Float Processed, and WNFP represents Window Non-Float Processed. Similarly, the GGC dataset has two class labels - Lower-Grade Glioma (LGG) and Glioblastoma Multiforme (GBM). Further, for the SAR dataset, there are six class labels - Spain (ES), France (FR), Germany (GE), Italy (IT), United Kingdom (UK), and United States (US). Due to space constraints in the table, abbreviations have been used. Also, the BCO dataset has 16 missing values for the variable Bare Nuclei. The technique Multivariate Imputation by Chained Equations⁶⁰ for computing missing values has been used for the same.

Fig. 1.

Sensor placement in tomato plants.

Fig. 2.

Data collection process through SpecWare 9 pro software.

Table 3.

Benchmarking datasets.

Dataset	Description	Independent variables	Class labels (samples)	#Samples
Breast cancer Wisconsin original (BCO)51	Breast measurements of breast cancer female patients to predict whether the cancer is benign or malignant	Clump Thickness, Uniformity of Cell Size, Uniformity of Cell Shape, Marginal Adhesion, Single Epithelial Cell Size, Bare Nuclei, Bland Chromatin, Normal Nucleoli, Mitoses	Benign (241)	699
			Malignant (458)
Glass identification (GI)52	Various element values present in the glass to identify the glass type	Refractive Index, Sodium, Magnesium, Aluminium, Silicon, Potassium, Calcium, Barium, Iron	Headlamps (29)	214
			Containers (13)
			Tableware (9)
			VWFP (17)
			WFP (70)
			WNFP (76)
Pima Indians diabetes (PID)52	Diagnostic measurements of Indian female patients, to predict whether the patient has diabetes or not	Pregnancies, Glucose, Blood Pressure, Skin Thickness, Insulin, Body Mass Index, Diabetes Pedigree Function, Age	Diabetic (268)	768
			Non-Diabetic (500)
Glioma grading clinical and mutation features (GGC)53	Clinical features of patients diagnosed with brain glioma to predict whether a patient is Lower-Grade Glioma (LGG) or Glioblastoma Multiforme (GBM)	Gender, Age_at_diagnosis, Race, IDH1, TP53, ATRX, PTEN, EGFR, CIC, MUC16, PIK3CA, NF1, PIK3R1, FUBP1, RB1, NOTCH1, BCOR, CSMD3, SMARCA4, GRIN2A, IDH2, FAT4, PDGFRA	LGG (487)	839
			GBM (352)
Heart failure clinical records (HFC)54	Clinical records of patients during their follow-up period who had heart failure	age, anaemia, creatinine phosphokinase, diabetes, ejection fraction, high blood pressure, platelets, serum creatinine, serum sodium, sex, smoking time	Survived (203)	299
			Died (96)
Differentiated thyroid cancer recurrence (DTC)55	Clinical features of patients collected over 15 years to predict recurrence of thyroid cancer	Age, Gender, Smoking, Hx Smoking, Hx Radiothreapy, Thyroid Function, Physical Examination, Adenopathy, Pathology, Focality, Risk, T, N, M, Stage, Response	Recurred (275)	383
			Not Recurred (108)
Rice (Cammeo and Osmancik) (RCO)56	Morphological features extracted from rice images to classify into two varieties	Area, Perimeter, Major Axis Length, Minor Axis Length, Eccentricity, Convex Area, Extent	Cammeo (1630)	3810
			Osmancik (2180)
Speaker accent recognition (SAR)57	Speakers from six different countries read English words to detect and recognize accents	Twelve features extracted through analysis of the sound signal of a word, specifically focusing on the most significant 1-second portion of its pronunciation	ES (29)	329
			FR (30)
			GE (30)
			IT (30)
			UK (45)
			US (165)

Data resampling

In supervised learning problems, the dataset includes predefined class labels, with each data point assigned to one of these groups. Data imbalance occurs when the number of samples in each class varies significantly. All the datasets discussed in subsection 2.1 exemplify this issue. Imbalanced data can lead to biased results favoring the majority class, causing minority class samples to be incorrectly predicted as the majority class⁶¹. Therefore, it is crucial to balance the data before further processing. In the current study, K-Means Synthetic Minority Oversampling Technique (KM-SMOTE) has been used for data balancing. The algorithm is briefly explained below:

• KM-SMOTE is a data balancing technique that combines the K-Means clustering algorithm with the SMOTE⁶². K-Means operates in three steps: grouping the data into k clusters, computing the centroids of these clusters, and reassigning data points to the nearest centroid’s group. These steps are repeated until data point assignments remain unchanged. SMOTE is an oversampling method that balances a dataset by generating synthetic minority class samples. It involves three steps: selecting a random minority point, randomly choosing one of its minority neighbors, and computing a new point along the line segment between them by multiplying the distance by a random weight between 0 and 1⁶³. However, SMOTE can produce noisy samples as it does not account for within-class imbalance. KM-SMOTE addresses this by applying SMOTE only within clusters that contain a significant number of minority points, avoiding areas with few or no minority points for synthetic data generation.

One of the popular techniques - Random OverSampling (ROS), has not been utilized here since it replicates the minority samples exactly and, therefore, may lead to overfitting in the case of small datasets⁶⁴.

Membership function based feature extraction (MFFE)

Membership functions define the extent of membership of elements belonging to a set, mapping a value x to a real interval between 0 and 1. In this study, two membership functions - triangular and gaussian, have been reformed and used for transforming the existing features in the datasets. The two membership functions can be defined as:

• Triangular Membership Function (TMF) It can be defined using three parameters - l, u, and m, such that

  2

  where l is the lower limit, u is the upper limit, and m is the mean of the data. The lower and upper limits are calculated by using the Fractional Mega Trend Diffusion (FMTD) function⁶⁵ and are given in the following equations:

  3

  4

  Here, v represents the variance of the data, and represent the number of samples less than and greater than the mean m, is the ratio of data points less than m to the total number of data points, and is the ratio of data points greater than m to the total number of data points. and can be calculated using the following:

  5

  The function has been modified⁵⁰ using a parameter p with values in the range , in the following manner:

  6

  If , then the reformed TMF returns to the original. Figure 3 shows the diagrammatic representation of the function with p values , , and . It can be noted that a smaller value of p results in a more “dome-like structure” rather than triangular. The data has a mean value of . The parameter h is a real number with values in the range - 0.99.
• Gaussian Membership Function (GMF) It can be defined using two parameters - mean m and standard deviation s of the data as

  7

  The function has been reformed by a parameter p with values in the range in the following manner:

  8

  For , the reformed GMF returns to the original. Figure 4 shows the diagrammatic representation of the function with p values . It can be noted that a smaller value of p results in a more “flat-top structure” rather than gaussian. The data has a mean value of and standard deviation .

