# Introduction The unique corpus of epigraphic monuments of St. Sophia of Kyiv belongs to the oldest inscriptions, which are the most valuable and reliable source to determine the time of construction of the main temple of Kyivan Rus. For example, they contain the cathedral inscriptions-graffiti dated back to 1018–1022, which reliably confirmed the foundation of the St. Sophia Cathedral in 1011. ![Example of the original image for the medieval graffito in St. Sophia Cathedral of Kyiv (Ukraine)][1] # Dataset Description A new image dataset of these carved Glagolitic and Cyrillic letters (CGCL) from [The Collection of Graffiti of St. Sophia Cathedral of Kyiv][2] was assembled and pre-processed to provide glyphs for recognition and prediction by multinomial logistic regression and deep neural network. At the moment the whole dataset consists of more than 7000 images, but only more than 2000 images for 34 types of letters (classes) are presented here, but this is permanently enlarged by the fresh contributions. # Previous Research Results ## Convolutional Neural Networks This dataset was used in our recent paper for automatic recognition of the historical letters (XI-XVIII centuries) carved on the stoned walls of St.Sophia cathedral in Kyiv (Ukraine). A new image dataset of these carved Glagolitic and Cyrillic letters (CGCL) was assembled and pre-processed for recognition and prediction by machine learning methods. The explanatory data analysis of CGCL and notMNIST datasets shown that the carved letters can hardly be differentiated by dimensionality reduction methods, for example, by t-distributed stochastic neighbor embedding (tSNE) due to the worse letter representation by stone carving in comparison to hand writing. The multinomial logistic regression (MLR) and a 2D convolutional neural network (CNN) models were applied. The MLR model demonstrated the area under curve (AUC) values for receiver operating characteristic (ROC) are not lower than 0.92 and 0.60 for notMNIST and CGCL, respectively. The CNN model gave AUC values close to 0.99 for both notMNIST and CGCL (despite the much smaller size and quality of CGCL in comparison to notMNIST) under condition of the high lossy data augmentation. CGCL dataset was published to be available for the data science community as an open source resource. The details on this dataset and related research could be found in the related publication ["Open Source Dataset and Machine Learning Techniques for Automatic Recognition of Historical Graffiti"][3]. ## Capsule Neural Networks In our other research work the capsule network was applied for both datasets in three regimes: without data augmentation, with lossless data augmentation, and lossy data augmentation. Despite the much worse quality of CGCL dataset and extremely low number of samples (in comparison to notMNIST dataset) the capsule network model demonstrated much better results than the previously used convolutional neural network (CNN). The training rate for capsule network model was 5-6 times higher than for CNN. The validation accuracy (and validation loss) was higher (lower) for capsule network model than for CNN without data augmentation even. The area under curve (AUC) values for receiver operating characteristic (ROC) were also higher for the capsule network model than for CNN model: 0.88-0.93 (capsule network) and 0.50 (CNN) without data augmentation, 0.91-0.95 (capsule network) and 0.51 (CNN) with lossless data augmentation, and similar results of 0.91-0.93 (capsule network) and 0.9 (CNN) in the regime of lossless data augmentation only. The confusion matrixes were much better for capsule network than for CNN model and gave the much lower type I (false positive) and type II (false negative) values in all three regimes of data augmentation. These results supports the previous claims that capsule-like networks allow to reduce error rates not only on MNIST digit dataset, but on the other notMNIST letter dataset and the more complex CGCL handwriting graffiti letter dataset also. Moreover, capsule-like networks allow to reduce training set sizes to 180 images even like in this work, and they are considerably better than CNNs on the highly distorted and incomplete letters even like CGCL handwriting graffiti. The details on this research could be found in the related publication ["Capsule Deep Neural Network for Recognition of Historical Graffiti Handwriting"][4]. # Acknowledgements The header photo was made by [Ivan Sedlovskyi][5] (2014) and shared under the Creative Commons Attribution-Share Alike 4.0 International license. The glyphs of letters from [The Collection of Graffiti of St. Sophia Cathedral of Kyiv][6] were prepared by students and teachers of National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" and can be used as an open science dataset under CC BY-NC-SA 4.0 license [Computer Engineering Department, Faculty of Informatics and Computer Engineering, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"][7]. We request that publications resulting from the use of this data attribute these 2 data sources: - [Mykhailo Hrushevsky Institute of Ukrainian Archaeography and Source Studies][8], Kyiv, Ukraine; - [Computer Engineering Department, Faculty of Informatics and Computer Engineering, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"][9], Kyiv, Ukraine; and cite the following publications: - Kornienko, V.V.: Korpus Hrafiti Sofii Kyivskoi, XI - pochatok XVIII_st, chastyny I-III (The Collection of Graffiti of St. Sophia of Kyiv, 11th – 17th centuries), Parts I-III, MykhailoHrushevsky Institute of Ukrainian Archeography and Source Studies, Kiev (in Ukrainian), (2010-2011). - N.Gordienko, P.Gang, Y.Gordienko, W.Zeng, O.Alienin, O.Rokovyi, & S. Stirenko, Open Source Dataset and Machine Learning Techniques for Automatic Recognition of Historical Graffiti. arXiv preprint arXiv:1808.10862 (2018). - N. Gordienko, Yu. Kochura, V.Taran, Peng Gang, Yu.Gordienko, S. Stirenko, Capsule Deep Neural Network for Recognition of Historical Graffiti Handwriting, arXiv preprint arXiv preprint arXiv:1809.06693 (2018). [1]: http://archeos.org.ua/wp-content/uploads/2013/05/%D0%93%D1%80%D0%B0%D1%84%D1%96%D1%82%D1%96.jpg [2]: http://archeos.org.ua/?page_id=2543 [3]: https://arxiv.org/abs/1808.10862 [4]: https://arxiv.org/abs/1809.06693 [5]: https://commons.wikimedia.org/wiki/File:St.Sophia_Cathedral,_Kyiv,_Ukraine_(4).jpg [6]: http://archeos.org.ua/?page_id=2543 [7]: http://comsys.kpi.ua [8]: http://archeos.org.ua [9]: http://comsys.kpi.ua