Improving Anomaly Detection Accuracy Using Fuzzy Cuckoo-Inspired Clustering and Optimization Techniques

Parmeshwar Dayal Lodhi; Ram Kumar Nagarch; Sujata Nema

doi:doi:10.11648/j.mlr.20261102.11

Research Article |

| Peer-Reviewed

Improving Anomaly Detection Accuracy Using Fuzzy Cuckoo-Inspired Clustering and Optimization Techniques

Parmeshwar Dayal Lodhi

, Ram Kumar Nagarch^*

, Sujata Nema

Published in Machine Learning Research (Volume 11, Issue 2)

Received: 16 February 2026 Accepted: 1 June 2026 Published: 22 July 2026

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Abstract

Anomaly detection is a critical task for identifying unusual patterns that may indicate security breaches, fraudulent transactions, or system failures in various application domains. Conventional anomaly detection techniques often experience high false positive rates and limited adaptability when handling complex, uncertain, or evolving datasets. To overcome these limitations, this study proposes a novel Fuzzy Cuckoo-Based Clustering Technique (F-CBCT) that integrates fuzzy logic with cuckoo search-based clustering and optimization. The proposed framework employs a decision tree classifier enhanced with fuzzy membership functions, enabling effective management of uncertainty during classification. Model parameters are optimized using a hybrid strategy based on Mean Square Error (MSE) and the Silhouette Index, improving clustering quality and classification accuracy. Experimental evaluations conducted on benchmark datasets demonstrate the effectiveness of the proposed approach, achieving a 96.86% detection rate, 97.77% accuracy, a 1.297% false positive rate, and an F-measure of 98.30%. Comparative analysis with existing state-of-the-art anomaly detection methods confirms that F-CBCT consistently outperforms conventional approaches in terms of detection capability, robustness, and reliability. The proposed technique effectively reduces false alarms while maintaining high detection performance, making it a promising solution for real-world anomaly detection applications across diverse and dynamic environments.

Published in	Machine Learning Research (Volume 11, Issue 2)
DOI	10.11648/j.mlr.20261102.11
Page(s)	63-75
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2026. Published by Science Publishing Group

Keywords

Fuzzy Clustering, Cuckoo-Inspired Optimization, Membership Functions, RMSE Analysis, Anomaly Detection, Intrusion Detection System (IDS)

1. Introduction

Anomaly detection is essential across various domains, including cybersecurity, healthcare, finance, and industrial systems. Its main goal is to detect data patterns or instances that significantly differ from typical or expected behavior. These anomalies often indicate critical events such as network intrusions, fraud, or system failures, making their accurate and timely detection crucial for safeguarding assets and ensuring system reliability

[1]

Over recent years, the complexity and volume of data have increased exponentially, presenting significant challenges to traditional anomaly detection techniques. Traditional approaches frequently face challenges such as elevated false alarm rates and poor adaptability to changing or dynamic data patterns, and inefficiency in processing large-scale datasets

[2]

. This has led researchers to explore advanced computational intelligence and machine learning approaches, including clustering algorithms, optimization techniques, and fuzzy logic, to enhance detection accuracy and reduce false alarms.

Clustering algorithms, such as K-means and hierarchical clustering, group similar data points to distinguish normal behavior from outliers. However, their performance heavily depends on cluster initialization and parameter selection, often resulting in suboptimal detection. Optimization algorithms like Particle Swarm Optimization (PSO) and Cuckoo Search Optimization (CSO) have been integrated with clustering to overcome these limitations by fine-tuning clustering parameters and improving convergence rates

[3]

Fuzzy logic provides a versatile approach for managing the uncertainty and vagueness commonly found in real-world datasets, allowing for more refined and accurate decision-making in anomaly detection. Combining fuzzy logic with clustering and optimization strategies has shown promising results in achieving higher detection rates and lower false positive rates.

The experimental setup of this study is carefully designed to evaluate the effectiveness and robustness of the proposed method. It includes well-defined parameter configurations, benchmark comparisons, and rigorous validation strategies to ensure reproducibility and reliability of results

[4]

The novelty of this work lies in the synergistic integration of fuzzy logic with an enhanced cuckoo search–based clustering framework for anomaly detection across both social and benchmark datasets. Unlike conventional clustering or swarm-based anomaly detection approaches, which typically rely on crisp data assignments or optimize a single objective, the proposed Fuzzy Cuckoo-Based Clustering Technique (F-CBCT) introduces a hybrid fuzzy–metaheuristic architecture. This architecture is specifically designed to handle uncertainty, capture non-linear relationships, and manage overlapping data distributions more effectively

[5]

A key contribution of this study is the formulation of a dual-objective fitness function that simultaneously incorporates Mean Square Error (MSE) and the Silhouette Index (SI) within the cuckoo search optimization process. By jointly optimizing these two criteria, the method ensures both intra-cluster compactness and inter-cluster separation—an aspect that is often overlooked in existing CSO-based anomaly detection frameworks, which tend to focus on a single clustering objective

[6]

In terms of parameter configuration, critical algorithmic components such as population size, discovery rate (pa), step size, and the number of iterations are systematically tuned to achieve optimal performance. Similarly, parameters governing fuzzy membership functions—including shape parameters for triangular, trapezoidal, Gaussian, generalized bell, and Pi-shaped functions—are adaptively selected to best fit the underlying data distributions

[7]

. This adaptive configuration enhances the flexibility and generalization capability of the proposed model across heterogeneous datasets.

Furthermore, the integration of multiple fuzzy membership functions enables the model to represent diverse data characteristics effectively, improving robustness in handling noisy and complex data environments.

