Оцінювання біологічного віку з використанням мереж Колмогорова–Арнольда на малих даних
This article explores the issue of the application of Kolmogorov–Arnold Networks (KAN) for biological age estimation using a dataset of 344 male patients. The dataset includes biomarkers related to bone health and body composition. To enhance model performance, data preprocessing techniques such as...
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| author | Slipchenko, Volodymyr Poliahushko, Liubov Rudyk, Volodymyr Shatylo, Vladyslav |
| author_facet | Slipchenko, Volodymyr Poliahushko, Liubov Rudyk, Volodymyr Shatylo, Vladyslav |
| author_institution_txt_mv | [
{
"author": "Volodymyr Slipchenko",
"institution": "National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv"
},
{
"author": "Liubov Poliahushko",
"institution": "National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv"
},
{
"author": "Volodymyr Rudyk",
"institution": "National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv"
},
{
"author": "Vladyslav Shatylo",
"institution": "National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv"
}
] |
| author_sort | Slipchenko, Volodymyr |
| baseUrl_str | http://journal.iasa.kpi.ua/oai |
| collection | OJS |
| datestamp_date | 2026-06-30T06:14:59Z |
| description | This article explores the issue of the application of Kolmogorov–Arnold Networks (KAN) for biological age estimation using a dataset of 344 male patients. The dataset includes biomarkers related to bone health and body composition. To enhance model performance, data preprocessing techniques such as polynomial interpolation for missing values and standardization were applied. Pearson and Spearman correlation analyses identified the most relevant biomarkers. Machine learning models were evaluated, along with neural networks and KANs. Experimental results demonstrate that KANs outperform traditional machine learning models and classical neural networks on small datasets. The optimal KAN architecture achieved a correlation coefficient of 0.93, a mean squared error of 18.81, and a mean absolute error of 2.8, surpassing the best-performing conventional models. These findings highlight the potential of KANs as a robust alternative for biological age estimation in resource-limited settings. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2026.2.12 |
| first_indexed | 2026-07-01T01:00:23Z |
| format | Article |
| fulltext |
V. H. Slipchenko, L. H. Poliahushko, V. I. Rudyk, V. V. Shatylo, 2026
Системні дослідження та інформаційні технології, 2026, № 2 183
UDC 004.89
DOI: 10.20535/SRIT.2308-8893.2026.2.12
ESTIMATING BIOLOGICAL
AGE USING KOLMOGOROV–ARNOLD NETWORKS
ON SMALL DATA
V.H. SLIPCHENKO, L.H. POLIAHUSHKO, V.I. RUDYK, V.V. SHATYLO
Abstract. This article explores the issue of the application of Kolmogorov–Arnold
Networks (KAN) for biological age estimation using a dataset of 344 male patients.
The dataset includes biomarkers related to bone health and body composition.
To enhance model performance, data preprocessing techniques such as polynomial
interpolation for missing values and standardization were applied. Pearson and
Spearman correlation analyses identified the most relevant biomarkers. Machine
learning models were evaluated, along with neural networks and KANs. Experimental
results demonstrate that KANs outperform traditional machine learning models and
classical neural networks on small datasets. The optimal KAN architecture achieved
a correlation coefficient of 0.93, a mean squared error of 18.81, and a mean absolute
error of 2.8, surpassing the best-performing conventional models. These findings
highlight the potential of KANs as a robust alternative for biological age estimation
in resource-limited settings.
Keywords: Kolmogorov–Arnold Networks, biological age, bone mass density,
machine learning, deep learning.
INTRODUCTION
Biological age (BA) is a comprehensive indicator of the functional state of the
human body. Unlike chronological age, which counts years from birth, biological
age assesses the physiological state of different body systems, reflecting the actual
rate of aging processes [1–3]. Typically, the assessment of biological age relies on
specific health markers, known as biomarkers.
One effective method for estimating biological age involves analyzing bone
tissue conditions. Age-related changes in bone density and structural characteristics
serve as reliable biomarkers, indicating an individual’s aging process and risks for
conditions such as osteoporosis and bone fractures [4]. Osteoporosis has become a
growing global health concern. Prevalence statistics for osteoporosis vary
significantly across populations: approximately 10 million individuals aged over
50 in the United States; 50 % of women and 20 % of men over 50 in the United
Kingdom; 25–62 % of postmenopausal women in India; and nearly 50 % of
individuals aged over 60 in Ukraine [5]. These data highlight the critical need for
accurate and timely diagnostic and preventive measures.