Fig. 3.

TMF with different values of p.

Fig. 4.

GMF with different values of p.

For feature extraction, the membership functions are applied to each feature of the training dataset. Consider a dataset having number of rows . Let a feature f has the following values for the 10 data points - . After the dataset is divided into a 70-30 train-test ratio, let the training set be and the testing set be . To compute the new feature using TMF, the following values are computed:

1. Mean of as .

2. Variance of as .

3. Ratio of data points less than mean - , to the total number of data points, (equation 5).

4. Ratio of data points greater than mean - to the total number of data points, (equation 5).

5. Lower limit, (equation 3, where the value of h is taken randomly from Table 5 as 0.014, since it will be optimised and will be obtained later).

6. Upper limit, (equation 4).

7. The new feature, using equation 6.

Using equation 6, with a value of (taken randomly from Table 5, since it will be optimised and will be obtained later), value for the first data point is obtained as:

9

Similarly, the other six values for are obtained, and the newly computed feature is added to the original dataset. At the testing time, the same process is repeated for to compute . However, this time, the previously computed values of during the training time will be used for transforming .

Table 5.

Optimised hyperparameter values for plant datasets.

Dataset	Model	Parameter	Value	Model	Parameter	Value
TomEBD (5-fold)	OKELM	C	2.414	ORBFNN		0.017
			2		k	250
	TMF-OKELM	C	5.321	TMF-ORBFNN		0.029
			8		k	246
		p	0.199		p	0.276
		h			h
	GMF-OKELM	C	29.471	GMF-ORBFNN		0.136
			2		k	120
		p	0.193		p	0.035
TomEBD (10-fold)	OKELM	C	0.794	ORBFNN		0.1
			2		k	295
	TMF-OKELM	C	16.72	TMF-ORBFNN		0.087
			1		k	292
		p	0.31		p	0.677
		h	0.014		h
	GMF-OKELM	C	205.345	GMF-ORBFNN		0.075
			1		k	293
		p	0.607		p	0.045
TPMD (5-fold)	OKELM	C	89.586	ORBFNN		0.09
			6		k	203
	TMF-OKELM	C	39.589	TMF-ORBFNN		0.083
			2		k	88
		p	0.448		p	0.248
		h			h
	GMF-OKELM	C	410.969	GMF-ORBFNN		0.159
			15		k	164
		p	0.265		p	0.052
TPMD (10-fold)	OKELM	C	0.702	ORBFNN		0.094
			1		k	135
	TMF-OKELM	C	289.324	TMF-ORBFNN		0.545
			491		k	104
		p	0.302		p	0.423
		h			h
	GMF-OKELM	C	167.622	GMF-ORBFNN		0.011
			338		k	173
		p	0.529		p	0.073

Figure 5 shows a diagrammatic representation of the application of the membership function TMF or GMF to each feature of the dataset to obtain new features. The enhanced dataset after feature extraction consists of features. The rationale behind this feature extraction process is that data points belonging to the same class will be mapped to real numbers that are much closer to each other compared to data points from different classes. Importantly, this feature extraction process is completely independent of the class variable, making it effective for real-time applications.

Fig. 5.

Membership function based feature extraction.

ML classifiers

ML aims to enable computers to make predictions over time, with or without using predefined knowledge about the data⁶⁶. ML techniques can be categorized into supervised learning, which involves predefined group labels (classification) or real-time values (regression); unsupervised learning, which has no predefined groupings; and reinforcement learning, which involves taking rewarding actions in specific situations. In this study, two supervised ML algorithms - KELM and RBFNN, are used to predict the class labels of two plant disease datasets and eight benchmark datasets. A brief explanation of these algorithms is provided below.

• KELM: This algorithm is designed using artificial neural networks with an input layer, a single hidden layer, followed by an output layer⁶⁷. The number of units in the input layer is decided by the number of features a data sample possesses. Consider the diagram in Fig. 6a. A data point belonging to the plant disease dataset has four features here - Leaf Wetness (LW), Soil Moisture (SM), Temperature (T), and Relative Humidity (RH). There are three hidden neurons (randomly chosen here), and the output represents a one-hot encoded value for the class labels - conducive and non-conducive, where l is the number of class labels. A single training example can be defined as for the diagrammatic representation of four features - LW, SM, T, and RH. Taking hidden neurons, class labels and features, let b be an matrix consisting of the weights assigned to the features on the input layer, and W be the matrix containing the weights for each output.

  

  Let represent the weights assigned to the features to calculate the output at the hidden neuron, and represent the weights assigned to the hidden neurons to calculate the output .

  

  Then the output at the hidden neuron i is given as , where is the bias term added at hidden neuron i. Please note that here, the dot represents the matrix multiplication operator. Let F be a matrix where each row corresponds to the output of all hidden neurons for a specific training example. Then, for m training examples ,

  

  The target output matrix Y is then given as:

  10

  Please note that F is not a square matrix and hence its inverse cannot be computed directly. When a matrix is not square or when the system of equations does not have a unique solution, the pseudo-inverse is used. Using the pseudo-inverse of F, the optimal weight matrix W can be computed as

  11

  where C is the regularization parameter, and is the transpose of F. Therefore, the ELM Eq. (10) for a training example can be written as

  12

  where .
  However, ELM is prone to overfitting and may get stuck in local minima. To prevent this, a kernel matrix can be introduced, resulting in KELM, and the above equation can be modified as

  13

  A kernel matrix represents the pairwise similarity between all the elements or data points. Various types of kernels such as linear, poly, radial basis function (RBF) are available for use⁶⁸. For this study, RBF kernel has been used for computing the closeness of two data points, and , as

