Article Sidebar
Main Article Content
In this paper we propose a novel algorithm based on the use of Principal Components Analysis for the determination of spherical coordinates of sampled cosmic ray flux distribution. We have also applied a deep neural network with encoder-decoder (E-D) architecture in order to filter-off variance noises introduced by sampling. We conducted a series of experiments testing the effectiveness of our estimations. The training set consisted of 92250 images and validation set of 37800 images. We have calculated mean absolute error (MAE) between real values and estimations. When E-D is applied, the number of cases (estimations) where MAE < 10 increases from 48% to 79% for θ and from 62% to 65% for ϕ, MAE < 5 increases from 24% to 45% for θ and from 47% to 52% for ϕ, MAE < 1 increases from 6% to 9% for θ and from 12% to 16% for ϕ, where θ is the zenith angle, and ϕ is the azimuthal angle. This is a significant change and it demonstrates the high utility of the E-D network use and shows the accuracy of the PCA-based algorithm. We also publish the source code used in our research in order to make it reproducible.
Article Details
M. G. Aartsen, M. Ackermann, J. Adams, J. Aguilar, M. Ahlers, et al. The IceCube Neutrino Observatory: instrumentation and online systems. Journal of Instrumentation, 12(03):P03012, 2017. https://doi.org/10.1088/1748-0221/12/03/P03012.
M. G. Aartsen, M. Ackermann, J. Adams, J. Aguilar, M. Ahlers, et al. Erratum: The IceCube Neutrino Observatory: instrumentation and online systems. Journal of Instrumentation, 19(05):E05001, 2024. https://doi.org/10.1088/1748-0221/19/05/E05001.
J. Abraham, P. Abreu, M. Aglietta, C. Aguirre, E. Ahn, et al. Atmospheric effects on extensive air showers observed with the surface detector of the Pierre Auger observatory. Astroparticle Physics, 32(2):89-99, 2009. https://doi.org/10.1016/j.astropartphys.2009.06.004.
J. Abraham, P. Abreu, M. Aglietta, C. Aguirre, E. Ahn, et al. Erratum to ``Atmospheric effects on extensive air showers observed with the surface detector of the Pierre Auger observatory'' [Astroparticle Physics 32(2) (2009), 89–99]. Astroparticle Physics, 33(1):65-67, 2010. https://doi.org/10.1016/j.astropartphys.2009.10.005.
R. Aloisio. Ultra High Energy Cosmic Rays an overview. Journal of Physics: Conference Series, 2429(1):012008, 2023. Proc. 12th Cosmic Ray International Seminar (CRIS 2022), 12-16 Sep 2022, Napoli, Italy. https://doi.org/10.1088/1742-6596/2429/1/012008.
A. D. Avrorin, A. V. Avrorin, V. M. Aynutdinov, R. Bannash, I. A. Belolaptikov, et al. Baikal-GVD. EPJ Web of Conferences, 136:04007, 2017. Proc. 6th Roma International Conference on Astroparticle Physics (RICAP16), 21-24 Jun, Roma, Italy. https://doi.org/10.1051/epjconf/201713604007.
K. Bajaj, D. K. Singh, and M. A. Ansari. Autoencoders based deep learner for image denoising. Procedia Computer Science, 171:1535-1541, 2020. Proc. 3rd International Conference on Computing and Network Communications (CoCoNet'19), 18-21 Dec, Trivandrum, Kerala, India. https://doi.org/10.1016/j.procs.2020.04.164.
O. Bar, Ł. Bibrzycki, M. Niedźwiecki, M. Piekarczyk, K. Rzecki, et al. Zernike moment based classification of cosmic ray candidate hits from CMOS sensors. Sensors, 21(22):7718, 2021. https://doi.org/doi.org/10.3390/s21227718.
Ł. Bibrzycki, D. Burakowski, P. Homola, M. Piekarczyk, M. Niedźwiecki, et al. Towards a global cosmic ray sensor network: CREDO detector as the first open-source mobile application enabling detection of penetrating radiation. Symmetry, 12(11):1802, 2020. https://doi.org/10.3390/sym12111802.
browarsoftware. cosmic_ray_spherical. GitHub. https://github.com/browarsoftware/cosmic_ray_spherical.
Y. Choi, S. Park, and S. Kim. Development of point cloud data-denoising technology for earthwork sites using encoder-decoder network. KSCE Journal of Civil Engineering, 26(11):4380-4389, 2022. https://doi.org/10.1007/s12205-022-0407-8.
