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. 2024 Sep 1;52(18):10836–10849. doi: 10.1093/nar/gkae749

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© The Author(s) 2024. Published by Oxford University Press on behalf of Nucleic Acids Research.

This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial License (https://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

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Figure 1. — Architecture of the Autoencoder and training robustness. (A) Schematic of the Autoencoder, an unsupervised machine learning algorithm. It consists of an encoder and a decoder and in between there is a bottleneck. The encoder transforms high-dimensional input data to a lower-dimensional latent space, while the decoder reconstructs the initial input data from the latent space. This process involves adjusting model parameters, primarily weights, and biases. Each dimension in the latent space corresponds to a latent variable. Here, χ₁, χ₂ and χ₃ represent three latent variables. (B) The variation of FVE with respect to the latent dimension (L_d). A L_d = 3 was chosen, ensuring an FVE of at least 0.85, signifying that the Autoencoder’s reconstruction captures a minimum of of the variance in the input data. (C) Training loss as a function of epochs for different latent space dimensions (L_d). Notably, the training loss achieves saturation for all L_d > 1 beyond 25 epochs. (D) Genome-wide contact probability map between the experimental and ML-derived Hi-C matrix. (E) Histogram of the absolute difference between experimental and ML-derived contact probability matrices. The Pearson correlation coefficient(PCC) is 0.94, and the absolute difference in mean values is 0.023, indicating a substantial agreement in chromosomal interactions.

Inline graphic — Architecture of the Autoencoder and training robustness. (A) Schematic of the Autoencoder, an unsupervised machine learning algorithm. It consists of an encoder and a decoder and in between there is a bottleneck. The encoder transforms high-dimensional input data to a lower-dimensional latent space, while the decoder reconstructs the initial input data from the latent space. This process involves adjusting model parameters, primarily weights, and biases. Each dimension in the latent space corresponds to a latent variable. Here, χ₁, χ₂ and χ₃ represent three latent variables. (B) The variation of FVE with respect to the latent dimension (L_d). A L_d = 3 was chosen, ensuring an FVE of at least 0.85, signifying that the Autoencoder’s reconstruction captures a minimum of of the variance in the input data. (C) Training loss as a function of epochs for different latent space dimensions (L_d). Notably, the training loss achieves saturation for all L_d > 1 beyond 25 epochs. (D) Genome-wide contact probability map between the experimental and ML-derived Hi-C matrix. (E) Histogram of the absolute difference between experimental and ML-derived contact probability matrices. The Pearson correlation coefficient(PCC) is 0.94, and the absolute difference in mean values is 0.023, indicating a substantial agreement in chromosomal interactions.