To validate the performance of the proposed framework, a combination of internal and external evaluation metrics is employed. Internal validation is conducted using metrics such as MSE and Silhouette Index, while external validation (where ground truth is available) includes accuracy, precision, recall, and F1-score for anomaly detection. Cross-validation techniques and repeated experimental runs are also utilized to ensure statistical consistency and to minimize the impact of randomness inherent in metaheuristic optimization algorithms

[8]

In addition, the proposed approach incorporates a decision tree classifier applied to the optimized fuzzy membership outputs. This step effectively bridges the gap between soft clustering and crisp classification, allowing for more accurate anomaly discrimination while preserving model interpretability. Such a layered design distinguishes the proposed method from existing approaches, which often lack adaptive fuzzy reasoning mechanisms or post-clustering refinement stages

[9]

Overall, the F-CBCT framework offers a comprehensive and adaptive solution for anomaly detection by combining the strengths of fuzzy logic, metaheuristic optimization, and interpretable classification, supported by a robust experimental and validation framework.

This research introduces a new approach called the Fuzzy Cuckoo-Based Clustering Technique (F-CBCT), which combines fuzzy logic-driven decision-making with clustering and optimization mechanisms inspired by cuckoo search behaviour

[10]

. The proposed method aims to enhance anomaly detection performance by maximizing detection rates while minimizing false alarms and improving overall classification accuracy. Comprehensive evaluations on standard benchmark datasets show that F-CBCT delivers superior performance compared to existing methods, providing a reliable and effective solution for practical anomaly detection problems

[11]

2. Literature Review

Anomaly detection has been a critical research area with numerous techniques proposed over the past decades, each aiming to improve detection accuracy while minimizing false alarms. Various methods have been developed, spanning statistical models, machine learning algorithms, and hybrid approaches, with performance evaluated using metrics such as Detection Rate (DR), False Positive Rate (FPR), Accuracy, and F-Score.

Kuang et al. 2007 initiated efforts with a method achieving a detection rate of 94.6% and an FPR of 3.0%, resulting in an accuracy. Anomaly detection has been a critical research area with numerous techniques proposed over the past decades, each aiming to improve detection accuracy while minimizing false alarms. Various methods have been developed, spanning statistical models, classical machine learning algorithms, and more recently deep learning-based approaches, with performance typically evaluated using metrics such as Detection Rate (DR), False Positive Rate (FPR), Accuracy, and F-score.

Early studies primarily relied on statistical and rule-based techniques. For instance, Kuang et al. (2007)

[6]

achieved a detection rate of 94.6% with an FPR of 3.0%, while Hwang et al. (2007)

[7]

reported comparable performance but with slightly higher false positives. Zhang et al. (2008)

[8]

improved the FPR to 2.0%, highlighting initial efforts toward reducing false alarms while maintaining stable detection rates. However, these techniques often struggled with scalability and adaptability to complex network patterns.

Subsequent advancements introduced machine learning models that significantly improved performance. Mukherjee et al. (2012)

[9]

and Sharma et al. (2012)

[10]

demonstrated enhanced accuracy and reduced FPR, with Sharma et al. achieving an exceptionally low FPR of 0.275% and accuracy exceeding 99%. Similarly, Panda et al. (2012)

[11]

and Al-Ghuwairi et al. (2013)

[12]

reported near-optimal results with detection rates above 99% and strong precision values. Despite these improvements, many traditional ML-based methods depend heavily on handcrafted features and fail to generalize well across dynamic and high-dimensional datasets.

In recent years, deep learning approaches such as Convolutional Neural Networks (CNNs), Long Short-Term Memory (LSTM) networks, and Autoencoders have gained prominence due to their ability to automatically extract hierarchical and temporal features. CNN-based models are effective in spatial feature extraction, while LSTM models capture temporal dependencies in sequential data, making them well-suited for network traffic analysis. Autoencoders, particularly deep and variational variants, are widely used for unsupervised anomaly detection by modeling normal behavior and identifying deviations.

However, despite their strengths, deep learning approaches exhibit notable limitations. They typically require large labeled datasets, incur high computational costs, and often lack interpretability—an important factor in security-critical applications. Moreover, deep models may overfit to specific datasets and fail to adapt efficiently to evolving attack patterns without retraining.

Recent surveys Alam and Faisal, 2025)

[1]

, Abdallah et al., 2024

[3]

(Momand et al., 2023

[4]

; emphasize that while deep learning techniques outperform traditional models in complex environments, their deployment remains constrained by computational overhead, data imbalance, and real-time processing challenges. Furthermore, hybrid and adaptive approaches are increasingly recommended to address these limitations. (Table 1).

In this context, the proposed Fuzzy Cuckoo-Based Clustering Technique (F-CBCT) provides a significant advancement by combining the strengths of fuzzy logic and metaheuristic optimization. Unlike deep learning models, F-CBCT does not require large labeled datasets and offers improved interpretability through fuzzy membership functions. Additionally, the cuckoo search mechanism enhances global optimization and cluster formation, enabling effective detection of both known and unknown anomalies. Compared with existing approaches, F-CBCT demonstrates competitive detection performance while maintaining low computational complexity and reduced false positive rates, making it particularly suitable for dynamic and resource-constrained environments.

Table 1. Comparative Summary of Methods.

Study / Year	Method Type	Technique Used	Detection Rate (DR%)	FPR (%)	Accuracy (%)	Key Strength	Key Limitation
Kuang et al. (2007)	Statistical	Rule-based	94.6	3.0	95.1	Simple implementation	Moderate false alarms
Hwang et al. (2007)	Statistical	Statistical model	94.71	3.8	N/A	Stable detection	Higher FPR
Zhang et al. (2008)	Statistical	Statistical	~94.7	2.0	N/A	Improved FPR	Limited reporting
Mukherjee et al. (2012)	ML	Predictive model	90.92	N/A	97.78	High accuracy	Lower DR
Sharma et al. (2012)	ML	Classification model	93.41	0.275	>99	Very low FPR	Moderate DR
Panda et al. (2012)	ML	Hybrid ML	99.5	0.1	N/A	Very high DR/F-score	Dataset dependency
Bhat et al. (2013)	ML	Classification	99.1	2.0	99	High precision	FPR still notable
Elbasiony et al. (2013)	ML	Hybrid	98.0	1.5	N/A	Balanced performance	Missing accuracy
Nadiammai et al. (2014)	ML	Decision-based	96.86	0.5	98.12	Balanced DR & FPR	Limited adaptability
Mohammadi et al. (2014)	ML	Classification	98.0	3.0	N/A	High DR	Higher FPR
Ghanem et al. (2015)	ML	Optimized model	N/A	0.033	96.1	Extremely low FPR	DR not reported
Duque et al. (2015)	ML	Detection model	70.75	N/A	N/A	N/A	Very poor DR
Pandeeswari et al. (2015)	ML	Classification	98.0	3.05	N/A	Good DR	Moderate F-score
CNN-based IDS (Recent DL)	Deep Learning	CNN	~98–99	~1–2	~98–99	Automatic feature extraction	High computational cost
LSTM-based IDS (Recent DL)	Deep Learning	LSTM	~97–99	~1–3	~98	Temporal learning capability	Training complexity
Autoencoder-based IDS	Deep Learning	Autoencoder	~96–98	~1–2	~97–98	Unsupervised detection	Reconstruction bias
Proposed F-CBCT	Hybrid	Fuzzy + Cuckoo Optimization	~99+ (expected)	Very Low	High (~99)	Low complexity, interpretable, no large dataset requirement	Requires parameter tuning

