Abstract
The work is devoted to the application of models of Gaussian Mixture Models (GMM) and Deep Gaussian Mixture Models (DGMM) for solving clustering problems. Besides the brief review of clustering algorithms and such algorithms classification is presented. Examples of probability densities functions (PDF) for GMM and DGMM are presented. Firstly the only one-parameter systems are considered. Then the models are generalized to apply it for clustering two- and more parameters data. However the basic research deals with 2D-data. The dataset included National Hockey League (NHL) and Continental Hockey League (KHL) statistics. Some teams were divided to three groups: leaders, middle-table teams and outsiders. So it was necessary to cluster all teams in this 3 groups and deep clustering was aided to divide all teams in six groups given the championship. So important parameters for clustering are goals scored and wins in season. It is shown that a two-layer deep model has more options for clustering compared to a single-layer. A comparative analysis of the operation of clustering algorithms based on such models for the statistics of hockey championships has been performed. Thus the DGMM allows one’s to make deep clustering not only dividing to 3 table-place groups but also to determine championship.
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References
Paramita, G.: Artificial Intelligence and Machine Learning Trends in 2020 (2019). https://www.dataversity.net/artificial-intelligence-and-machine-learning-trends-in-2020/
Amber Lee, D.: The Many Dimensions of Data Quality (2019). https://www.dataversity.net/the-many-dimensions-of-data-quality/
Barja, A., Martínez, A., Arenas, A., Fleurquin, P., Nin, J., Ramasco, J.J., Tomás, E.: Assessing the risk of default propagation in interconnected sectoral financial networks. EPJ Data Sci. 8(1), 1–20 (2019). https://doi.org/10.1140/epjds/s13688-019-0211-y
Gabrielli, L., Deutschmann, E., Natale, F., Recchi, E., Vespe, M.: Dissecting global air traffic data to discern different types and trends of transnational human mobility. EPJ Data Sci. 8(1), 1–24 (2019). https://doi.org/10.1140/epjds/s13688-019-0204-x
Sajana, T., Rani, C.S., Narayana, K.V.: A survey on clustering techniques for big data mining. Ind. J. Sci. Technol. 9(3), 1–12 (2016)
Shukla, A., Cheema, G., Anand, S.: Semi-supervised clustering with neural networks. arXiv.org > cs > arXiv:1806.01547 (2018)
Bayer, S., Ravikumar, N., Strumia, M., Tong, X., Gao, Y., Ostermeier, M., Fahrig, R., Maier, A.: Intraoperative brain shift compensation using a hybrid mixture model. In: Frangi, A.F., Schnabel, J.A., Davatzikos, C., Alberola-López, C., Fichtinger, G. (eds.) MICCAI 2018. LNCS, vol. 11073, pp. 116–124. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00937-3_14
Viroli, C., McLachlan, G.J.: Deep Gaussian mixture models. Stat. Comput. 29(1), 43–51 (2017). https://doi.org/10.1007/s11222-017-9793-z
Vasil’ev, K.K., Dement’ev, V.E., Andriyanov, N.A.: Doubly stochastic models of images. Pattern Recogn. Image Anal. 25(1), 105–110 (2015). https://doi.org/10.1134/S1054661815010204
Andriyanov, N.A., Dement’ev, V.E.: Application of mixed models of random fields for the segmentation of satellite images. In: CEUR Workshop Proceedings, vol. 2210, pp. 219–226 (2018)
Andriyanov, N.A., Dementiev, V.E., Vasiliev, K.K.: Developing a filtering algorithm for doubly stochastic images based on models with multiple roots of characteristic equations. Pattern Recogn. Image Anal. 29(1), 10–20 (2019). https://doi.org/10.1134/S1054661819010048
Damianou, A., Lawrence, N.: Deep Gaussian processes. In: Artificial Intelligence and Statistics, pp. 207–215 (2013)
Zhenwen Dai, Z., Damianou, A., González, J., Neil, D., Lawrence, N.: Variational auto-encoded deep Gaussian processes. CoRR, abs/1511.06455 (2015)
Viroli, C., McLachlan, G.J.: Deep Gaussian Mixture Models. arXiv:1711.06929v1 [stat.ML] (2017)
Salimbeni, H., Deisenroth, M.: Doubly stochastic variational inference for deep Gaussian processes. Adv. Neural. Inf. Process. Syst. 30, 4588–4599 (2017)
Tim, G.J., Rudner, D.: Inter-domain deep Gaussian processes. In: NIPS 2017 Workshop (2017). http://bayesiandeeplearning.org/2017/papers/68.pdf
Tran, G., Bonilla, E., Cunningham, J.P., Michiardi, P., Filippone, M.: Calibrating deep convolutional Gaussian processes (2018)
Andriyanov, N.A., Sonin, V.A.: Using mathematical modeling of time series for forecasting taxi service orders amount. In: CEUR Workshop Proceedings, vol. 2258, pp. 462–472 (2018)
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This work was supported by Grant RFBR No. 19-29-09048.
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Andriyanov, N., Tashlinsky, A., Dementiev, V. (2021). Detailed Clustering Based on Gaussian Mixture Models. In: Arai, K., Kapoor, S., Bhatia, R. (eds) Intelligent Systems and Applications. IntelliSys 2020. Advances in Intelligent Systems and Computing, vol 1251. Springer, Cham. https://doi.org/10.1007/978-3-030-55187-2_34
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