Conventionally, statistical methods such as regression analysis and principal
component analysis have been used to estimate biological age [6]. However,
machine learning, in particular neural network-based models, has recently emerged
as a more efficient approach for managing complex and multidimensional medical
data. For instance, neural network models such as ST-ResNet achieved a mean
absolute error (MAE) of only 0.455 years, while BoNet+ showed a MAE of 0.76
V. H. Slipchenko, L. H. Poliahushko, V. I. Rudyk, V. V. Shatylo
ISSN 1681–6048 System Research & Information Technologies, 2026, № 2 184
years, even when dealing with low-quality X-ray images [7, 8]. Nevertheless, these
advanced models generally require large training datasets.
However, a significant challenge in this field remains the accurate prediction
of biological age when small datasets are available. This situation is common in
medical research conducted in resource-limited countries such as Ukraine. Under
such conditions, classical machine learning methods often show errors of more than
six years [9, 10]. One potential solution to this issue is the application of
Kolmogorov–Arnold Networks (KAN) [11], which have recently demonstrated
high performance even with limited data samples [12, 13].
The aim of this study is to evaluate the effectiveness of Kolmogorov–Arnold
Networks (KAN) in estimating the biological age of men by analyzing their bone
tissue conditions, particularly in situations of limited data availability.
To this aim, the following objectives have been defined:
analyze and preprocess medical data to identify correlations between bone
health indicators and biological age;
compare the predictive accuracy of KAN with traditional machine learning
methods and other neural network models;
determine the optimal configuration and parameters of the KAN model for
the most accurate biological age estimation.
The results of this study will help improve methods for early detection of bone
aging and risk assessment for osteoporosis. The results can support preventive
healthcare globally and help advance biological age research, especially in
countries such as Ukraine, where collecting large amounts of medical data is
difficult.
MATERIALS AND METHODS
Dataset. In this study, a dataset provided by the D.F. Chebotarev Institute of
Gerontology of the National Academy of Medical Sciences of Ukraine [14] was
used. The dataset includes the following biomarker indicators: body mass index
(BMI), the fracture risk assessment tool score (FRAX) for all bones and the hip
only, data on bone mass density of the lumbar spine, right and left femoral neck,
proximal right and left femur, radial bone, and trabecular bone score, obtained from
345 male patients aged 40 to 92 years (mean age 59 years). More detailed
information about the dataset is provided in Table 1.
T a b l e 1 . Detailed information about the dataset
Biomarker name Unit Mean SE
Body mass index (BMI) kg/m2 27.182 0.243
10-year probability of major osteoporotic fractures (FRAX-all) % 3.174 0.085
10-year probability of hip fractures (FRAX-hip) % 1.771 0.044
Lumbar spine bone mineral density (LS-BMD) g/cm2 1.023 0.011
Femoral right neck bone mineral density (FN-BMD-R) g/cm2 0.765 0.008
Femoral left neck bone mineral density (FN-BMD-L) g/cm2 0.767 0.008
Proximal right femur (hip) bone mineral density (Hip-BMD-R) g/cm2 0.955 0.009
Proximal left femur (hip) bone mineral density (Hip-BMD-L) g/cm2 0.964 0.009
Bone mineral density ultra-distal radius of the forearm (UDR-BMD) g/cm2 0.744 0.005
The trabecular bone scores (TBS) units 1.32 0.006
Estimating biological age using Kolmogorov–Arnold networks on small data
Системні дослідження та інформаційні технології, 2026, № 2 185
Pre-processing. To restore missing values in the dataset, a second-order
polynomial interpolation method was used, specifically the interpolate method with
the order = 2 parameter from the pandas library [15]. This method approximates
missing data by constructing a polynomial of the specified order. This approach
allows for the retention of rows where only a few indicators have missing values,
thereby increasing the accuracy of subsequent analysis.