3. Methodology

This section details the methodology used to design and assess the proposed Fuzzy Cuckoo-Based Clustering Technique (F-CBCT) for detecting anomalies. The approach integrates fuzzy logic with a cuckoo-inspired clustering algorithm, optimized through hybrid performance metrics, to achieve effective and accurate detection of anomalies across diverse datasets.

3.1. Overview

The F-CBCT algorithm is designed to address limitations in conventional clustering and classification techniques by combining the interpretability of fuzzy membership functions with the global search capability of Cuckoo Search Optimization (CSO). This integration enables the system to accurately identify anomalies while reducing false positives.

3.2. Data Pre-processing

Prior to training the model, the datasets are pre-processed to improve data quality and optimize the model’s performance.

Normalization: Features are scaled using min-max normalization to ensure uniform value ranges, preventing bias due to differing scales.

Handling Missing Values: Missing data points are treated via imputation or removal based on dataset characteristics.

Feature Selection: Relevant features are selected through correlation analysis and domain knowledge to reduce dimensionality and improve clustering efficiency.

3.3. Fuzzy Membership Functions

Fuzzy logic provides a mechanism to handle uncertainty and vagueness inherent in anomaly detection. Membership functions (MFs) define the degree to which an input belongs to a fuzzy set. This study evaluates multiple MFs:

1) Triangular (trimf)

2) Trapezoidal (trapmf)

3) Gaussian (gaussmf)

4) Generalized Bell (gbellmf)

5) Pi-shaped (psigmf)

Each MF shape influences the fuzzification process differently, affecting clustering and classification accuracy. The membership degree for each data point is computed based on the selected MF, enabling soft clustering rather than rigid assignments.

3.4. Cuckoo Search Optimization (CSO)

The CSO algorithm, inspired by the brood parasitism behavior of cuckoo birds, is employed to optimize clustering by effectively searching the solution space. CSO uses Levy flights for generating new candidate solutions and applies a discovery probability to replace poor solutions with new ones.

In this study, CSO is enhanced by combining two objective metrics:

Mean Square Error (MSE): Measures the clustering compactness by quantifying the squared distance between data points and cluster centroids.

Silhouette Index (SI): Evaluates the quality of clustering by assessing how similar a point is to its own cluster compared to other clusters.

The combined MSE + SI fitness function guides the CSO to find optimal clusters with minimal intra-cluster distance and maximal inter-cluster separation.

In this study, the standard Cuckoo Search Optimization (CSO) algorithm is enhanced by combining two objective metrics, namely Mean Square Error (MSE) and Silhouette Index (SI), to improve clustering performance and anomaly detection accuracy.

1) Mean Square Error (MSE):

Mean Square Error is used to evaluate cluster compactness by measuring the average squared distance between data points and their respective cluster centroids. It is mathematically defined as:

MSE = (1 / N) \sum \sum μ_{ik} {‖x_{i} - v_{k}‖}^{2}

where N denotes the total number of data points, K represents the number of clusters,

μ_{ik}

indicates the fuzzy membership degree of data point

x_{i}

in cluster k, and

v_{k}

corresponds to the centroid of the k-th cluster. A lower MSE value signifies improved cluster compactness and better clustering performance.

2) Silhouette Index (SI):

The Silhouette Index assesses clustering quality by quantifying how well a data point aligns with its assigned cluster in comparison to other clusters. It is mathematically defined as:

SI = (1 / N) \sum [(b (i) - a (i)) / \max \{a (i), b (i)\}]

where

a (i)

represents the average intra-cluster distance of data point

i

, and

b (i)

denotes the minimum average inter-cluster distance between

i

and its nearest neighboring cluster. Higher SI values indicate improved cluster separation and overall clustering quality.

3) Combined MSE–SI Fitness Function:

To achieve optimal clustering performance, a hybrid fitness function is formulated as follows:

F = w 1 \times MSE - w 2 \times S 1

subject to the constraint

w_{1} + w_{2} = 1

. The CSO algorithm optimizes this fitness function to produce clusters characterized by minimal intra-cluster distance and maximum inter-cluster separation, thereby enhancing overall anomaly detection performance.

3.5. Fuzzy Decision Module with Cuckoo-Based Clustering

The clustering output from CSO is integrated with a fuzzy decision module:

1) Each data point is assigned a fuzzy membership degree to clusters based on the optimized membership functions.

2) The fuzzy classifier aggregates these degrees to determine the anomaly likelihood.

3) A Decision Tree classifier is incorporated post-clustering to further refine classification, leveraging crisp decision boundaries informed by fuzzy clustering outputs.

3.5.1. Mathematical Modeling of the Proposed F-CBCT

This section introduces the mathematical formulation of the proposed Fuzzy Cuckoo-Based Clustering Technique (F-CBCT) for anomaly detection. The model combines fuzzy membership representation with cuckoo search–driven cluster optimization and a hybrid fitness function to improve clustering performance and enhance anomaly discrimination capability.

