A Hybrid Dynamic Time Warping and Multi-BMU Self-Organizing Map for Time-series Clustering

Rina Dewi Indahsari; Siti Sendari; Wahyu Sakti  Gunawan Irianto; Samsul  Arifin; Dyah Lestari

doi:10.29207/resti.v10i5.7937

Authors

Rina Dewi Indahsari Universitas Negeri Malang https://orcid.org/0009-0007-2778-2611
Siti Sendari Universitas Negeri Malang
Wahyu Sakti Gunawan Irianto Universitas Negeri Malang
Samsul Arifin Institut Teknologi dan Bisnis Asia Malang
Dyah Lestari Universitas Negeri Malang

DOI:

https://doi.org/10.29207/resti.v10i5.7937

Keywords:

dynamic time warping, multi-BMU, self-organizing map, temporal pattern analysis, time-series clustering

Abstract

Time-series clustering remains challenging because many SOM-based studies still improve either temporal similarity measurement or winner adaptation separately, leaving limited evidence on the effect of integrating both components in a single framework. This study proposes a hybrid Self-Organizing Map (SOM) that combines Dynamic Time Warping (DTW) and a multi-Best Matching Unit (multi-BMU) mechanism for temporal pattern clustering. The proposed approach replaces Euclidean distance with DTW in representative-neuron selection and extends learning from a single BMU to a top-k winner scheme with k=3. The model was evaluated on 2,505 room-lighting time-series samples of length 25 collected over 60 weeks in an office building in Indonesia. Four models were compared across 10 independent runs: M1 (standard SOM), M2 (SOM + DTW), M3 (SOM + multi-BMU), and M4 (hybrid SOM + DTW + multi-BMU). The results show that M4 achieved the best clustering quality, with the highest mean Silhouette score (0.768300), the lowest Davies–Bouldin Index (0.4011), and the highest Calinski–Harabasz Index (233.1750). In contrast, M1 retained the lowest mean Topographic Error (0.150858). Statistical tests confirmed significant differences among models. Although the proposed model increases computational complexity compared with standard SOM, the use of a DTW window constraint helps reduce the alignment cost while preserving temporal sensitivity. The integration of DTW and multi-BMU substantially improves temporal cluster quality, although it is accompanied by reduced topological preservation and increased computational complexity.

Downloads

Download data is not yet available.

References

[1] A. Alqahtani, M. Ali, X. Xie, and M. W. Jones, “Deep Time-Series Clustering: A Review,” Electronics, vol. 10, no. 23, p. 3001, Dec. 2021, doi: 10.3390/electronics10233001.

[2] C. Ji et al., “Time series classification with random temporal features,” Journal of King Saud University - Computer and Information Sciences, vol. 35, no. 9, p. 101783, Oct. 2023, doi: 10.1016/j.jksuci.2023.101783.

[3] Ł. Borchmann, D. Jurkiewicz, F. Graliński, and T. Górecki, “Dynamic Boundary Time Warping for sub-sequence matching with few examples,” Expert Systems with Applications, vol. 169, p. 114344, May 2021, doi: 10.1016/j.eswa.2020.114344.

[4] A. Javed, D. M. Rizzo, B. S. Lee, and R. Gramling, “Somtimes: self organizing maps for time series clustering and its application to serious illness conversations,” Data Mining and Knowledge Discovery, vol. 38, no. 3, pp. 813–839, 2024, doi: 10.1007/s10618-023-00979-9.

[5] A. Wibawa, A. B. Putra Utama, H. Elmunsyah, U. Pujianto, F. Dwiyanto, and L. Hernandez, “Time-series analysis with smoothed Convolutional Neural Network,” Journal of Big Data, vol. 9, p. 44, Apr. 2022, doi: 10.1186/s40537-022-00599-y.