For data normalization, the StandardScaler method from the sklearn library [16]
was employed, which scales the values of all indicators to a range from -1 to 1, with
the mean value being centered around zero. The transformation is implemented
through the following formulas: 𝑧 = 𝑥 − 𝜇𝜎 , 𝜇 = 1𝑛 (𝑥 ),
𝜎 = 1𝑛 (𝑥 − 𝜇) ,
where z is the scale value; x is the current value; μ is the mean value; n is the sample
size; and σ is the standard deviation.
This transformation ensures that all features contribute equally to the learning
process, preventing any single variable from dominating due to differences in scale.
Correlations. To evaluate the correlation of indicators with the target
variable, namely the chronological age of participants, Pearson and Spearman
correlation coefficients were used [17]. Pearson’s method measures the linear
relationship between continuous variables, while Spearman’s coefficient assesses
monotonic relationships and is more robust against outliers and non-normally
distributed data. The p-value was used to determine the statistical significance of
the observed correlations [18], with correlations at p < 0.05 considered statistically
significant. The t-statistic was calculated to quantify how much the observed
correlations deviate from zero in terms of standard error [19].
Accuracy metrics. To evaluate the effectiveness and accuracy of the
predictions, several metrics were used, including the coefficient of determination
(R2), mean absolute error (MAE), mean squared error (MSE), and the Pearson’s
correlation coefficient (r) between chronological and biological age. R2 measures
how well a model explains the variance in the target variable (ranging from 0 to 1).
MAE measures the average absolute error and is less sensitive to outliers, while
MSE squares the errors, making it more sensitive to larger discrepancies.
Machine learning. For machine learning tasks, the sklearn library was
utilized, along with compatible libraries such as xgboost [20], lightgbm [21], and
catboost [22], which provide enhanced and specialized models. These libraries
offer a comprehensive range of algorithms, from classical methods like linear
regression, decision trees, and K-nearest neighbors to advanced techniques like
boosting, bagging, and ensemble models. The inclusion of xgboost and lightgbm
brings efficient gradient boosting algorithms that are highly effective in handling
large datasets, while catboost offers robust solutions for categorical data. Together,
these libraries enable the use of both traditional and state-of-the-art machine
learning models.
V. H. Slipchenko, L. H. Poliahushko, V. I. Rudyk, V. V. Shatylo
ISSN 1681–6048 System Research & Information Technologies, 2026, № 2 186
To find the optimal parameters for testing each of the models, the
GridSearchCV method from the sklearn library was used. It performs cross-
validation for each combination of parameters, allowing the selection of the best-
performing set of hyperparameters based on model performance metrics. This
process helps ensure that the model achieves its maximum efficiency by tuning
parameters such as learning rate, number of estimators, or maximum depth,
depending on the specific algorithm used.
For deep learning, the Keras library was employed, built on top of TensorFlow
[23], providing a flexible and efficient framework for neural network development.
The optimizers module from TensorFlow was used to fine-tune model training,
offering various optimization algorithms such as Adagrad, Adam, and RMSprop to
enhance convergence speed and accuracy. Additionally, the metrics module was
used to track model performance during training and validation, ensuring effective
evaluation of loss and accuracy. To improve network expressiveness, the
Parametric Rectified Linear Unit (PReLU) activation layer was incorporated [24],
allowing adaptive learning of activation parameters, which helps mitigate issues
like vanishing gradients and enhances model generalization. These components
collectively contributed to the effective implementation and optimization of neural
network models in this study.
In 2024, Kolmogorov–Arnold Networks (KAN) were introduced as a
promising alternative to Multi-Layer Perceptron (MLP) [25]. Unlike MLPs, which
have fixed activation functions on nodes (neurons), KANs have learnable activation
functions on edges (weights). KANs do not have linear weights – each weight
parameter is replaced by a univariate function parameterized as a spline. To work
with the software implementation of these networks, the pykan library [26]
developed by the authors of the original article was used.
RESULTS
To preserve information in the already small dataset, the data was first sorted by
chronological age. Then, polynomial interpolation was used to replace all zero or
missing values with approximated values based on the neighboring patients’ ages. This
approach allowed retaining rows with missing values for some markers, instead
of discarding them and filling in the missing data with values close to the actual ones.
As a result of the initial processing, the dataset contains 344 rows, each
consisting of 10 biomarkers and the patients’ chronological ages (Fig. 1).