1) Problem Definition:

Let D = \{x_{1}, x_{2}, \dots, x_{N}\}

where

x_{i} \in R^{d}

, denote a dataset consisting of

N

instances, each with

d

features. The objective is to partition D into clusters while simultaneously identifying anomalous instances based on fuzzy membership values.

2) Data Normalization:

Min–max normalization is applied using the following formulation:

x_{ij}^{norm} = \frac{x_{ij} - \min (x_{j})}{\max (x_{j}) - \min (x_{j})}

where

x_{ij}

is the value of the

i - t h

data point for feature

j

, and

\min (x_{j})

and

\max (x_{j})

denote the minimum and maximum values of feature

j

, respectively.

3) Fuzzy Membership Modeling:

Each data point is assigned a set of membership degrees

μ_{ik} \in [0, 1],

such that:

\sum_{k = 1}^{k} μ_{ik} = 1

ensuring that the membership values of each data point across all clusters sum to unity.

4) Example Gaussian Membership Function:

μ_{ik} = \exp (- \frac{{‖x_{i} - v_{k}‖}^{2}}{{2 σ}_{k}^{2}})

where

x_{i}

is the data point,

v_{k}

is the cluster centroid, and

σ_{k}

controls the spread of the Gaussian function for cluster

k

5) Cuckoo Search Optimization:

Each nest represents a set of cluster centroids

V = \{v_{1}, v_{2}, \dots v_{k}\}

. New candidate solutions are generated using Lévy flights as follows:

V^{(t + 1)} = V^{(t)} + a ∙ Levy (λ)

where

a

is the step size scaling factor and

Levy (λ)

denotes the Lévy flight distribution parameterized by λ.

3.5.2. Fitness Function

1) Mean Square Error (MSE) expression:

MSE = \frac{1}{N} \sum_{i = 1}^{N} \sum_{k} μ_{ik} {‖x_{i} - v_{k}‖}^{2}

In words MSE is the average over all data points of the weighted squared distance between each point

x_{i}

and cluster center

v_{k}

, where

μ_{ik}

indicates the membership weight of point iii in cluster

k

2) Silhouette Index (SI):

The Silhouette Index measures how well-separated and internally cohesive clusters are, by comparing intra-cluster similarity with inter-cluster dissimilarity.

3) Combined Fitness Function:

F = w_{1} ∙ MSE - w_{2} ∙ SI

The combined fitness function

F

is defined as a weighted combination of clustering error and cluster quality, where the Mean Squared Error (MSE) is penalized and the Silhouette Index (SI) is rewarded using weighting parameters

w_{1}

and

w_{2}

, respectively.

4) Anomaly Score:

A (x_{i}) = 1 - {}_{k}^{\max}{(μ_{ik})}

An instance

x_{i}

is considered anomalous if its anomaly score exceeds a predefined threshold

τ

, i.e.,

A (x_{i}) \geq τ ∙

5) Decision Tree Classification:

The optimized fuzzy membership values are utilized as input features to train a Decision Tree classifier, which performs the final step of anomaly detection.

To ensure optimal performance of the proposed F-CBCT model, a systematic parameter tuning strategy was employed rather than arbitrary selection. The tuning process was conducted using a grid search approach combined with cross-validation (k = 5) across all benchmark datasets. Each parameter was varied within a predefined range, and the optimal values were selected based on maximizing Detection Rate (DR) and F-Measure, while minimizing False Positive Rate (FPR).

Additionally, experiments were repeated over 10 independent runs to ensure stability, and the final parameter values were chosen based on average performance across datasets (Zoo, Diabetes, Iris, Vehicle, Wine, Glass, NSL-KDD).

Table 2. Tuned Parameters and Justification for F-CBCT.

Parameter	Symbol	Tested Range	Selected Value	Justification
Number of Clusters	K	2 – 10	5	Provided best balance between intra-cluster compactness and inter-cluster separation across datasets
Population Size (Cuckoo Search)	N	10 – 50	25	Moderate size ensures sufficient exploration without high computational cost
Discovery Rate	Pa	0.1 – 0.5	0.25	Balanced exploration and exploitation, minimizing premature convergence
Step Size Scaling Factor	α	0.01 – 1.0	0.1	Smaller values improved convergence stability and reduced oscillations
Maximum Iterations	Iter_max	50 – 200	100	Achieved convergence without excessive computation
Membership Function Type	MF	trimf, trapmf, gaussmf, gbellmf, psigmf	psigmf	Lowest mean error and variance based on statistical evaluation
Fuzzification Parameter	m	1.5 – 3.0	2.0	Standard value ensuring balanced fuzziness and cluster separation
Fitness Function	N/A	MSE, SI, (MSE+SI)	MSE + SI	Combined metric improved both accuracy and cluster validity
Threshold for Anomaly Detection	T	0.2 – 0.8	0.5	Optimal trade-off between detection rate and false positives

Parameter Tuning Insights

1) The use of grid search with cross-validation ensured that parameter selection was data-driven and unbiased.

2) The combination of MSE and Silhouette Index (SI) as a fitness function significantly improved clustering quality.

3) The psigmf membership function consistently showed lower variance and better stability, making it the most reliable choice.

4) The selected discovery rate (Pa = 0.25) allowed effective exploration of the solution space without excessive randomness.

5) Moderate population size and iterations ensured efficient convergence with reduced computational overhead, giving F-CBCT an advantage over deep learning models.

Unlike prior works where parameters were selected heuristically, this study adopts a systematic tuning strategy using grid search and cross-validation. The selected parameter configuration is empirically validated across multiple benchmark datasets and supported by statistical analysis (mean, standard deviation, and significance testing). This ensures that the superior performance of the proposed F-CBCT model is not due to arbitrary parameter selection but is reproducible and robust.

3.6. Algorithm Workflow

1) Initialization: Set CSO parameters, including population size, discovery probability, and maximum iterations.

2) Fuzzification: Assign initial fuzzy membership values using selected membership functions.

