TITLE = {{A new Sinkhorn algorithm with Deletion and Insertion operations}}, AUTHOR = {Brun, Luc and Ga{"u}z{`e}re, Benoit and Bougleux, S{'e}bastien and Yger, Florian}, TYPE = {Research Report}, INSTITUTION = {{GREYC, UMR 6072}}, YEAR = {2021}, MONTH = Nov, KEYWORDS = {Sinkhorn algorithm ; Linear Sum Assignment problem}, url = {Pdf(HAL):=https://hal.archives-ouvertes.fr/hal-03454896/file/main.pdf,HAL:=https://hal.archives-ouvertes.fr/hal-03454896, ArXiv:=https://arxiv.org/abs/2111.14565, Pdf(ArXiv):=https://arxiv.org/pdf/2111.14565}, HAL_ID = {hal-03454896}, HAL_VERSION = {v1}, theme="pattern", abstract="This report is devoted to the continuous estimation of an epsilon-assignment. Roughly speaking, an epsilon assignment between two sets V1 and V2 may be understood as a bijective mapping between a sub part of V1 and a sub part of V2 . The remaining elements of V1 (not included in this mapping) are mapped onto an epsilon pseudo element of V2 . We say that such elements are deleted. Conversely, the remaining elements of V2 correspond to the image of the epsilon pseudo element of V1. We say that these elements are inserted. Our algorithms are iterative and differentiable and may thus be easily inserted within a backpropagation based learning framework such as artificial neural networks."