Fig. 1. Initial data set
Estimating biological age using Kolmogorov–Arnold networks on small data
Системні дослідження та інформаційні технології, 2026, № 2 187
Using Pearson and Spearman methods, the corresponding correlation
coefficients, p-values, and t-statistics were obtained, as presented in Table 2.
Given the low correlation, the variables with an absolute correlation of less
than 0.15, namely BMI, LS-BMD, Hip-BMD-R, and Hip-BMD-L, were excluded
from the dataset. After this, all data were standardized using the StandardScaler
method and split into two parts: the training set (75 %, 258 rows) and the test set
(25 %, 86 rows).
T a b l e 2 . Correlation of biomarkers with chronological age
Biomarker
name
Pearson’s
correlation
Pearson’s
p-value
Pearso’s
t-statistics
Spearman’s
correlation
Spearman’s
p-value
Spearman’s
t-statistics
BMI 0.012 8.30618×10-1 0.2141 0.008 8.84701×10-1 0.1451
FRAX-all 0.176 1.05890×10-3 3.3027 0.231 1.53804×10-5 4.3862
FRAX-hip 0.636 2.55892×10-40 15.2229 0.726 1.17256×10-57 19.5464
LS-BMD 0.129 1.68264×10-2 2.4023 0.115 3.32615×10-2 2.1376
FN-BMD-R -0.192 3.45605×10-4 -3.6149 -0.199 1.98422×10-4 -3.7618
FN-BMD-L -0.180 8.04475×10-4 -3.3815 -0.202 1.63985×10-4 -3.8112
Hip-BMD-R -0.132 1.40984×10-2 -2.4674 -0.128 1.71852×10-2 -2.3944
Hip-BMD-L -0.123 2.24059×10-2 -2.2938 -0.132 1.45014×10-2 -2.4571
UDR-BMD -0.357 9.13084×10-12 -7.0636 -0.354 1.35219×10-11 -7.0009
TBS -0.192 3.49754×10-4 -3.6117 -0.224 2.82140×10-5 -4.2448
For the automatic selection of the best parameters for training the machine
learning models, the GridSearchCV method was used with the accuracy parameter
set to neg_mean_squared_error. The obtained results are presented in Table 3.
T a b l e 3 . Best parameters for training models
Model’s name Best parameters
KNeighborsRegressor 'n_neighbors': 5
GradientBoostingRegressor 'max_depth': 4, 'n_estimators': 200
RandomForestRegressor 'max_depth': 10, 'n_estimators': 200
XGBRegressor 'learning_rate': 0.1, 'max_depth': 3, 'n_estimators': 100
LGBMRegressor 'learning_rate': 0.1, 'max_depth': 4, 'n_estimators': 100
CatBoostRegressor 'depth': 5, 'iterations': 200, 'learning_rate': 0.1
AdaBoostRegressor 'estimator': XGBRegressor(), 'learning_rate': 0.5,
'n_estimators': 50
BaggingRegressor 'max_samples': 1.0, 'n_estimators': 500
BayesianRidge 'alpha_1': 1e-06, 'alpha_2': 1e-06, 'lambda_1': 1e-08,
'lambda_2': 1e-06
ElasticNet 'alpha': 0.01, 'l1_ratio': 0.1, 'max_iter': 500
PLSRegression 'n_components': 4
DecisionTreeRegressor 'max_depth': 30, 'min_samples_split': 5
Lasso 'alpha': 0.1
MLPRegressor 'activation': 'relu', 'alpha': 0.01, 'hidden_layer_sizes':
(50, 50), 'max_iter': 3000, 'solver': 'adam'
After determining the optimal parameters, the models were trained and tested,
with the results shown in Table 4. The highest accuracy metrics were achieved
by the CatBoostRegressor model, with a correlation coefficient between the
predicted biological and chronological age of 0.92, MSE of 21.71, MAE of 3.12,
and R2 of 0.84.