M. T. Dova, L. N. Epele, and A. G. Mariazzi. Particle density distributions of inclined air showers. Nuovo Cim. C, 24(4-5):745-750, 2001. https://www.sif.it/riviste/sif/ncc/econtents/2001/024/04-05/article/5.
D. Droz, A. Tykhonov, X. Wu, and M. Deliyergiyev. Neural networks for TeV cosmic electrons identification on the DAMPE experiment. In: Proc. The European Physical Society Conference on High Energy Physics PoS(EPS-HEP2021), vol. 398 of Proceedings of Science, p. 045. Online - Hamburg, Germany, 26-30 Jul 2021, published in 2022. https://doi.org/10.22323/1.398.0045.
V. Dutta, M. Choraś, M. Pawlicki, and R. Kozik. A deep learning ensemble for network anomaly and cyber-attack detection. Sensors, 20(16):4583, 2020. https://doi.org/10.3390/s20164583.
V. Dutta, M. Pawlicki, R. Kozik, and M. Choraś. Unsupervised network traffic anomaly detection with deep autoencoders. Logic Journal of the IGPL, 30(6):912-925, 2022. https://doi.org/10.1093/jigpal/jzac002.
J. Glombitza, M. Erdmann, M. Vieweg, and M. Dohmen. Deep learning based air shower reconstruction at the Pierre Auger Observatory. In: Proc. DPG Spring meeting 2019, vol. Aachen 2019 issue of Verhandlungen der Deutschen Physikalischen Gesellschaft. Aachen, Germany, 25-29 Mar 2019. https://inis.iaea.org/records/dwvnb-hhf07.
K. Greisen. Cosmic ray showers. Annual Review of Nuclear Science, 10(1):63-108, 1960. https://doi.org/10.1146/annurev.ns.10.120160.000431.
Y. Guo and B. W.-K. Ling. Spherical coordinate-based kernel principal component analysis. Signal, Image and Video Processing, 15(3):511-518, 2021. https://doi.org/10.1007/s11760-020-01771-8.
T. Hachaj, Ł. Bibrzycki, and M. Piekarczyk. Recognition of cosmic ray images obtained from CMOS sensors used in mobile phones by approximation of uncertain class assignment with deep convolutional neural network. Sensors, 21(6):1963, 2021. https://doi.org/10.3390/s21061963.
T. Hachaj, Ł. Bibrzycki, and M. Piekarczyk. Fast training data generation for machine learning analysis of cosmic ray showers. IEEE Access, 11:7410-7419, 2023. https://doi.org/10.1109/ACCESS.2023.3237800.
T. Hachaj and M. Piekarczyk. The practice of detecting potential cosmic rays using CMOS cameras: Hardware and algorithms. Sensors, 23(10):4858, 2023. https://doi.org/10.3390/s23104858.
T. Hachaj, M. Piekarczyk, and J. Wąs. Searching of potentially anomalous signals in cosmic-ray particle tracks images using rough k-means clustering combined with eigendecomposition-derived embedding. In: Proc. International Joint Conference on Rough Sets (IJCRS 2023), vol. 14481 of Lecture Notes in Computer Science, pp. 431-445. Springer, Kraków, Poland, 5-8 Oct 2023. https://doi.org/10.1007/978-3-031-50959-9_30.
P. Hasiec, A. Świtoński, H. Josiński, and K. Wojciechowski. Anomaly detection of motion capture data based on the autoencoder approach. In: Proc. International Conference on Computational Science (ICCS 2023 2023), vol. 14074 of Lecture Notes in Computer Science, pp. 611-622. Springer, 3-5 Jul 2023. https://doi.org/10.1007/978-3-031-36021-3_59.
P. Homola, D. Beznosko, G. Bhatta, Ł. Bibrzycki, M. Borczyńska, et al. Cosmic-ray extremely distributed observatory. Symmetry, 12(11):1835, 2020. https://doi.org/10.3390/sym12111835.
P. Homola, V. Marchenko, A. Napolitano, R. Damian, R. Guzik, et al. Observation of large scale precursor correlations between cosmic rays and earthquakes with a periodicity similar to the solar cycle. Journal of Atmospheric and Solar-Terrestrial Physics, 247:106068, 2023. https://doi.org/10.1016/j.jastp.2023.106068.
J. Jaworek-Korjakowska and R. Tadeusiewicz. Determination of border irregularity in dermoscopic color images of pigmented skin lesions. In: Proc. 2014 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pp. 6459-6462. IEEE, Chicago, IL, USA, 26-30 Aug 2014. https://doi.org/10.1109/EMBC.2014.6945107.
