The radio observation of 21,cm-line signal from the Epoch of Reionization (EoR) enables us to explore the evolution of galaxies and intergalactic medium in the early universe. However, the detection and imaging of the 21,cm-line signal are tough due to the foreground and instrumental systematics. In order to overcome these obstacles, as a new approach, we propose to take a cross correlation between observed 21,cm-line data and 21,cm-line images generated from the distribution of the Lyman-$alpha$ emitters (LAEs) through machine learning. In order to create 21,cm-line maps from LAE distribution, we apply conditional Generative Adversarial Network (cGAN) trained with the results of our numerical simulations. We find that the 21,cm-line brightness temperature maps and the neutral fraction maps can be reproduced with correlation function of 0.5 at large scales $k<0.1~{rm Mpc}^{-1}$. Furthermore, we study the detectability of the the cross correlation assuming the the LAE deep survey of the Subaru Hyper Suprime Cam, the 21,cm observation of the MWA Phase II and the presence of the foreground residuals. We show that the signal is detectable at $k < 0.1~{rm Mpc}^{-1}$ with 1000 hours of MWA observation even if the foreground residuals are 5 times larger than the 21,cm-line power spectrum. Our new approach of cross correlation with image construction using the cGAN can not only boost the detectability of EoR 21,cm-line signal but also allow us to estimate the 21,cm-line auto-power spectrum.
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