V. H. Slipchenko, L. H. Poliahushko, V. I. Rudyk, V. V. Shatylo
ISSN 1681–6048 System Research & Information Technologies, 2026, № 2 188
T a b l e 4 . Machine learning model testing results
Model’s name r MSE MAE R2 Time, s
KNeighborsRegressor 0.7051 73.0693 6.7744 0.4693 0.0046
GradientBoostingRegressor 0.9055 25.5564 3.2612 0.8144 0.1401
RandomForestRegressor 0.9122 23.8812 3.1461 0.8265 0.2318
XGBRegressor 0.9146 23.1514 3.0412 0.8319 0.0264
LGBMRegressor 0.9065 25.0477 3.1219 0.8181 0.0137
CatBoostRegressor 0.9231 21.7106 3.1161 0.8423 0.1668
AdaBoostRegressor 0.9162 23.1531 3.1663 0.8318 2.1076
BaggingRegressor 0.9147 23.2832 3.0378 0.8309 0.8463
BayesianRidge 0.7788 59.1709 6.4304 0.5703 0.0034
ElasticNet 0.7789 59.3665 6.4434 0.5688 0.0019
PLSRegression 0.7750 59.2691 6.4271 0.5695 0.0031
DecisionTreeRegressor 0.8882 30.5093 3.7819 0.7784 0.0025
Lasso 0.7795 59.5585 6.4594 0.5674 0.0019
MLPRegressor 0.9123 24.1630 3.3032 0.8245 2.9501
In addition to the selected machine learning methods, several neural network
models with different architectures were tested (the number of neurons in the
corresponding layers is indicated in the name, e.g., MLP_64_32_1 – first layer with
64 neurons, second layer with 32 neurons, third layer with 1 neuron). The following
fixed parameters were chosen for each network: Adagrad optimizer with a learning
rate of 0.01, mean absolute error loss function and batch_size equal to 25.
The best accuracy was achieved by the model with the following architecture:
an input layer with 6 neurons (corresponding to the number of input parameters),
the first hidden layer with 128 neurons, the second hidden layer with 64 neurons,
the third hidden layer with 16 neurons, and an output layer with 1 neuron. After
testing, it demonstrated the following results: a correlation coefficient between the
predicted biological and chronological age of 0.91, MSE of 22.83, MAE of 3.13,
and R2 of 0.83. A comparison with other models is presented in Table 5.
T a b l e 5 . Results of testing classical neural networks
Model’s name r MSE MAE R2 Time, s
MLP_256_128_64_16_1 0.8823 35.7992 4.3178 0.7401 1.2639
MLP_128_64_32_16_1 0.9098 27.2812 3.8839 0.8018 1.4921
MLP_128_32_16_8_1 0.8993 26.3451 3.5427 0.8086 1.9737
MLP_64_32_16_8_1 0.9056 24.8910 3.7605 0.8192 2.9644
MLP_32_16_8_1 0.8487 39.5009 4.7729 0.7131 4.4202
MLP_16_64_32_16_1 0.9039 25.4172 3.4627 0.8154 3.0542
MLP_64_32_1 0.8585 43.9039 4.3985 0.6990 5.1929
MLP_128_64_16_1 0.9146 22.8338 3.1285 0.8341 2.1848
Several variants of the Kolmogorov–Arnold network were also tested, as
shown in Table 6. The corresponding architectural parameters are specified in the
model’s name: KAN_6_1_1_grid3_k3 – input layer dimension 6, number of hidden
neurons 1, output layer dimension 1, grid intervals 3, cubic spline 3.
The optimal architecture was found to be the KAN model with 6 input para-
meters, 3 hidden layers, a grid size of 3, and a spline of order 5. The correlation
coefficient reached 0.93, MSE was 18.81, MAE was 2.8, and R2 was 0.86.