  14

  Here, represents the RBF kernel parameter. Generally, is taken as the variance value of the data. However, it can be fine-tuned for optimized results.
• RBFNN: This algorithm also comprises a three-layered neural network - an input layer, a hidden layer, and an output layer⁶⁹. However, the number of neurons in the hidden layer is determined by some clustering algorithm applied to the data on the firsthand. The clustering algorithm is used for clustering the data, which returns the generated cluster centers for k clusters. Hence, k neurons are present in the hidden layer. However, since k-means produces sharp clusters, this may lead to a few data points not belonging to any of the defined clusters. To overcome this, RBF is used as the activation function for each hidden neuron, resulting in a smooth transitioning of the clusters. RBF is used at each hidden neuron to compute the distance between a data point x and the cluster center represented by the neuron. Therefore, the equation for every hidden neuron i can be given as:

  15

  where is the euclidean distance between the data point x with n features and centroid , given as

  16

  After applying the RBFs to all data points, a matrix M is obtained, where each row corresponds to a training data point, and each column corresponds to a hidden neuron (or cluster center). The learned weights matrix W that connects the hidden layer to the output layer of the network is then obtained using a least squares regression approach. Using the Moore-Penrose pseudoinverse solution⁷⁰, which comes from solving the normal equations of linear regression, W can be obtained as:

  17

  where y is the one-hot encoded class label matrix. For the prediction task, the RBFs of the test samples are computed using the same k cluster centers obtained during training, resulting in a matrix T. The label prediction for the test samples is then accomplished using the equation:

  18

  A diagrammatic representation of the network is shown in Fig. 6b. A data point comprises two features - LW and SM, and there are three hidden neurons representing cluster centers. Each computes on the data point x, and the neuron outputs, along with the train labels, are used for weights optimization. The output layer consists of two units representing the two class labels - conducive and non-conducive.

Fig. 6.

ML algorithms.

Hyperparameter optimization

Hyperparameters are the model parameters in ML that control the learning process and are not inferred while training⁷¹. For example, the number of hidden neurons in a neural network is pre-specified and not decided during model training. Thus, the number of hidden neurons can be treated as the hyperparameter of the neural network model. Choosing the correct value of the hyperparameters is a crucial task and should be done wisely. In the current study, the feature extraction and classification process has been optimized by fine-tuning the parameters used in membership functions and the hyperparameters utilized by ML classifiers - KELM and RBFNN. The optimized algorithms are called OKELM and ORBFNN. The Optuna framework available in python⁷² has been utilized for the optimization of parameters, which uses a Bayesian optimization algorithm for the purpose⁷³. It is a scalable architecture that uses parallel and distributed computing for the optimization process. Bayesian optimization works through the following steps:

• Initial sampling: Randomly select an initial set of hyperparameter configurations and evaluate the objective function on these points to create an initial dataset.

• Build a substitute model: Construct a probabilistic model of the objective function, which provides a probability distribution over possible functions that fit the observed data.

• Acquisition function: Use an acquisition function to determine the next hyperparameter configuration to evaluate. This function balances exploration (trying new areas) and exploitation (refining known good areas).

• Update the substitute model: Evaluate the objective function at the new data point suggested by the acquisition function and update the substitute model with this new information.

• Iterate: Repeat the process (steps 3 and 4) until a stopping criterion is met, such as a predefined number of iterations or convergence of the objective function.

The optuna framework requires an objective to be maximized or minimized, along with the range of parameters that are to be optimized. The performance measure - Accuracy has been considered as the objective to be maximized by the classifiers. Accuracy represents the ratio of the correct number of predictions to the total number of predictions⁷⁴. The hyperparameters that have been fine-tuned, along with their possible value ranges, are shown in Table 4. The table also indicates the distribution type for each parameter. Notably, the parameter of ORBFNN is related to the parameter of OKELM by the relationship . Additionally, the parameter k of ORBFNN, which represents the number of clusters used by k-Means and, consequently, the number of neurons in the hidden layer, is constrained by the number of training samples in the dataset. Since there cannot be more non-fuzzy clusters than there are data samples, the range for k is set to accommodate all five datasets. The range for the parameter h for OKELM has been selected based on the study⁶⁵.

Table 4.

Hyperparameter range.

	Parameter	Type	Range
Feature extraction
Membership Function
TMF	p		[0.01, 1]
	h
GMF	p		[0.01, 1]
Classification
Classifier
OKELM	C		[0.5, 500]
		int	[1, 500]
ORBFNN			[0.01, 1]
	k	int	[1, 300]

Preliminary experiments

To inform the decision-making process for selecting resampling methods and ML classifiers in this study, preliminary experiments were conducted using the real-time collected dataset TomEBD. The procedure is as follows:

• Balancing the dataset: The dataset was balanced using three resampling techniques: SMOTE, KM-SMOTE, and Support Vector Machine SMOTE (SVM-SMOTE)⁷⁵, resulting in three balanced datasets alongside the original imbalanced dataset.

• Classification: Classification was performed on the imbalanced and the three balanced datasets using six traditional ML classifiers: kNN⁷⁶, SVM⁷⁷, RF⁷⁸, Artificial Neural Network (ANN)⁷⁹, KELM, and RBFNN. This resulted in a total of 24 models.

• Feature extraction: No feature extraction mechanism was utilized in these experiments.

• Hyperparameter tuning: The hyperparameters for all six classifiers were tuned using the Optuna framework over 100 iterations.

The results, summarized in Fig. 7, indicate that models balanced with KM-SMOTE consistently outperformed those balanced with other techniques or left imbalanced. Among these, the KELM and RBFNN models on the KM-SMOTE balanced dataset achieved mean accuracy values of 85.82% and 85.96%, respectively, outperforming all other models. Consequently, KM-SMOTE was chosen for resampling in the current study, followed by feature extraction (using TMF or GMF) and classification using the KELM and RBFNN classifiers.

Fig. 7.

Preliminary experiments results.