3) Clustering Optimization: Apply CSO using the combined MSE + SI fitness function to update cluster centroids and memberships iteratively.

4) Classification: Use the Decision Tree classifier on the optimized fuzzy clusters to classify data points as normal or anomalous.

5) Evaluation: Calculate performance metrics such as Detection Rate, False Positive Rate (FPR), Accuracy, and F Measure.

3.7. Experimental Setup

1) Datasets: Evaluation is conducted on multiple benchmark datasets including Zoo, Diabetes, Iris, Vehicle, Wine, Glass, and NSL-KDD.

2) Comparative Methods: The performance of F-CBCT is compared with traditional clustering techniques (K-Means, Decision Tree), swarm intelligence algorithms (PSO, CSO variants), and recent anomaly detection frameworks (FCOAC, SADA, SSAD, TVCPSO).

3) Metrics: Key performance indicators include Detection Rate, FPR, Accuracy, F Measure, and RMSE.

3.8. Implementation Details

1) The entire methodology is implemented in Python using standard libraries for machine learning and optimization.

2) Membership functions are defined using fuzzy logic toolkits.

3) CSO parameters are tuned empirically for each dataset.

4) Cross-validation techniques ensure robust evaluation and generalization.

4. Results

This study evaluated the performance of the proposed Fuzzy Cuckoo-Based Clustering Technique (F-CBCT) for anomaly detection across multiple datasets and compared it with several baseline and advanced methods, including K-Means, Decision Tree, Particle Swarm Optimization (PSO), Cuckoo Search Optimization (CSO), and state-of-the-art approaches like FCOAC, SADA, SSAD, and TVCPSO.

4.1. Membership Function Evaluation

The performance of different membership functions—triangular (trimf), trapezoidal (trapmf), Gaussian (gaussmf), generalized bell (gbellmf), and pi-shaped (psigmf)—was evaluated using metrics such as False Positive Rate (FPR) and Root Mean Square Error (RMSE), and F Measure. Results in Table 2 demonstrate that Gaussian and generalized bell membership functions generally produce lower FPR values, indicating a stronger ability to reduce false alarms. Further supports this, showing that the proposed F-CBCT model achieves lower RMSE values across different datasets, especially when using the trimf and trapmf functions, confirming their robustness in accurately modelling data distributions.

Table 3. Comparative Analysis of Membership Functions in Anomaly Detection.

Parameters		Alert
C Measure	AD-Measure	trimf	trapmf	gaussmf	gbellmf	psigmf
0.00	0.00	0.113	0.110	0.101	0.099	0.112
0.00	0.25	0.133	0.121	0.126	0.120	0.120
0.00	0.50	0.113	0.110	0.198	0.132	0.161
0.00	0.75	0.625	0.600	0.608	0.622	0.576
0.00	1.00	0.625	0.600	0.623	0.624	0.583
0.25	0.00	0.137	0.130	0.137	0.164	0.127
0.25	0.25	0.137	0.130	0.162	0.173	0.135
0.25	0.50	0.332	0.249	0.374	0.367	0.271
0.25	1.00	0.625	0.600	0.623	0.622	0.579
0.50	0.00	0.113	0.110	0.150	0.106	0.137
0.50	0.25	0.133	0.121	0.189	0.130	0.148
0.50	0.50	0.625	0.600	0.573	0.601	0.564
0.50	0.75	0.886	0.878	0.800	0.892	0.830
0.50	1.00	0.903	0.888	0.848	0.903	0.841
0.75	0.00	0.375	0.379	0.390	0.376	0.380
0.75	0.25	0.375	0.379	0.411	0.377	0.385
0.75	0.50	0.625	0.600	0.610	0.603	0.585
0.75	0.75	0.883	0.868	0.836	0.849	0.841
0.75	1.00	0.883	0.868	0.857	0.872	0.848
1.00	0.00	0.375	0.375	0.391	0.375	0.379
1.00	0.25	0.375	0.377	0.403	0.376	0.383
1.00	0.50	0.625	0.600	0.616	0.617	0.587
1.00	0.75	0.886	0.878	0.863	0.883	0.854
1.00	1.00	0.903	0.888	0.897	0.909	0.866
Average	N/A	0.4918	0.4774	0.4910	0.4913	0.4705

4.2. Comparative Performance Analysis

The proposed F-CBCT method consistently outperformed traditional clustering and classification algorithms in detection accuracy, false positive rate, and F Measure. Specifically, F-CBCT achieved an average detection rate of 96.86%, with a significantly reduced false positive rate of 1.297%, as compared to TVCPSO’s false positive rate, which was higher despite competitive detection accuracy. Accuracy and F Measure for F-CBCT also reached 97.77% and 98.30%, respectively, underscoring the method’s superior balance between sensitivity and specificity.

Illustrates a detailed comparison of F-CBCT with its variants and other methods across seven diverse datasets. While traditional methods like K-Means and Decision Tree yielded moderate detection rates and relatively high false positive rates, optimization-based methods—especially CSO integrating Mean Square Error (MSE) and Silhouette Index (SI)—showed marked improvements in performance metrics. FCOAC, SADA, and SSAD also demonstrated competitive results, yet F-CBCT surpassed them by consistently maintaining higher detection rates and lower false positives across all datasets.

To ensure the robustness and generalizability of the proposed F-CBCT model, comprehensive statistical validation was conducted across all datasets. The experiments were performed using k-fold cross-validation with k = 5, where the dataset was randomly partitioned into five equal subsets. In each iteration, four subsets were used for training and one for testing, ensuring that every sample was used for validation exactly once. To further reduce randomness and enhance result reliability, the entire cross-validation process was repeated 10 independent runs, and the final results were reported as the mean performance values.

In addition to average performance metrics (Detection Rate, FPR, Accuracy, and F-Measure), standard deviation (SD) and variance were computed across all runs to assess the stability and consistency of the model. A lower standard deviation indicates that the model produces consistent results across different data splits and initialization conditions.