Estimating biological age using Kolmogorov–Arnold networks on small data
Системні дослідження та інформаційні технології, 2026, № 2 189
T a b l e 6 . Results of testing Kolmogorov–Arnold networks
Model’s name r MSE MAE R2 Time, s
KAN_6_1_1_grid3_k3 0.8998 26.7811 3.4477 0.8055 3.5169
KAN_6_3_1_grid3_k3 0.9146 22.8338 3.1285 0.8342 4.3357
KAN_6_6_1_grid3_k3 0.9237 20.9441 2.9502 0.8479 4.8969
KAN_6_12_1_grid3_k3 0.9250 20.0287 2.8131 0.8545 6.0963
KAN_6_1_1_grid6_k3 0.8998 26.7811 3.4476 0.8055 3.5388
KAN_6_3_1_grid6_k3 0.9323 18.8108 2.7960 0.8634 4.3032
KAN_6_6_1_grid6_k3 0.9237 20.9441 2.9502 0.8479 4.8697
KAN_6_12_1_grid6_k3 0.9250 20.0287 2.8131 0.8545 6.1817
KAN_6_1_1_grid3_k5 0.8998 26.7811 3.4476 0.8055 3.5465
KAN_6_3_1_grid3_k5 0.9323 18.8108 2.7960 0.8634 4.2122
KAN_6_6_1_grid3_k5 0.9237 20.9441 2.9502 0.8479 4.8501
For each of the best models, the corresponding correlation plots between the
predicted biological and chronological age were constructed (Fig. 2).
Fig. 2. Correlation graphs of models with the best accuracy rates
Fig. 3 visualizes the architecture of the network that demonstrated the highest
accuracy, namely KAN_6_3_1_grid3_k5.
Fig. 3. Network architecture KAN_6_3_1_grid3_k5
V. H. Slipchenko, L. H. Poliahushko, V. I. Rudyk, V. V. Shatylo
ISSN 1681–6048 System Research & Information Technologies, 2026, № 2 190
DISCUSSION
This study is the first to apply the Kolmogorov–Arnold Networks (KAN) method
for determining the biological age of men based on bone mineral density (BMD)
parameters and several other key biomarkers. The obtained results demonstrate
high estimation accuracy (correlation coefficient r = 0.93, MAE = 2.8 years),
surpassing classical approaches, including conventional and advanced machine
learning models as well as deep learning techniques.
In comparison with previous studies, one notable work is that of Grygorieva
et al. [27], which analyzed a mixed sample of 121 individuals (77 women and
44 men) and employed multiple regression methods to estimate the biological age
of bone tissue. That study achieved a correlation coefficient r = 0.615 and
MAE = 8.16 years. In our research, despite utilizing a larger dataset (344
participants, all male), the accuracy significantly improved due to the
implementation of KAN. This underscores the ability of KAN to more effectively
model the nonlinear relationships between biomarkers and biological age.
Another relevant example is a model developed for estimating the biological
age of women, which analyzed a dataset with over 3200 individuals and achieved
high accuracy (r = 0.93-0.94 and MAE = 2.1-2.2 years) [5]. However, this model
was trained on a substantially larger dataset. In contrast, our method achieves
comparable results (MAE = 2.8 years) even with a smaller sample size (344 men).
This suggests that KAN can be an effective solution for tasks with limited data
availability, particularly when focusing on the male population's specific
characteristics.
A distinctive feature of this study is its exclusive focus on a male cohort. Many
previous studies either primarily included women or utilized mixed samples, which
could introduce biases due to sex-based differences in bone structure and density.
By concentrating solely on men, we developed a more stable and homogeneous
model that better accounts for the specific age-related and metabolic characteristics
of the male body.
Another advantage of the proposed approach is its reliance on numerical
biomarkers (such as DXA and FRAX) rather than imaging data, making the model
less dependent on variations in diagnostic equipment settings and types. This
universality facilitates the system's implementation in different clinical settings and
could enhance the accuracy of osteoporosis risk screening and other age-related
bone conditions.
Nevertheless, certain limitations should be noted. First, despite achieving
higher accuracy compared to traditional methods, the overall sample size (344
individuals) remains relatively small for broad population generalizations. Second,
the study was conducted exclusively on Ukrainian men, which may affect the
generalizability of the results to other ethnic groups. Future research aims to expand
the dataset, including representatives from different age groups, and further analyze
the practical aspects of implementing this method in clinical practice.
Thus, the application of the Kolmogorov–Arnold Networks method for
determining the biological age of men has demonstrated high accuracy and superiority
over classical approaches. The obtained results have potential applications in the early
prediction of age-related changes in the skeletal system and the timely diagnosis of
osteoporosis. Additionally, they could serve as a foundation for developing
personalized recommendations in preventive and sports medicine.