Research framework

In this study, six models were tested for plant disease classification: OKELM, ORBFNN, TMF-OKELM, GMF-OKELM, TMF-ORBFNN, and GMF-ORBFNN, where OKELM and ORBFNN are two baseline models without feature extraction (NoFE). The methodology is illustrated in Fig. 8.

Fig. 8.

Research methodology.

The process begins with data collection and handling missing values. The imbalanced datasets are resampled using the KM-SMOTE technique to obtain balanced datasets. These datasets are then divided into training and testing sets using the Stratified k-fold cross-validation technique⁸⁰, ensuring proportional representation of classes. In k-fold cross-validation, the data is split into k subsets, each of which serves as test data once, while the remaining subsets are used for training, resulting in k validation scores or accuracy values. This study explores 5-fold and 10-fold cross-validation techniques.

The training data is enhanced through feature extraction techniques - TMF or GMF, whose parameters h and p are optimized using Optuna. The enhanced dataset is then used for training the classifiers - OKELM and ORBFNN - also optimized with Optuna. Optuna provides the optimized values of all the parameters, which are then tested for performance on the test data. The test data is first enhanced using the feature extraction techniques, utilizing the statistical values and optimized parameters and computed during training. This is followed by the classification of test data using OKELM and ORBFNN, with optimized parameters k and for ORBFNN and and C for OKELM. Performance is evaluated by calculating the mean accuracy across all k-folds, and the four models are compared to identify the best one. Additionally, classifiers were tested without any feature extraction techniques to verify the impact of feature extraction, resulting in two additional baseline models for comparison. Finally, all six models undergo the Friedman and Bonferroni Dunn tests for verifying whether there is a significant difference in their performance, and the best model is selected.

The algorithms for TMF and GMF are shown in Algorithms 1 and 2. Here, X represents the original data, p and h represent the optimized parameters, and training is a boolean variable which indicates whether X is training data or test data. The proposed approach - MFFE (using TMF or GMF) followed by ORBFNN (similarly for OKELM) is depicted in Algorithm 3. Finally, the parameter tuning for accuracy optimization of the model TMF-ORBFNN is shown in Algorithm 4. Here, X represents the independent variables, and Y represents the class label or dependent variable. Note that TMF or GMF are not used before the classification. Instead, they are used inside the classifier during training and testing. The classifiers are provided with the original data, and feature extraction is utilized inside the fit and predict methods of the classifiers. A similar approach can be used for the other three models as well.

The proposed methodology aligns with current trends in computational intelligence that focus on hybrid learning and intelligent optimization to improve the generalization and adaptability of the models. Modern methods focus not only on improving accuracy but also on achieving faster, more efficient, and reliable performance, especially in IoT and sensor-based applications. In this context, the proposed framework integrates membership function-based feature extraction with neural network classification, optimized through Optuna-based Bayesian optimization for efficient hyperparameter tuning. This automated optimization process is faster and more stable than traditional metaheuristic algorithms. Overall, the proposed approach offers a lightweight and adaptable solution that provides a good balance between accuracy and generalization for real-world sensor-based classification tasks.

Algorithm 1.

TMF.

Algorithm 2.

GMF.

To expedite computations, the implementation utilized the vectorization method. Python’s Scikit-learn library⁸¹ was employed for the implementation, and the results were visualized using the matplotlib library in Python. Hyperparameters were optimized over 500 iterations to maximize mean accuracy. The significance of hyperparameters in accuracy optimization was demonstrated through graphs generated using the Optuna framework. The implementations were carried out on macOS Big Sur Version 11.3.1 with 8GB RAM.

Algorithm 3.

MFFE–ORBFNN framework.

Algorithm 4.

Parameter optimization using Optuna.

Results and discussion

This section provides the analysis results of the study. It is divided into seven subsections. Subsections "Performance on plant datasets" and "Performance on benchmarking datasets" show the performance of the six models on the two plant datasets and the eight benchmarking datasets. Subsection "Friedman and post-hoc Bonferroni-Dunn test" illustrates the performance difference verification of the models using Friedman and post-hoc Bonferroni Dunn test. Further, the importance of the hyperparameters in the accuracy optimization of the models is presented in subsection "Hyperparameter importance", followed by time complexity analysis in subsection "Time complexity analysis". Subsection "Comparison with the existing studies" contrasts the proposed technique with the state-of-the-art. Finally, subsection "Discussion" provides a discussion.

Performance on plant datasets

All six models - OKELM, ORBFNN, TMF-OKELM, GMF-OKELM, TMF-ORBFNN, and GMF-ORBFNN - were assessed for performance on two plant datasets: TomEBD and TPMD. The mean accuracy results are depicted in Fig. 9a and b, considering both 5-fold and 10-fold cross-validation. Several observations can be drawn:

• OKELM (10-fold) outperformed OKELM (5-fold) for both datasets. Similarly, ORBFNN (10-fold) performed better than ORBFNN (5-fold). However, models with TMF feature extraction generally performed better with 5-fold cross-validation, except TMF-OKELM (10-fold), which performed better on the TomEBD dataset.

• Models incorporating feature extraction (TMF or GMF) generally outperformed the baseline models for both datasets, except for one instance where GMF-OKELM (5-fold) underperformed compared to OKELM (5-fold) for the TomEBD dataset. This highlights the significant impact of feature extraction on plant disease classification.

• TMF-OKELM and TMF-ORBFNN consistently outperformed GMF-OKELM and GMF-ORBFNN, respectively, for both datasets. However, there was one exception where GMF-OKELM (10-fold) performed better than TMF-OKELM (10-fold) for the TPMD dataset. Nonetheless, TMF is generally preferred over GMF for feature extraction in plant disease datasets due to its superior performance in most cases.

• Notably, TMF-ORBFNN (5-fold) emerged as the top-performing model among all, achieving mean accuracies of 87.02% for TomEBD and 98.85% for TPMD. Hence, the combination of TMF for feature extraction followed by ORBFNN for classification proves to be highly efficient for plant disease datasets.

Fig. 9.

Mean accuracy on TomEBD and TPMD.

The optimized values of the hyperparameters for both datasets are also shown in Table 5. The following observations can be made:

• The regularization parameter C tends to be small when no features are extracted, while it is quite large when feature extraction is followed by classification. This suggests that the extracted features are causing overfitting due to the small dataset size, necessitating extensive regularization.

