Fireworks-Optimized Clustering and SVM Tested for Enterprise Budget Control

A computational framework that combines an optimized clustering algorithm with weighted support vector machine classification reached 93.67% accuracy in a held-out test of departmental budget settlement grades and 94.00% mean accuracy in fivefold cross-validation. The study developed the system to address two separate tasks in enterprise financial control: identifying unusual records in budget-execution data and evaluating the final accounts of individual departments. Its results were reported for financial and non-financial records from one listed company covering 2020 to 2022, rather than for a broad sample of organizations, so the findings demonstrate performance within a single-enterprise dataset rather than established generalizability across the corporate sector.

The system’s risk-control module uses a Fireworks Algorithm to improve K-means clustering. K-means divides records into groups by repeatedly assigning each data point to its nearest centroid and recalculating those centroids. Its results can depend heavily on the initial centers, which are conventionally selected at random. A poorly distributed set of starting points may lead the procedure toward a local rather than global optimum. The Fireworks Algorithm simulates explosions to search for promising initial centers, combining global exploration with local refinement. Candidate solutions arise from the original “fireworks,” ordinary explosion sparks and Gaussian-mutated sparks, with the most promising candidates used to initialize K-means. In this way, the optimization primarily targets the stability and quality of the cluster structure rather than changing the underlying K-means assignment procedure.

Before distances were calculated, all 15 financial indicators were transformed to a common range of zero to one through min-max normalization. This step prevents indicators with larger numerical scales from dominating the Euclidean-distance measure used to compare records. The researchers tested cluster counts of two, three, four and five, and evaluated each result with the mean silhouette coefficient, which balances cohesion within clusters against separation between them. Three clusters produced the highest reported value, 0.67 plus or minus 0.01, compared with 0.54 plus or minus 0.02 for two clusters, 0.59 plus or minus 0.02 for four and 0.52 plus or minus 0.02 for five. A one-way analysis of variance found statistically significant differences among the four settings, with p below 0.001, supporting the selection of three clusters for this dataset.

Among the 410 retained samples, the three-group solution separated most observations into compact concentrations while leaving some records far from the centers of their assigned groups. The study treated those dispersed observations as candidates for detailed investigation, including possible unreasonable expenditure, abnormal contract-payment methods and improper use of financial accounts. That interpretation should not be confused with independently confirmed fraud or financial misconduct: clustering identifies statistical outliers or unusual combinations of indicators, and financial personnel would still need to examine each flagged record. A visual comparison with a two-stage mixed K-means approach showed the Fireworks-optimized method producing more distinct groupings and more prominent dispersed points in the researchers’ analysis, although the comparison was conducted only on the available sample.

The second module evaluates departmental final accounts using a hierarchy of 15 indicators. Their relative importance was assigned through the Analytic Hierarchy Process, a multi-criteria method that combines qualitative judgments with quantitative analysis. A six-member panel—three enterprise financial and budget personnel, one internal auditor and two financial-management researchers—used Saaty’s one-to-nine scale to compare indicators in pairs. The resulting judgment matrices passed consistency checks before the weights were calculated. This design allows management expertise to enter the model explicitly, but it also means that the weighting scheme depends on the panel’s judgments and the particular organization whose financial requirements shaped the indicator set.

Five indicators received the largest comprehensive weights: the budget-execution difference rate for special-project expenditure, the difference rate between financial-subsidy income budget and final accounts, the personnel-expenditure difference rate, the difference rate for non-financial income budget and final accounts, and the carry-forward and balance rate of financial subsidies. Their respective weights were 0.141, 0.1169, 0.116, 0.114 and 0.113, together accounting for nearly 60% of the total. The researchers then used the weighted indicator values as inputs to an SVM classifier. A radial-basis kernel expressed pairwise similarity through an exponential function of the squared distance between observations, allowing the model to represent nonlinear relationships among the 15 features while controlling the trade-off between model complexity and fitting error.

The department-level experiment used 100 valid samples, with a random 70% used for training and the remaining 30% reserved for testing. Under that partition, the SVM achieved 97.10% training accuracy and 93.67% test accuracy. Its average modeling times were 50.02 milliseconds for the training set and 40.10 milliseconds for the test set, the shortest reported times among the compared approaches. A supplementary stratified fivefold cross-validation divided the 100 samples into five subsets of 20, preserving the class proportions of the settlement grades. Each subset served once as an independent test set, while the other four supplied the training data. Fold accuracies ranged from 90.00% to 100.00%, with a mean of 94.00%, a standard deviation of 4.18 percentage points and a 95% confidence interval of 88.81% to 99.19%.

Under unified experimental conditions, the study also compared the AHP-SVM model with PCA-SVM and ARI-MA-LS-SVM using the same 100 departmental samples, 15 indicators, preprocessing and train-test splits. The competing models use feature dimensionality reduction and feature optimization, respectively, before SVM evaluation, and their inputs were reconstructed for the current dataset. The plain SVM was the fastest, while ARI-MA-LS-SVM produced accuracy close to the proposed model but required a more complex structure and longer modeling time. The comparisons suggest that the gain came not from a different classification algorithm alone but from integrating carefully weighted financial indicators with the SVM. That conclusion remains specific to the study’s data, preprocessing choices and evaluation protocol.

An ablation analysis further examined the contribution of the AHP weights. Test accuracy rose from 90.33% for an unweighted raw SVM to 93.67% for the complete AHP-weighted model, while mean fivefold cross-validation accuracy increased from 91.00% plus or minus 3.35% to 94.00% plus or minus 4.18%. Intermediate models used equal weights, AHP weights for the five highest-ranked indicators, or weights for the top ten. The overall upward trend was consistent with the hypothesis that emphasizing the most informative financial dimensions improves discrimination of settlement levels. The SVM’s own feature-importance ranking also placed personnel-expenditure, special-project and subsidy-related difference measures among its five leading indicators, broadly aligning with the independent AHP ranking.

Together, the two modules present a modular approach to internal budget control: unsupervised clustering screens for unusual expenditure patterns, while supervised classification grades departmental final accounts. The results are promising within the tested company, including a clearly preferred three-cluster solution and stable classification performance across folds, but the evidence remains bounded by the sample. The clustering dataset contained 410 records from one enterprise, while the evaluation model used 100 departmental samples. Organizational structures, budgeting practices, financial policies and control standards may differ substantially in other companies, potentially changing both cluster structure and predictive performance. In addition, changing management strategies or regulations can shift the distribution of financial data over time. The authors therefore identify cross-enterprise, cross-industry and longer-period validation, together with adaptive model updating, as necessary next steps before the framework can be considered transferable to broader financial-management environments.

Subject of Research: Machine-learning methods for clustering budget-execution anomalies and evaluating departmental financial settlement grades

Article Title: Optimization method of internal financial budget execution and control based on SVM and clustering algorithm

Article References: Liu, X. (2026). Optimization method of internal financial budget execution and control based on SVM and clustering algorithm. Discover Artificial Intelligence, 6(1), Article 1176. https://doi.org/10.1007/s44163-026-02135-w

Image Credits: AI Generated

DOI: 10.1007/s44163-026-02135-w

Keywords: enterprise budget control, Fireworks Algorithm, K-means clustering, support vector machine, Analytic Hierarchy Process, financial risk screening, departmental final accounts, budget execution, internal financial control, machine learning, Optimization, method