Estimating biological age using Kolmogorov–Arnold networks on small data
Системні дослідження та інформаційні технології, 2026, № 2 191
CONCLUSIONS
As a result of this study, Kolmogorov–Arnold Networks (KAN) were applied for
the first time to estimate biological age, leading to the following conclusions:
– the indicators of bone mineral density in men show a sufficient correlation
with chronological age, making them viable for biological age estimation;
– when estimating the biological age of men based on bone mineral density data,
machine learning methods based on boosting, particularly the CatBoostRegressor,
yield slightly better results (r=0.92, MSE=21.71, MAE=3.12, R²=0.84) compared
to neural network models (r=0.91, MSE=22.83, MAE=3.13, R²=0.83);
– in an identical task, Kolmogorov–Arnold Networks demonstrated a slightly
higher correlation between chronological and biological age (r=0.93), but significantly
lower errors (MSE=18.81, MAE=2.8, R²=0.86), indicating superior performance;
– given the limited dataset, the results suggest that KAN models outperform
neural networks and other machine learning methods, particularly in small data
scenarios.
ACKNOWLEDGMENTS
The authors would like to thank DSc, Prof. N. Grygorieva and PhD, Sr. Research Fellow
A. Musiienko from the D.F. Chebotarev Institute of Gerontology of the National
Academy of Medical Sciences of Ukraine for providing the data used in this study.
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Received 26.03.2025
Estimating biological age using Kolmogorov–Arnold networks on small data
Системні дослідження та інформаційні технології, 2026, № 2 193
INFORMATION ON THE ARTICLE
Volodymyr H. Slipchenko, ORCID: 0000-0002-3405-0781, National Technical
University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine, e-mail:
ddpolytechnic2016@gmail.com
Liubov H. Poliahushko, ORCID: 0000-0003-3287-8523, National Technical University
of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine, e-mail:
liubovpoliagushko@gmail.com
Volodymyr I. Rudyk, ORCID: 0009-0004-4774-6579, National Technical University of
Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine, e-mail:
rudyk.volodymyr@lll.kpi.ua
Vladyslav V. Shatylo, ORCID: 0000-0001-5395-2097, National Technical University of
Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine, e-mail: v.shatylo@kpi.ua
ОЦІНЮВАННЯ БІОЛОГІЧНОГО ВІКУ З ВИКОРИСТАННЯМ МЕРЕЖ
КОЛМОГОРОВА–АРНОЛЬДА НА МАЛИХ ДАНИХ / В.Г. Сліпченко,
Л.Г. Полягушко, В.І. Рудик, В.В. Шатило
Анотація. Досліджено можливості застосування мереж Колмогорова–
Арнольда (KAN) для оцінювання біологічного віку на основі аналізу вибірки,
що складалася з 344 чоловіків. Набір даних містить біомаркери, які
характеризують стан кісткової тканини та склад тіла. Для підвищення точності
прогнозування використано методи попереднього оброблення даних, зокрема
поліноміальну інтерполяцію пропущених значень і стандартизацію показників.
Кореляційний аналіз за Пірсоном і Спірменом дав змогу визначити найбільш
значущі біомаркери для побудови моделі. Здійснено порівняльне тестування
традиційних моделей машинного навчання, класичних нейронних мереж і
мереж KAN. Результати експерименту показали, що архітектура KAN
перевершує інші підходи за роботи з невеликими вибірками. Зокрема,
оптимальна конфігурація KAN продемонструвала коефіцієнт кореляції 0,93,
середньоквадратичну помилку 18,81 та середню абсолютну помилку 2,8 року,
що є суттєво кращими показниками, ніж у конвенційних моделей. Отримано
результати, що підтверджують перспективність використання KAN для
оцінювання біологічного віку, особливо в умовах обмежених наборів медичних
даних.