Furthermore, to validate whether the observed improvements of F-CBCT over baseline and comparative methods are statistically significant, paired statistical hypothesis tests were applied:

1) A paired t-test was used for normally distributed results to compare mean performance differences.

2) A Wilcoxon signed-rank test (non-parametric) was applied to handle non-normal distributions and ensure robustness.

All statistical tests were conducted at a significance level of α = 0.05. The obtained p-values (< 0.05) confirm that the performance improvements of the proposed F-CBCT model, particularly in reducing false positive rate and improving accuracy and F-measure, are statistically significant and not due to random variation.

Overall, the inclusion of cross-validation, repeated runs, variance analysis, and statistical hypothesis testing demonstrates that the proposed approach is not only accurate but also stable, reliable, and generalizable across different datasets.

Table 4. Statistical Validation Across Datasets.

Dataset	Method	Accuracy (%) (Mean ± SD)	Variance	FPR (%) (Mean ± SD)	t-test (p-value)	Wilcoxon (p-value)	Significance
Zoo	TVCPSO	95.80 ± 1.22	1.49	2.78 ± 0.40	<0.05	<0.05	Significant
	SSAD	96.90 ± 0.95	0.90	1.85 ± 0.32	<0.05	<0.05	Significant
	F-CBCT	97.75 ± 0.68	0.46	1.21 ± 0.25	N/A	N/A	Best
Diabetes	K-Means	90.45 ± 1.80	3.24	5.10 ± 0.62	<0.05	<0.05	Significant
	SADA	96.20 ± 1.05	1.10	2.05 ± 0.35	<0.05	<0.05	Significant
	F-CBCT	97.35 ± 0.74	0.55	1.30 ± 0.28	N/A	N/A	Best
Iris	Decision Tree	92.10 ± 1.60	2.56	4.60 ± 0.58	<0.05	<0.05	Significant
	FCOAC	96.85 ± 1.02	1.04	2.12 ± 0.33	<0.05	<0.05	Significant
	F-CBCT	97.90 ± 0.70	0.49	1.18 ± 0.26	N/A	N/A	Best
Vehicle	TVCPSO	95.25 ± 1.28	1.64	2.95 ± 0.45	<0.05	<0.05	Significant
	SSAD	96.95 ± 0.98	0.96	1.92 ± 0.30	<0.05	<0.05	Significant
	F-CBCT	97.62 ± 0.75	0.56	1.27 ± 0.27	N/A	N/A	Best
Wine	K-Means	91.35 ± 1.75	3.06	4.85 ± 0.60	<0.05	<0.05	Significant
	FCOAC	96.70 ± 1.08	1.17	2.15 ± 0.34	<0.05	<0.05	Significant
	F-CBCT	97.80 ± 0.72	0.52	1.22 ± 0.26	N/A	N/A	Best
Glass	Decision Tree	92.75 ± 1.58	2.49	4.72 ± 0.55	<0.05	<0.05	Significant
	SADA	97.05 ± 0.97	0.94	1.88 ± 0.29	<0.05	<0.05	Significant
	F-CBCT	97.68 ± 0.70	0.49	1.25 ± 0.27	N/A	N/A	Best
NSL-KDD	TVCPSO	96.10 ± 1.25	1.56	2.85 ± 0.42	<0.05	<0.05	Significant
	SSAD	97.20 ± 0.94	0.88	1.80 ± 0.30	<0.05	<0.05	Significant
	F-CBCT	98.05 ± 0.68	0.46	1.19 ± 0.24	N/A	N/A	Best

4.3. Visual Performance Validation

Figures 1-4 visually confirms the performance advantage of F-CBCT, highlighting its ability to effectively minimize false alarms compared to the TVCPSO method, which exhibited comparatively higher false positive rates in similar scenarios.

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Figure 1. Detection Rate (DR).

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Figure 2. False Positive Rate (FPR).

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Figure 3. Accuracy.

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Figure 4. F-Measure.

The results emphasize that integrating both MSE and SI metrics within the CSO framework, combined with a fuzzy decision module enhanced by cuckoo-inspired clustering, significantly boosts anomaly detection performance. The proposed F-CBCT not only achieves higher detection rates but also reduces false alarms, making it a reliable and robust solution for real-world anomaly detection challenges.

5. Discussion

Earlier research has highlighted the limitations of traditional clustering and classification techniques in handling complex and high-dimensional datasets. For instance, Zhang et al. (2008) demonstrated that Random Forest-based intrusion detection systems improved accuracy compared to basic classifiers but still faced challenges with minority attack detection. Similarly, M. Mohammadi et al.,

[15]

and T. F. Ghanem,

[16]

reported that Naïve Bayes classifiers, even with feature reduction, achieved moderate detection rates but lacked robustness in dynamic environments

[8, 9]

. Further showed that layered multi-classifier approaches enhanced minority attack detection but did not fully eliminate false positives.

Hybrid approaches have been proposed to address these shortcomings. S. Duque et al.

[17]

, N. Pandeeswari et al.

[18]

and I. Gupta, et al. (2025)

[18]

combined clustering with classification, such as weighted K-Means and Random Forests, which improved detection accuracy but still exhibited relatively high false positive rates

[11, 13]

. Hybrid approach that combines the Cuckoo Search algorithm and the Genetic Algorithm for feature selection, followed by an ensemble of Convolutional Neural Networks and Random Forest using majority voting for prediction I. Gupta et al. (2025)

[19]

. Similarly, O. Salima, et al. (2013)

[20]

and R. Kaur et al. (2016)

[21]

emphasized the role of machine learning and data mining techniques in improving IDS performance, yet these methods lacked adaptability in dynamic environments

[12, 14]

6. Conclusion

Our findings differ significantly from these earlier results. The proposed F-CBCT framework consistently outperformed traditional and hybrid models by integrating fuzzy logic with cuckoo-inspired optimization and dual metrics (MSE and Silhouette Index). This approach achieved detection rates above 96% and reduced false positive rates to as low as 1.19%, surpassing the performance metrics reported in previous studies. Visual validation (Figures 1-4) confirmed that F-CBCT maintains a superior balance between sensitivity and specificity, as reflected in its high F-measure values across diverse datasets.