• The shape parameter of RBF - , in ORBFNN models, has small values resulting in wider-shaped kernels. This indicates that the clusters formed are widely spread.

• The number of clusters k, used by the k-means algorithm in ORBFNN models, has larger values, indicating that many clusters have been formed, thus reducing the within-cluster variability. Consequently, the data points are much closer to their respective cluster centroids.

• The modification parameter p of TMF has smaller values in the case of OKELM models (less than 0.5), indicating a gradual increase in the mapped value as the original feature value increases. In the case of ORBFNN models, p in TMF has slightly larger values indicating a sharper transformation.

• In the case of GMF, p values are quite high with OKELM and much lower (less than 0.1) in the case of ORBFNN. These lower values of p imply that the function is mapping a large subset of a feature to near 1 values, which is not much effective for feature enhancement. Therefore, TMF can be used for feature enhancement in small plant-based datasets.

Figure 10 shows the optimization history plots (obtained during the optimization process using Optuna) for mean accuracy optimization over 500 iterations for the model TMF-ORBFNN (5-folds) for both datasets. The blue dots represent the objective value - mean accuracy, and the red line represents the optimal value. It can be observed that the model reaches the optimum objective value at an earlier stage for both datasets - iteration 159 for the TomEBD dataset and iteration 119 for the TPMD dataset.

Fig. 10.

TMF-ORBFNN (5-fold) optimization history.

Performance on benchmarking datasets

To test the validity of the proposed approach, eight diverse non-plant-based benchmark datasets - BCO, GI, PID, GGC, HFC, DTC, RCO, and SAR were used for performance evaluation. The accuracy values obtained by the TMF-ORBFNN (5-fold) model on all eight benchmarking datasets are shown in Fig. 11. It can be observed that the model achieves high accuracy values for all eight datasets.

Fig. 11.

TMF-ORBFNN (5-fold) Accuracy values on benchmark datasets.

The optimized values of the hyperparameters for the model TMF-ORBFNN (5-fold), for all eight datasets, are shown in Table 6. The following observations can be made from the table:

Table 6.

Optimised TMF-ORBFNN hyperparameter values for benchmark datasets.

Dataset	Parameters
		k	p	h
BCO	0.27	143	0.84	0.14
GI	0.132	246	0.694	0.91
PID	0.15	243	0.152	0.34
GGC	0.075	34	0.92	0.71
HFC	0.07	51	0.64	0.68
DTC	0.029	233	0.836	0.94
RCO	0.289	210	0.05	0.8
SAR	0.03	290	0.97	0.96

• The shape parameter of RBF, in ORBFNN models, has very small values for all the datasets, resulting in wider-shaped kernels and therefore widely spread clusters.

• The number of clusters k, used by the k-means algorithm in ORBFNN models, has large values for the datasets - BCO, GI, PID, DTC, RCO, and SAR. A larger number of clusters reduces the intra-cluster variance, leading to the data points being much closer to the cluster centroids. However, in the datasets - GGC and HFC, k values are quite small, indicating that the data has a lower level of variability, fewer unique patterns, or more easily identifiable groupings.

• The parameter p, which decides the shape of the TMF, has a lower value for the PID and RCO datasets, and an intermediate value for BCO, GI, HFC, and DTC, indicating a gradual increase in the function mapping - more of a dome-like structure. For other datasets - GGC and SAR, the value of p is closer to 1, indicating a nearly linear transformation using the original triangular membership function.

Additionally, to compare the TMF-ORBFNN (5-fold) model with its counterparts, three representative datasets - BCO (with imputed missing values), PID (a medical dataset) and GI (a multi-class dataset) have been selected, and the performance of all models on these three datasets has been analysed. The results are shown in Fig. 12. The following observations are made from the figure.

• GMF-based models underperformed in most cases, with baseline models performing better or equivalent to them. This is due to the inefficiency of the features extracted through GMF, attributed to the lower values of the modifying parameter p. Therefore, GMF is ineffective for feature extraction in non-plant-based datasets.

• OKELM-based models generally performed poorly compared to ORBFNN-based models. Additionally, feature extraction did not significantly improve OKELM models, with OKELM sometimes outperforming TMF-OKELM or GMF-OKELM. Thus, feature extraction followed by OKELM classification is inefficient for benchmark datasets.

• ORBFNN consistently underperformed compared to TMF-ORBFNN across all datasets, by 0.33% on BCO, 1.97% on GI, and 1.4% on PID. Hence, feature extraction followed by ORBFNN classification is effective for non-plant-based datasets.

• The models TMF-ORBFNN and GMF-ORBFNN performed much better than the models TMF-OKELM and GMF-OKELM for all three datasets, indicating that ORBFNN is a more effective classifier than OKELM.

• The model TMF-ORBFNN (5-fold) performed best among all models across all three datasets, achieving mean accuracies of 98.36% for BCO, 91.97% for GI, and 84.05% for PID. Therefore, feature extraction using the TMF approach followed by ORBFNN classification proves highly effective for these diverse datasets.

Figure 13 shows the optimization history for the three representative datasets using the TMF-ORBFNN (5-fold) model. It can be noted that the optimized mean accuracy values for the three datasets have been achieved multiple times (as indicated by multiple blue dots on the optimized red line level). Therefore, several combinations of the hyperparameter values may lead to the optimal solution. However, the optimized hyperparameter values are shown in Table 6 only for the first iteration that leads to it. For all the datasets, the optimized mean accuracy value has been achieved in early iterations, at iteration 168 for BCO, 240 for GI and 156 for PID.

Fig. 12.

Performance on three representative benchmark datasets.

Fig. 13.

TMF-ORBFNN (5-fold) Optimization History for Benchmark Datasets.

Friedman and post-hoc Bonferroni–Dunn test

The Friedman Test⁸² is a non-parametric statistical test that is used to test whether the performance of M models on D datasets is significantly different from each other or not. The null hypothesis states that there is no difference in the performance of the classifiers. This section analyses the performance difference of the six models on all the 10 datasets. The test involves the following steps:

1. For each dataset, the models are ranked based on the classification accuracy. The best-performing classifier gets the rank of 1, the second-best gets 2, and so on. The average rank , for each classifier over all the datasets is computed. Table 7 shows the ranking of all the classifiers on the 10 datasets, followed by the average rank obtained by them.