H. Josiński, D. Kostrzewa, A. Michalczuk, A. Świtoński, and K. Wojciechowski. Feature extraction and HMM-based classification of gait video sequences for the purpose of human identification. In: A. Nawrat and Z. Kuś, eds., Vision Based Systemsfor UAV Applications, vol. 481 of Studies in Computational Intelligence, pp. 233-245. Springer, 2013. https://doi.org/10.1007/978-3-319-00369-6_15.
O. Kalashev, I. Kharuk, G. Rubtsov, on behalf of the Baikal-GVD Collaboration, et al. Machine learning based background rejection for Baikal-GVD neutrino telescope. Journal of Physics: Conference Series, 2438:012099, 2023. Proc. 20th International Workshop on Advanced Computing and Analysis Techniques in Physics Research, 29 Oct - 3 Dec 2021, Virtual and Daejeon, South Korea. https://doi.org/10.1088/1742-6596/2438/1/012099.
M. Karbowiak, M. Orzechowski, T. Wibig, Ł. Bibrzycki, P. Kovacs, et al. Small shower array for education purposes-the CREDO-Maze Project. In: Proc. 37th International Cosmic Ray Conference PoS(ICRC2021), vol. 395 of Proceedings of Science, p. 219. Online - Berlin, Germany, 21-23 Jul 2021, published in 2022. https://doi.org/10.22323/1.395.0219.
D. P. Kingma and J. Ba. Adam: A method for stochastic optimization. In: Proc. 3rd Int. Conf. Learning Representations, ICLR 2015. San Diego, CA, 7-9 May 2015. Accessible in arXiv. https://doi.org/10.48550/arXiv.1412.6980.
P. Koundal, R. Abbasi, M. Ackermann, J. Adams, IceCube Collaboration, et al. Composition analysis of cosmic-rays at IceCube Observatory using graph neural networks. In: Proc. 27th European Cosmic Ray Symposium - PoS(ECRS), vol. 423 of Proceedings of Science, p. 085. Nijmegen, The Netherlands, 25-29 Jul, 2022, published in 2023. https://doi.org/10.22323/1.423.0085.
R. Kumar. Tracking cosmic rays by crayfis (cosmic rays found in smartphones) global detector. In: Proc. The 34th International Cosmic Ray Conference PoS(ICRC2015), vol. 236 of Proceedings of Science, p. 1234. The Hague, The Netherlands, 30 Jul - 6 Aug 2015, published in 2016. https://doi.org/10.22323/1.236.1234.
R. Nirwan and N. Bertschinger. Rotation invariant householder parameterization for Bayesian PCA. In: K. Chaudhuri and R. Salakhutdinov, eds., Proc. 36th International Conference on Machine Learning, vol. 97 of Proceedings of Machine Learning Research, pp. 4820-4828. PMLR, Long Beach, CA, USA, 9-15 Jun 2019. https://proceedings.mlr.press/v97/nirwan19a.html.
R. D. Parsons and S. Ohm. Background rejection in atmospheric Cherenkov telescopes using recurrent convolutional neural networks. The European Physical Journal C, 80(5):363, 2020. https://doi.org/10.1140/epjc/s10052-020-7953-3.
Particle Data Group, R. L. Workman, V. D. Burkert, V. Crede, E. Klempt, et al. Review of particle physics. Progress of Theoretical and Experimental Physics, 2022(8):083C01, 2022. https://doi.org/10.1093/ptep/ptac097.
Particle Data Group, P. A. Zyla, R. M. Barnett, J. Beringer, O. Dahl, et al. Review of Particle Physics. Progress of Theoretical and Experimental Physics, 2020(8):083C01, 2020. https://doi.org/10.1093/ptep/ptaa104.
M. Piekarczyk, O. Bar, Ł. Bibrzycki, M. Niedźwiecki, K. Rzecki, et al. CNN-based classifier as an offline trigger for the CREDO experiment. Sensors, 21(14):4804, 2021. https://doi.org/10.3390/s21144804.
M. Piekarczyk and T. Hachaj. On the search for potentially anomalous traces of cosmic ray particles in images acquired by CMOS detectors for a continuous stream of emerging observational data. Sensors, 24(6):1835, 2024. https://doi.org/10.3390/s24061835.