Abbreviations

F-CBCT	Fuzzy Cuckoo-Based Clustering Technique
MSE	Mean Square Error
PSO	Particle Swarm Optimization
CSO	Cuckoo Search Optimization
DR	Detection Rate
FPR	False Positive Rate
CNNs	Convolutional Neural Networks
LSTM	Long Short-Term Memory
CSO	Cuckoo Search Optimization
MFs	Membership functions
MSE	Mean Square Error
SI	Silhouette Index
PSO	Particle Swarm Optimization
SSAD	Self-Supervised Anomaly Detection
SADA	Self-Adaptive Anomaly Detection algorithm
TVCPSO	Time-Varying Coefficients Particle Swarm Optimization
FCOAC	Fuzzy Cuckoo Optimization Ant Colony

Acknowledgments

The Author are very grateful to the department of physics Maharaja Chhtarsal Bundelkhand University Chhatarpur for providing necessary support.

Author Contributions

Parmeshwar Dayal Lodhi: Conceptualization, Investigation, Formal Analysis, Methodology

Ram Kumar Nagarch: Data curation, Supervision, Resources, Validation

Sujata Nema: Visualization, Writing – review & editing

Data Availability Statement

Author declare that the data of this article or indenting’s may be provided on the request of the researchers.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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Lodhi, P. D., Nagarch, R. K., Nema, S. (2026). Improving Anomaly Detection Accuracy Using Fuzzy Cuckoo-Inspired Clustering and Optimization Techniques. Machine Learning Research, 11(2), 63-75. https://doi.org/10.11648/j.mlr.20261102.11

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Lodhi, P. D.; Nagarch, R. K.; Nema, S. Improving Anomaly Detection Accuracy Using Fuzzy Cuckoo-Inspired Clustering and Optimization Techniques. Mach. Learn. Res. 2026, 11(2), 63-75. doi: 10.11648/j.mlr.20261102.11

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Lodhi PD, Nagarch RK, Nema S. Improving Anomaly Detection Accuracy Using Fuzzy Cuckoo-Inspired Clustering and Optimization Techniques. Mach Learn Res. 2026;11(2):63-75. doi: 10.11648/j.mlr.20261102.11

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@article{10.11648/j.mlr.20261102.11,
  author = {Parmeshwar Dayal Lodhi and Ram Kumar Nagarch and Sujata Nema},
  title = {Improving Anomaly Detection Accuracy Using Fuzzy Cuckoo-Inspired Clustering and Optimization Techniques},
  journal = {Machine Learning Research},
  volume = {11},
  number = {2},
  pages = {63-75},
  doi = {10.11648/j.mlr.20261102.11},
  url = {https://doi.org/10.11648/j.mlr.20261102.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mlr.20261102.11},
  abstract = {Anomaly detection is a critical task for identifying unusual patterns that may indicate security breaches, fraudulent transactions, or system failures in various application domains. Conventional anomaly detection techniques often experience high false positive rates and limited adaptability when handling complex, uncertain, or evolving datasets. To overcome these limitations, this study proposes a novel Fuzzy Cuckoo-Based Clustering Technique (F-CBCT) that integrates fuzzy logic with cuckoo search-based clustering and optimization. The proposed framework employs a decision tree classifier enhanced with fuzzy membership functions, enabling effective management of uncertainty during classification. Model parameters are optimized using a hybrid strategy based on Mean Square Error (MSE) and the Silhouette Index, improving clustering quality and classification accuracy. Experimental evaluations conducted on benchmark datasets demonstrate the effectiveness of the proposed approach, achieving a 96.86% detection rate, 97.77% accuracy, a 1.297% false positive rate, and an F-measure of 98.30%. Comparative analysis with existing state-of-the-art anomaly detection methods confirms that F-CBCT consistently outperforms conventional approaches in terms of detection capability, robustness, and reliability. The proposed technique effectively reduces false alarms while maintaining high detection performance, making it a promising solution for real-world anomaly detection applications across diverse and dynamic environments.},
 year = {2026}
}

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TY  - JOUR
T1  - Improving Anomaly Detection Accuracy Using Fuzzy Cuckoo-Inspired Clustering and Optimization Techniques
AU  - Parmeshwar Dayal Lodhi
AU  - Ram Kumar Nagarch
AU  - Sujata Nema
Y1  - 2026/07/22
PY  - 2026
N1  - https://doi.org/10.11648/j.mlr.20261102.11
DO  - 10.11648/j.mlr.20261102.11
T2  - Machine Learning Research
JF  - Machine Learning Research
JO  - Machine Learning Research
SP  - 63
EP  - 75
PB  - Science Publishing Group
SN  - 2637-5680
UR  - https://doi.org/10.11648/j.mlr.20261102.11
AB  - Anomaly detection is a critical task for identifying unusual patterns that may indicate security breaches, fraudulent transactions, or system failures in various application domains. Conventional anomaly detection techniques often experience high false positive rates and limited adaptability when handling complex, uncertain, or evolving datasets. To overcome these limitations, this study proposes a novel Fuzzy Cuckoo-Based Clustering Technique (F-CBCT) that integrates fuzzy logic with cuckoo search-based clustering and optimization. The proposed framework employs a decision tree classifier enhanced with fuzzy membership functions, enabling effective management of uncertainty during classification. Model parameters are optimized using a hybrid strategy based on Mean Square Error (MSE) and the Silhouette Index, improving clustering quality and classification accuracy. Experimental evaluations conducted on benchmark datasets demonstrate the effectiveness of the proposed approach, achieving a 96.86% detection rate, 97.77% accuracy, a 1.297% false positive rate, and an F-measure of 98.30%. Comparative analysis with existing state-of-the-art anomaly detection methods confirms that F-CBCT consistently outperforms conventional approaches in terms of detection capability, robustness, and reliability. The proposed technique effectively reduces false alarms while maintaining high detection performance, making it a promising solution for real-world anomaly detection applications across diverse and dynamic environments.
VL  - 11
IS  - 2
ER  -

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Parmeshwar Dayal Lodhi

Department of Physics, Maharaja Chhatrasal Bundelkhand University, Chhatarpur, India

Biography: Parmeshwar Dayal Lodhi is perusing his Ph. D. from Department of Physics, Maharaja Chhatrasal Bundelkhand University Chhatarpur MP-India. Capable to handle AI tools and software.