Ключові слова: мережі Колмогорова–Арнольда (KAN), біологічний вік,
мінеральна щільність кісткової тканини, машинне навчання, глибинне
навчання.
|
| id | journaliasakpiua-article-365272 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-01T01:00:23Z |
| publishDate | 2026 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
| record_format | ojs |
| resource_txt_mv | journaliasakpiua/db/58884a6b565340e71e941a2ff662aedb.pdf |
| spelling | journaliasakpiua-article-3652722026-06-30T06:14:59Z Estimating biological age using Kolmogorov–Arnold networks on small data Оцінювання біологічного віку з використанням мереж Колмогорова–Арнольда на малих даних Slipchenko, Volodymyr Poliahushko, Liubov Rudyk, Volodymyr Shatylo, Vladyslav мережі Колмогорова–Арнольда біологічний вік мінеральна щільність кісткової тканини машинне навчання глибинне навчання Kolmogorov–Arnold Networks biological age bone mass density machine learning deep learning This article explores the issue of the application of Kolmogorov–Arnold Networks (KAN) for biological age estimation using a dataset of 344 male patients. The dataset includes biomarkers related to bone health and body composition. To enhance model performance, data preprocessing techniques such as polynomial interpolation for missing values and standardization were applied. Pearson and Spearman correlation analyses identified the most relevant biomarkers. Machine learning models were evaluated, along with neural networks and KANs. Experimental results demonstrate that KANs outperform traditional machine learning models and classical neural networks on small datasets. The optimal KAN architecture achieved a correlation coefficient of 0.93, a mean squared error of 18.81, and a mean absolute error of 2.8, surpassing the best-performing conventional models. These findings highlight the potential of KANs as a robust alternative for biological age estimation in resource-limited settings. Досліджено можливості застосування мереж Колмогорова–Арнольда (KAN) для оцінювання біологічного віку на основі аналізу вибірки, що складалася з 344 чоловіків. Набір даних містить біомаркери, які характеризують стан кісткової тканини та склад тіла. Для підвищення точності прогнозування використано методи попереднього оброблення даних, зокрема поліноміальну інтерполяцію пропущених значень і стандартизацію показників. Кореляційний аналіз за Пірсоном і Спірменом дав змогу визначити найбільш значущі біомаркери для побудови моделі. Здійснено порівняльне тестування традиційних моделей машинного навчання, класичних нейронних мереж і мереж KAN. Результати експерименту показали, що архітектура KAN перевершує інші підходи за роботи з невеликими вибірками. Зокрема, оптимальна конфігурація KAN продемонструвала коефіцієнт кореляції 0,93, середньоквадратичну помилку 18,81 та середню абсолютну помилку 2,8 року, що є суттєво кращими показниками, ніж у конвенційних моделей. Отримано результати, що підтверджують перспективність використання KAN для оцінювання біологічного віку, особливо в умовах обмежених наборів медичних даних. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2026-06-30 Article Article Peer-reviewed Article application/pdf https://journal.iasa.kpi.ua/article/view/365272 10.20535/SRIT.2308-8893.2026.2.12 System research and information technologies; No. 2 (2026); 183-193 Системные исследования и информационные технологии; № 2 (2026); 183-193 Системні дослідження та інформаційні технології; № 2 (2026); 183-193 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/365272/350719 |
| spellingShingle | мережі Колмогорова–Арнольда біологічний вік мінеральна щільність кісткової тканини машинне навчання глибинне навчання Slipchenko, Volodymyr Poliahushko, Liubov Rudyk, Volodymyr Shatylo, Vladyslav Оцінювання біологічного віку з використанням мереж Колмогорова–Арнольда на малих даних |
| title | Оцінювання біологічного віку з використанням мереж Колмогорова–Арнольда на малих даних |
| title_alt | Estimating biological age using Kolmogorov–Arnold networks on small data |
| title_full | Оцінювання біологічного віку з використанням мереж Колмогорова–Арнольда на малих даних |
| title_fullStr | Оцінювання біологічного віку з використанням мереж Колмогорова–Арнольда на малих даних |
| title_full_unstemmed | Оцінювання біологічного віку з використанням мереж Колмогорова–Арнольда на малих даних |
| title_short | Оцінювання біологічного віку з використанням мереж Колмогорова–Арнольда на малих даних |
| title_sort | оцінювання біологічного віку з використанням мереж колмогорова–арнольда на малих даних |
| topic | мережі Колмогорова–Арнольда біологічний вік мінеральна щільність кісткової тканини машинне навчання глибинне навчання |
| topic_facet | мережі Колмогорова–Арнольда біологічний вік мінеральна щільність кісткової тканини машинне навчання глибинне навчання Kolmogorov–Arnold Networks biological age bone mass density machine learning deep learning |
| url | https://journal.iasa.kpi.ua/article/view/365272 |
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