J. S. Pryga, W. Stanek, K. W. Woźniak, P. Homola, K. Almeida Cheminant, et al. Analysis of the capability of detection of extensive air showers by simple scintillator detectors. Universe, 8(8):425, 2022. https://doi.org/10.3390/universe8080425.
D. B. Reusch, R. B. Alley, and B. C. Hewitson. Relative performance of self-organizing maps and principal component analysis in pattern extraction from synthetic climatological data. Polar Geography, 29(3):188-212, 2005. https://doi.org/10.1080/789610199.
K. Sargsyan, J. Wright, and C. Lim. GeoPCA: a new tool for multivariate analysis of dihedral angles based on principal component geodesics. Nucleic Acids Research, 40(3):e25-e25, 2012. https://doi.org/10.1093/nar/gkr1069.
K. Sargsyan, J. Wright, and C. Lim. GeoPCA: a new tool for multivariate analysis of dihedral angles based on principal component geodesics. Nucleic Acids Research, 43(21):10571–10572, 2015. (This is a correction to Sargsyan et al., GeoPCA: a new tool..., 2012. https://doi.org/10.1093/nar/gkv1000.
M. Savić, A. Dragić, D. Maletić, N. Veselinović, R. Banjanac, et al. A novel method for atmospheric correction of cosmic-ray data based on principal component analysis. Astroparticle Physics, 109:1-11, 2019. https://doi.org/10.1016/j.astropartphys.2019.01.006.
J. Stasielak, P. Malecki, D. Naumov, V. Allakhverdian, on behalf of the Baikal-GVD Collaboration, et al. High-energy neutrino astronomy—Baikal-GVD neutrino telescope in Lake Baikal. Symmetry, 13(3):377, 2021. https://doi.org/10.3390/sym13030377.
Z. Szadkowski and K. Pytel. Trigger based on a fuzzy logic for a detection of very inclined cosmic rays in the surface detector of the Pierre Auger Observatory. In: Proc. 2019 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), pp. 1-5. IEEE, Auckland, New Zealand, 20-23 May 2019. https://doi.org/10.1109/I2MTC.2019.8827075.
R. Tadeusiewicz, R. Chaki, and N. Chaki. Exploring neural networks with C#. CRC Press, Boca Raton, 2015. https://doi.org/10.1201/b17332.
J. Takalo. Extracting hale cycle related components from cosmic-ray data using principal component analysis. Solar Physics, 297(9):113, 2022. https://doi.org/10.1007/s11207-022-02048-8.
The Pierre Auger Collaboration. The Pierre Auger Cosmic Ray Observatory. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 798:172-213, 2015. https://doi.org/10.1016/j.nima.2015.06.058.
The Pierre Auger Collaboration, A. Aab, P. Abreu, M. Aglietta, J. Albury, et al. Extraction of the muon signals recorded with the surface detector of the Pierre Auger Observatory using recurrent neural networks. Journal of Instrumentation, 16(07):P07016, 2021. https://doi.org/10.1088/1748-0221/16/07/P07016.
C. Tian, L. Fei, W. Zheng, Y. Xu, W. Zuo, et al. Deep learning on image denoising: An overview. Neural Networks, 131:251-275, 2020. https://doi.org/10.1016/j.neunet.2020.07.025.
J. Vandenbroucke, S. BenZvi, S. Bravo, K. Jensen, P. Karn, et al. Measurement of cosmic-ray muons with the distributed electronic cosmic-ray observatory, a network of smartphones. Journal of Instrumentation, 11(04):P04019, 2016. https://doi.org/10.1088/1748-0221/11/04/p04019.
T. Wibig. Small shower CORSIKA simulations. Chinese Physics C, 45(8):085001, 2021. https://doi.org/10.1088/1674-1137/ac0099.
M. Yu, T. B. Anderson, Y. Chen, S. Coutu, T. LaBree, et al. Machine learning applications on event reconstruction and identification for ISS-CREAM. In: Proc. 37th International Cosmic Ray Conference PoS(ICRC2021), vol. 395, p. 061. Proceedings of Science, Online - Berlin, Germany, 21-23 Jul 2021, published in 2022. https://doi.org/10.22323/1.395.0061.
D. Zheng, S. H. Tan, X. Zhang, Z. Shi, K. Ma, et al. An unsupervised deep learning approach for real-world image denoising. In: Proc. 8th International Conference on Learning Representations (ICLR). Virtual, 26 Apr - 1 May 2020. Published in OpenReview. https://openreview.net/forum?id=tIjRAiFmU3y.