[6] Q.-V. Doan, H. Kusaka, T. Sato, and F. Chen, “S-SOM v1.0: a structural self-organizing map algorithm for weather typing,” 2021, Accessed: Sep. 18, 2025. doi: 10.5194/gmd-14-2097-2021

[7] A. Pranolo et al., “Enhanced Multivariate Time Series Analysis Using LSTM: A Comparative Study of Min-Max and Z-Score Normalization Techniques,” ILKOM Jurnal Ilmiah, vol. 16, no. 2, pp. 210–220, Aug. 2024, doi: 10.33096/ilkom.v16i2.2333.210-220.

[8] J. K. Krishnan and K. Mitra, “A modified Kohonen map algorithm for clustering time series data,” Expert Systems with Applications, vol. 201, p. 117249, Sep. 2022, doi: 10.1016/j.eswa.2022.117249.

[9] A. W. Saputra, A. P. Wibawa, U. Pujianto, A. B. P. Utama, and A. Nafalski, “LSTM-based Multivariate Time-Series Analysis: A Case of Journal Visitors Forecasting,” ILKOM Jurnal Ilmiah, vol. 14, no. 1, pp. 57–62, Apr. 2022, doi: 10.33096/ilkom.v14i1.1106.57-62.

[10] L. E. Ekemeyong Awong and T. Zielinska, “Comparative Analysis of the Clustering Quality in Self-Organizing Maps for Human Posture Classification,” 2023, Accessed: May 06, 2026. doi: 10.3390/s23187925

[11] P. H. Franses and T. Wiemann, “Intertemporal Similarity of Economic Time Series: An Application of Dynamic Time Warping,” Computational Economics, vol. 56, no. 1, pp. 59–75, Apr. 2020, doi: 10.1007/s10614-020-09986-0.

[12] S. Sendari, A. B. P. Utama, N. S. F. Putri, P. Widiharso, and R. J. Putra, “K-Means and Fuzzy C-Means Optimization using Genetic Algorithm for Clustering Questions,” International Journal of Advanced Science and Computer Applications, vol. 1, no. 1, pp. 1–9, Jan. 2022, doi: 10.47679/ijasca.v1i1.2.

[13] A. P. Wibawa et al., “Mean-Median Smoothing Backpropagation Neural Network to Forecast Unique Visitors Time Series of Electronic Journal,” Journal of Applied Data Sciences, vol. 4, no. 3, pp. 163–174, Sep. 2023, doi: 10.47738/jads.v4i3.97.

[14] L. Bermúdez, I. Morillo, and A. Salazar, “Supervised clustering using SOM for severity-based pattern detection in urban traffic crashes,” Expert Systems with Applications, vol. 316, p. 131895, Jun. 2026, doi: 10.1016/j.eswa.2026.131895.

[15] X. Li et al., “Integration of self-organizing map and Monte Carlo simulation for ecological risk prediction of heavy metal attenuation in groundwater,” Ecotoxicology and Environmental Safety, vol. 302, p. 118761, Sep. 2025, doi: 10.1016/j.ecoenv.2025.118761.

[16] K. Li et al., “Using dynamic time warping self-organizing maps to characterize diurnal patterns in environmental exposures,” Scientific Reports, vol. 11, no. 1, p. 24052, Dec. 2021, doi: 10.1038/s41598-021-03515-1.

[17] M. C. G. Kopland and E. J. Giltay, “Dynamic Time Warp (DTW) as a scalable, data-efficient, and clinically relevant analysis of dynamic processes in patients with psychiatric disorders: a tutorial,” Journal of Eating Disorders, vol. 13, no. 1, p. 230, Oct. 2025, doi: 10.1186/s40337-025-01414-8.

[18] S. Sendari et al., “Common-Sensical Incentive Reward in Deep Actor-Critic Reinforcement Learning for Mobile Robot Navigation,” 2024, ICIC International 学会: 02. doi: 10.24507/ijicic.20.02.373.

[19] K. Li et al., “Using dynamic time warping self-organizing maps to characterize diurnal patterns in environmental exposures,” Scientific Reports, vol. 11, no. 1, p. 24052, Dec. 2021, doi: 10.1038/s41598-021-03515-1.