2. The Friedman test statistic, is calculated as:

   19

   For and , is obtained.
3. Using , a better statistic is obtained⁸³ as

   20

4. Taking level of significance , the critical value of degrees of freedom is obtained. . The corresponding p-value obtained is 0.0036. We reject the null hypothesis if (or ), which is true. Hence, the null hypothesis can be rejected, and the alternative hypothesis, which states that there is a significant difference in the performance of the classifiers, can be accepted.

Table 7.

Ranks achieved by the six models on the en datasets.

Dataset	OKELM	ORBFNN	TMF-OKELM	TMF-ORBFNN	GMF-OKELM	GMF-ORBFNN
TomEBD	3	6	2	1	5	4
TPMD	4	5	2	1	6	3
BCO	6	2.5	4	1	5	2.5
GI	5	3	2	1	6	4
PID	6	4	3	1	5	2
GGC	5	3	6	1	2	4
HFC	5	3	6	2	4	1
DTC	2	6	4	5	1	3
RCO	3	5	6	1	2	4
SAR	6	3	5	1	4	2
Average Rank	4.5	4.05	4	1.5	4	2.95
Difference	3	2.55	2.5	0	2.5	1.45

Significant values are in bold.

To analyse the performance difference of the other classifiers with the control classifier - TMF-ORBFNN, a post-hoc Bonferroni-Dunn test⁸² has been conducted, which states whether the control classifier is significantly different from the others. If the average ranks of the classifiers are different from the average rank of the control classifier by at least a critical difference CD, then we say that the control classifier performs significantly differently from the others. The difference between the ranks is also shown in Table 7. CD is computed as

21

where the critical value of is pre-defined for specific M and D values⁸².

Taking for , . The critical differences diagram is shown in Fig. 14. The models beyond the orange line denote a significant difference from the control classifier - TMF-ORBFNN. By looking at the figure and the differences shown in Table 7 and considering the CD value, the following observations can be made:

• The control classifier, TMF-ORBFNN, performs significantly differently compared to the OKELM, ORBFNN, TMF-OKELM, and GMF-OKELM classifiers. However, it does not show a significant difference when compared to GMF-ORBFNN. This is likely because they share a similar classification method (ORBFNN).

• The baseline models, OKELM and ORBFNN, do not have a significant difference between them, as their average ranks are very close. However, when feature extraction techniques - TMF and GMF are introduced, a significant difference emerges between the two classifiers, TMF-ORBFNN and GMF-OKELM. This highlights the importance of feature extraction methods in the final classification process.

Fig. 14.

Critical difference diagram.

Hyperparameter importance

The impact of hyperparameters on accuracy optimization is analyzed for the models ORBFNN (5-fold) and TMF-ORBFNN (5-fold). This analysis focuses on understanding their significance before and after feature extraction, considering both plant-based and the three representative non-plant-based datasets. The importance graphs have been generated using the optuna library during the optimization process and are shown in Fig. 15. The following observations have been made:

• The parameter has the most significant impact on accuracy optimization, both with and without feature extraction, for both plant-based datasets. In the ORBFNN model (Fig. 15a and c), shows an importance of 100% and 96%, respectively, while the number of clusters k has a minimal impact. In the TMF-ORBFNN model, holds the highest importance at 92% for TomEBD. However, with feature extraction, k gains more significance, with an impact of 2% for TomEBD and 64% (the highest) for TPMD.

• The importance of feature extraction parameters p and h is shown in Fig. 15b and d. The parameter p significantly impacts accuracy optimization by 6% for TomEBD, but only 1% for TPMD. The parameter h plays a minimal role in optimization, with an importance of for both plant-based datasets.

• A similar pattern is observed for the non-plant-based datasets PID and BCO. The parameter is most significant for ORBFNN, with an importance of 79% for PID and 60% for BCO. With feature extraction, k becomes most important, with an 86% impact for PID (Fig. 15i and j) and 71% for BCO (Fig. 15e and f).

• The parameters p and h have a small impact on PID and BCO datasets.

• For the non-plant-based dataset - GI, the parameter k is most important for optimization in both models. For ORBFNN, k has a 97% significance, while has 3% (Fig. 15g). With feature extraction, the significance of k reduces to 96%, while increases to 4% (Fig. 15h). The parameters p and h again have very little impact.

It can be observed from above that although the parameters p and h have little impact on the overall accuracy maximization, the feature extraction process has a great impact on the classifier parameters beta and k. This indicates that the extracted features are contributing significantly to the accuracy maximization process.

Fig. 15.

Hyperparameter importance for ORBFNN and TMF-ORBFNN.

Time complexity analysis

The time complexity of the proposed model TMF-ORBFNN, can be computed in three parts: .

1. The time complexity of KM-SMOTE can further be divided into two parts: K-Means , where is the number of samples in the minority class, c is the number of clusters, i is the total iterations, and f is the number of features, and SMOTE , where is the number of samples in each cluster, and is the number of nearest neighbors to consider. Therefore, the overall time complexity becomes , where and can reach in the worst case.

2. The time complexity of TMF can be clearly computed as O(f.n) since it requires a single pass over the entire dataset.

3. The time complexity of RBFNN can be computed in three steps - K-Means clustering (O(n.k.i.f)), where k is the number of RBF clusters, distance calculation between each data point and RBF center (O(n.f.k)), and weight computation using linear least squares . Hence, the total time complexity becomes . Further, optimizing RBFNN over j iterations lead to the final complexity of

Therefore, the total time complexity of TMF-ORBFNN on a balanced dataset using KM-SMOTE is:

22

23

It can be observed that the time complexity is highly influenced by the total data samples n, optimization iterations j, and RBF clusters k.