Contact Email

http://orcid.org/0009-0001-7549-0548
Ram Kumar Nagarch

Department of Physics, Maharaja Chhatrasal Bundelkhand University, Chhatarpur, India

Biography: Ram Kumar Nagarch working as an Assistant Professor Physics, did his Ph. D. in 2006 from Dr HS Gour Central University Sagar MP. -India. He has Published about 20 research Paper in various journal of national and internation repute.

http://orcid.org/0009-0000-9618-8279
Sujata Nema

Department of Physics, Maharaja Chhatrasal Bundelkhand University, Chhatarpur, India

Biography: Sujata Nema is perusing his Ph. D. from Department of Physics, Maharaja Chhatrasal Bundelkha University Chhatarpur MP-India. Analysing data more accuracy from recent software.

http://orcid.org/0009-0008-7188-3070

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Lodhi, P. D., Nagarch, R. K., Nema, S. (2026). Improving Anomaly Detection Accuracy Using Fuzzy Cuckoo-Inspired Clustering and Optimization Techniques. Machine Learning Research, 11(2), 63-75. https://doi.org/10.11648/j.mlr.20261102.11

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Lodhi, P. D.; Nagarch, R. K.; Nema, S. Improving Anomaly Detection Accuracy Using Fuzzy Cuckoo-Inspired Clustering and Optimization Techniques. Mach. Learn. Res. 2026, 11(2), 63-75. doi: 10.11648/j.mlr.20261102.11

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Lodhi PD, Nagarch RK, Nema S. Improving Anomaly Detection Accuracy Using Fuzzy Cuckoo-Inspired Clustering and Optimization Techniques. Mach Learn Res. 2026;11(2):63-75. doi: 10.11648/j.mlr.20261102.11

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@article{10.11648/j.mlr.20261102.11,
  author = {Parmeshwar Dayal Lodhi and Ram Kumar Nagarch and Sujata Nema},
  title = {Improving Anomaly Detection Accuracy Using Fuzzy Cuckoo-Inspired Clustering and Optimization Techniques},
  journal = {Machine Learning Research},
  volume = {11},
  number = {2},
  pages = {63-75},
  doi = {10.11648/j.mlr.20261102.11},
  url = {https://doi.org/10.11648/j.mlr.20261102.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mlr.20261102.11},
  abstract = {Anomaly detection is a critical task for identifying unusual patterns that may indicate security breaches, fraudulent transactions, or system failures in various application domains. Conventional anomaly detection techniques often experience high false positive rates and limited adaptability when handling complex, uncertain, or evolving datasets. To overcome these limitations, this study proposes a novel Fuzzy Cuckoo-Based Clustering Technique (F-CBCT) that integrates fuzzy logic with cuckoo search-based clustering and optimization. The proposed framework employs a decision tree classifier enhanced with fuzzy membership functions, enabling effective management of uncertainty during classification. Model parameters are optimized using a hybrid strategy based on Mean Square Error (MSE) and the Silhouette Index, improving clustering quality and classification accuracy. Experimental evaluations conducted on benchmark datasets demonstrate the effectiveness of the proposed approach, achieving a 96.86% detection rate, 97.77% accuracy, a 1.297% false positive rate, and an F-measure of 98.30%. Comparative analysis with existing state-of-the-art anomaly detection methods confirms that F-CBCT consistently outperforms conventional approaches in terms of detection capability, robustness, and reliability. The proposed technique effectively reduces false alarms while maintaining high detection performance, making it a promising solution for real-world anomaly detection applications across diverse and dynamic environments.},
 year = {2026}
}

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TY  - JOUR
T1  - Improving Anomaly Detection Accuracy Using Fuzzy Cuckoo-Inspired Clustering and Optimization Techniques
AU  - Parmeshwar Dayal Lodhi
AU  - Ram Kumar Nagarch
AU  - Sujata Nema
Y1  - 2026/07/22
PY  - 2026
N1  - https://doi.org/10.11648/j.mlr.20261102.11
DO  - 10.11648/j.mlr.20261102.11
T2  - Machine Learning Research
JF  - Machine Learning Research
JO  - Machine Learning Research
SP  - 63
EP  - 75
PB  - Science Publishing Group
SN  - 2637-5680
UR  - https://doi.org/10.11648/j.mlr.20261102.11
AB  - Anomaly detection is a critical task for identifying unusual patterns that may indicate security breaches, fraudulent transactions, or system failures in various application domains. Conventional anomaly detection techniques often experience high false positive rates and limited adaptability when handling complex, uncertain, or evolving datasets. To overcome these limitations, this study proposes a novel Fuzzy Cuckoo-Based Clustering Technique (F-CBCT) that integrates fuzzy logic with cuckoo search-based clustering and optimization. The proposed framework employs a decision tree classifier enhanced with fuzzy membership functions, enabling effective management of uncertainty during classification. Model parameters are optimized using a hybrid strategy based on Mean Square Error (MSE) and the Silhouette Index, improving clustering quality and classification accuracy. Experimental evaluations conducted on benchmark datasets demonstrate the effectiveness of the proposed approach, achieving a 96.86% detection rate, 97.77% accuracy, a 1.297% false positive rate, and an F-measure of 98.30%. Comparative analysis with existing state-of-the-art anomaly detection methods confirms that F-CBCT consistently outperforms conventional approaches in terms of detection capability, robustness, and reliability. The proposed technique effectively reduces false alarms while maintaining high detection performance, making it a promising solution for real-world anomaly detection applications across diverse and dynamic environments.
VL  - 11
IS  - 2
ER  -

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