[20] L. Qiu, C. Qiu, and C. Song, “ESDTW: Extrema-based shape dynamic time warping,” Expert Systems with Applications, vol. 239, p. 122432, Apr. 2024, doi: 10.1016/j.eswa.2023.122432.

[21] N. Kumar, S. K. Sood, and M. Saini, “Internet of Vehicles (IoV) based Framework for Vehicle Degradation using Multidimensional Dynamic Time Warping (MDTW),” Expert Systems with Applications, vol. 224, p. 120038, Aug. 2023, doi: 10.1016/j.eswa.2023.120038.

[22] N. Vaughan, “Nearest centroid classifier for multivariate time series using DTW-MP centroid,” Expert Systems with Applications, vol. 318, p. 132069, Jul. 2026, doi: 10.1016/j.eswa.2026.132069.

[23] N. P. Rougier and G. Is. Detorakis, “Randomized Self-Organizing Map,” Neural Comput, vol. 33, no. 8, pp. 2241–2273, Jul. 2021, doi: 10.1162/neco_a_01406.

[24] T. Widiyaningtyas, I. A. E. Zaeni, and P. Y. Wahyuningrum, “Self-Organizing Map (SOM) For Diagnosis Coronary Heart Disease,” 2019 4th International Conference on Information Technology, Information Systems and Electrical Engineering (ICITISEE), pp. 286–289, Nov. 2019, doi: 10.1109/ICITISEE48480.2019.9003746.

[25] G. C. Cardarilli, L. Di Nunzio, R. Fazzolari, M. Re, and S. Spano, “AW-SOM, an Algorithm for High-Speed Learning in Hardware Self-Organizing Maps,” IEEE Trans. Circuits Syst. II, vol. 67, no. 2, pp. 380–384, Feb. 2020, doi: 10.1109/TCSII.2019.2909117.

[26] H. Mayatopani and N. Handayani, “Implementation of Self-Organizing Map (SOM) Algorithm for Image Classification of Medicinal Weeds,” Dec. 2023, Accessed: Apr. 13, 2024. doi: 10.29207/resti.v7i3.4755

[27] N. M. Hai, T. V. Lang, and T. The Van, “Improving the Efficiency of Semantic Image Retrieval Using a Combined Graph and SOM Model,” IEEE Access, vol. 11, pp. 140646–140659, 2023, doi: 10.1109/ACCESS.2023.3333678.

[28] X. Fan, S. Zhang, X. Xue, R. Jiang, S. Fan, and H. Kou, “An Improved Self-Organizing Map (SOM) Based on Virtual Winning Neurons,” Symmetry, vol. 17, no. 3, p. 449, Mar. 2025, doi: 10.3390/sym17030449.

[29] S. Jamil et al., “Multi Self-Organizing Map (SOM) Pipeline Architecture for Multi-View Clustering,” IEEE Access, vol. 12, pp. 85806–85821, 2024, doi: 10.1109/ACCESS.2024.3412950.

[30] A. Abdelaziz, V. Santos, M. S. Dias, and A. N. Mahmoud, “A hybrid model of self-organizing map and deep learning with genetic algorithm for managing energy consumption in public buildings,” Journal of Cleaner Production, vol. 434, p. 140040, Jan. 2024, doi: 10.1016/j.jclepro.2023.140040.

[31] J. Deng et al., “Potential Global Invasion Risk of Scale Insect Pests Based on a Self-Organizing Map,” Insects, vol. 14, no. 7, p. 572, Jun. 2023, doi: 10.3390/insects14070572.

[32] S. Licen, A. Astel, and S. Tsakovski, “Self-organizing map algorithm for assessing spatial and temporal patterns of pollutants in environmental compartments: A review,” Science of The Total Environment, vol. 878, p. 163084, Jun. 2023, doi: 10.1016/j.scitotenv.2023.163084.