Comparison with the existing studies

This subsection compares the results of the proposed approach on the plant datasets TomEBD and TPMD, as well as the eight benchmarking datasets against existing state-of-the-art methods. For the TomEBD dataset, the study⁵⁰ focused on disease classification and feature extraction. However, their method relied on the availability of class labels during feature extraction, making it impractical for real-time disease prediction. Table 8 presents a comparison between the current study and existing state-of-the-art methods across all 10 datasets, using accuracy as the metric. Please note that there are only a few studies on the DTC dataset since it has been recently introduced.

Table 8.

Comparison with state-of-the-art.

Dataset	Model	Year	Accuracy
TomEBD	KELM-KM15	2024	85.82%
	II-SN-OXGB14	2024	84%
	FFFT+OKELM50	2022	79.15%
	ROS+FFFT+OKELM50	2022	78.77%
	SMOTE+FFFT+OKELM50	2022	77.06%
	IMPST+FFFT+OKELM50	2022	80.32%
	Proposed TMF-ORBFNN	-	87.02%
TPMD	SVM-GA-RF84	2022	95.42%
	GRU85	2021	93.88%
	RF29	2021	93.24%
	SVM-SPM86	2021	98.65%
	MGSVM87	2021	94.74%
	SMOTE-BaggedCart88	2021	98.65%
	IMPST-ELM23	2020	89.91%
	SVM-LR89	2020	92.37%
	Proposed TMF-ORBFNN	-	98.85%
BCO	II-SN-OXGB14	2024	97.45%
	LightGBM90	2022	95.3%
	SVC-L191	2022	97%
	K-Means92	2021	95.95%
	MIEA93	2020	85%
	AEEMCD94	2019	95.24%
	GA-FS-Rotation Forest95	2017	96.78%
	Proposed TMF-ORBFNN	-	98.36%
GI	CRM-PM with NSGAII96	2022	85.71%
	SMOTE-GR-kNN97	2021	77.67%
	WWO-DCM98	2021	64.73%
	FWkNN using Distance Weight99	2020	67.05%
	ABCoDT100	2019	70.37%
	NS-kNN101	2017	60.81%
	OADT102	2015	76.67%
	Proposed TMF-ORBFNN	-	91.97%
PID	Ensemble approach KNN103	2022	76.69%
	RF104	2022	79.57%
	HGA-Adaboost105	2021	78.1%
	Voting Classifier106	2021	79.08%
	XGB107	2021	78.91%
	BinJOA-SM108	2020	78.04%
	Optimized R-GRNN Oracle109	2019	81.14%
	GA Naïve Bayes110	2017	78.69%
	GA_MLP NN111	2016	79.13%
	Proposed TMF-ORBFNN	-	84.05%
GGC	XGBoost112	2024	88%
	mRMR-LASSO-SVM113	2023	87.007%
	Voting-based feature selection114	2022	87.6%
	Proposed TMF-ORBFNN	-	89.24%
HFC	Stochastic Generalized Linear Regression115	2024	85.6%
	Ensemble approach KNN103	2022	68.79%
	WKNN116	2021	73.2%
	Stratified LR with three features117	2020	83.8%
	Proposed TMF-ORBFNN	-	88.91%
DTC	Multi-layer Perceptron118	2024	85.7%
	Proposed TMF-ORBFNN	-	96.01%
RCO	Support Vector Machine119	2024	93.53%
	Stochastic Generalized Linear Regression115	2024	93.8%
	Deep Neural Network120	2021	93.04%
	KNN116	2021	92.6%
	Logistic Regression121	2019	93.02%
	Proposed TMF-ORBFNN	-	94.02%
SAR	RF122	2021	95.28%
	kNN-Mel-Frequency Cepstral Coefficients123	2021	96.05%
	Proposed TMF-ORBFNN	-	97.38%

Significant values are in bold.

The results demonstrate that for all datasets, TMF-ORBFNN outperformed the existing state-of-the-art techniques. The proposed approach achieved an improvement ranging from 1.2% to 9.96% for TomEBD, 0.2% to 8.94% for TPMD, 0.51% to 13.36% for BCO, 6.26% to 31.16% for GI, 2.91% to 7.36% for PID, 1.24% to 2.23% for GGC, 3.31% to 20.12% for HFC, 10.31% for DTC, and 1.33% to 2.1% for SAR. Thus, TMF-ORBFNN proves to be highly effective for feature extraction and classification in numeric datasets with fewer features.

Table 9 further shows the comparison of the proposed TMF-ORBFNN with the study⁵⁰, as well as the baseline ORBFNN without any feature extraction on the two plant datasets.

Table 9.

Ablation: Comparison of proposed class-independent MFFE, Bhatia & Chug (2022) class-dependent FFFT, and no feature extraction.

Dataset	Method	Accuracy (%)	Feature count	Runtime (s)	Notes
TomEBD	No FE	83.83%	5	1 min 15 sec	Baseline (ORBFNN on raw features)
	Bhatia & Chug (2022)	80.32%	15	Not Mentioned	Class-dependent FFFT
	Proposed MFFE (class-independent)	87.02%	10	1 min 46 sec	Proposed TMF-ORBFNN
TPMD	No FE	97.24%	5	48 sec	Baseline (ORBFNN on raw features)
	Bhatia & Chug (2023)	98.01%	15	Not Mentioned	Class-dependent FFFT
	Proposed MFFE (class-independent)	98.95%	10	1 min 17 sec	Proposed TMF-ORBFNN

Significant values are in bold.

Discussion

The results of the current study underscore the effectiveness of the proposed TMF-ORBFNN model for plant disease classification and its application to other benchmarking datasets. This model demonstrated superior performance across all datasets evaluated, highlighting several key factors contributing to its success. The TMF-ORBFNN model achieved the highest mean accuracy for all datasets tested. This performance can be attributed to

• Balanced Data Using KM-SMOTE: The KM-SMOTE technique was instrumental in generating synthetic samples in denser regions, thus avoiding the creation of noisy samples. This resulted in a more representative and balanced dataset, which is crucial for training robust models.

• Feature Enhancement with TMF: The TMF feature extraction technique effectively transformed the original input data into more insightful features. This facilitated better learning and generalization by the classifier, leading to improved model performance.

• Robustness of ORBFNN: The ORBFNN algorithm proved to be robust and efficient, with a fast implementation and high tolerance towards input noise, which is beneficial when dealing with real-world data.

The further analysis of hyperparameter importance revealed that feature extraction using TMF plays a significant role in accuracy optimization. This insight emphasizes the necessity of careful tuning of p and h to achieve optimal model performance. The dominance of and k in the optimization process for ORBFNN models further highlights the importance of these parameters in defining the model’s capability to classify data effectively.

Although advanced multi-layer and hybrid models like physics-informed neural networks (PINNs) can combine domain knowledge with ML¹²⁴, they often require high computational power and take longer to train because they optimize both data-based and physics-based losses at the same time. In addition, their performance depends greatly on having accurate physical equations and clear boundary conditions, which makes them less suitable for complex or noisy real-world data, such as sensor-based agricultural datasets.

Additionally, recent bio-inspired metaheuristic algorithms, such as GA, PSO, and ALO, have been widely used for feature selection and hyperparameter tuning^{14,24,42,43,50,125}. While these approaches have shown strong optimization capabilities, they often involve high iteration counts and increased computational complexity, leading to long execution times. In contrast, the Optuna-based optimization strategy provides an efficient Bayesian framework for parameter tuning with fewer evaluations, offering a better balance between accuracy and efficiency. We tested the proposed TMF-ORBFNN model using different optimization methods, including GA, PSO, and ALO, and the accuracies obtained on the plant datasets over 500 iterations are shown in Table 10. The results show that the model performed better when optimized with the Optuna framework compared to the other metaheuristic algorithms.

Table 10.

TMF-ORBFNN accuracy on plant datasets using meta-heuristic optimizers.

Optimizer	TomEBD	TPMD
ALO	84.83%	98.6%
PSO	83.83%	98.16%
GA	82.44%	98.39%

The proposed TMF-ORBFNN model also outperformed existing state-of-the-art techniques across all datasets with substantial improvements. The independence of the feature extraction process from class labels makes it particularly suitable for scenarios where class labels are not readily available. Moreover, the proposed framework can be effectively integrated into edge and mobile computing devices for real-time field use. Since low computational power and less memory are required for the feature extraction and classification processes, they can be implemented on lightweight devices such as Raspberry Pi, Arduino-based sensor nodes or Android-based mobile applications. In such a system, local sensor data (e.g., temperature, humidity, soil moisture) can be processed directly on the device to predict the occurrence of the disease without relying on cloud connectivity. This on-device prediction ability enables timely alerts to farmers even in places with poor or no internet connection, making the proposed method more useful for precision agriculture and better crop management.

Conclusion and future scope

The current study emphasizes feature extraction prior to classification in small-sized sensor-based plant datasets using the MFFE mechanism. MFFE operates independently of class variables to improve disease detection in sensor-based plant disease datasets. Two membership functions - TMF and GMF have been reformed to extract richer and unbiased features by computing all transformation parameters solely on the training data. The enhanced datasets were then classified using OKELM and ORBFNN, resulting in four distinct models along with two baseline models. The models’ parameters were optimized using the Optuna framework based on Bayesian Optimization for enhanced performance.

The findings highlight that the proposed TMF-ORBFNN model with 5-fold cross-validation exhibited outstanding performance on both the plant-based as well as non-plant-based benchmarking datasets, demonstrating robustness and generalization capabilities. Further, the Friedman and Bonferroni–Dunn tests show that the TMF–ORBFNN combination performed significantly differently than the alternative models. The time complexity analysis confirmed that the proposed method offers an effective trade-off between computational cost and accuracy improvement. Therefore, removing class-variable dependency and reducing statistical bias while transforming features significantly enhances model generalizability for classification tasks in small numeric datasets. It can be concluded that the proposed model, TMF-ORBFNN, can be used for feature extraction followed by classification in small-sized numeric datasets to achieve good results.

However, the proposed approach has some limitations. The feature extraction and parameter optimization processes prior to classification might be slow compared to direct classification. Although vectorized implementations have significantly improved computational speed, handling a large number of data points might require additional computational resources. Moreover, collecting sensor-based data is often costly and may introduce noise in the data due to variations in the environment or sensor calibration errors. Additionally, the current work is validated primarily on tomato crop datasets; further testing across different crops and environmental conditions is needed to evaluate the scalability and robustness of the models. In the future, focus can be made on developing low-cost sensors and extending the proposed framework to multi-crop disease prediction systems. Faster implementations of feature extraction techniques with noise filtering mechanisms can be proposed. Additionally, combining feature selection techniques and other classifiers could yield even better performance. An online real-time application can also be developed that will continuously monitor the weather parameters and alarm the agricultural workers in case the conditions are unfavourable.

Author contributions

All authors contributed to the study design and data collection. Structure of the paper was conceptualized by Prof. Amit Prakash Singh. The dataset and techniques were selected by Dr. Anuradha Chug after thorough investigations. The coding part and first draft of the manuscript was written by Dr. Ayushi Gupta and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Funding

This research is endorsed by the Department of Science and Technology (DST) under a project with reference number “DST/ Reference.No.T-319/2018-19”. We thank them for their support.

Data availability

The TomEBD dataset belongs to multiple agencies of the Govt. of India and needs approval before making it public. Therefore, with the approval of appropriate agency, data will be made public at a later stage. The benchmarking datasets are available at the following publicly-accessible sites: BCO - https://archive.ics.uci.edu/dataset/15/breast+cancer+wisconsin+original. GI - https://archive.ics.uci.edu/ml/datasets/glass+identification. PID - https://www.kaggle.com/uciml/pima-indians-diabetes-database. GGC - https://archive.ics.uci.edu/dataset/759/glioma+grading+clinical+and+mutation+features+dataset. HFC - https://archive.ics.uci.edu/dataset/519/heart+failure+clinical+records. DTC - https://archive.ics.uci.edu/dataset/915/differentiated+thyroid+cancer+recurrence. RCO - https://archive.ics.uci.edu/dataset/545/rice+cammeo+and+osmancik. SAR - https://archive.ics.uci.edu/dataset/518/speaker+accent+recognition. The rest of the data that support the findings of this study are available from the corresponding author upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.