of dimensionality: <latexit sha1_base64="hdIIwFbOeK4PwlwQnFOTa3sU+CQ=">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</latexit> n scales like O(1/precisiond) <latexit sha1_base64="H3mOTgsaL9HmzSNYU49BvmLw4p4=">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</latexit> n <latexit sha1_base64="l776QCPF7PuoZ8PQC+Wq/1Nkc0I=">AAAC8HicjVHLSsQwFD1T3+Nr1KWb4igIwtARUZeiCC4VnHFARdIYa7DT1DRVVPwId+7ErT/gVr9C/AP9C29iBR+IprQ9Ofeck9wkTGOZmSB4LnkdnV3dPb195f6BwaHhyshoM1O55qLBVax0K2SZiGUiGkaaWLRSLVg7jMVWeLRi61snQmdSJZvmLBW7bRYl8kByZojaq8xM7mgZHZrsOJcR01qdTvqridEqldzXIspjpuW5E9f2KtWgFrjh/wT1AlRRjHVVecIO9qHAkaMNgQSGcAyGjJ5t1BEgJW4XF8RpQtLVBS5RJm9OKkEKRuwRfSOabRdsQnObmTk3p1ViejU5fUyRR5FOE7ar+a6eu2TL/pZ94TLt3s7oHxZZbWINDon9y/eh/K/P9mJwgEXXg6SeUsfY7niRkrtTsTv3P3VlKCElzuJ9qmvC3Dk/ztl3nsz1bs+WufqLU1rWznmhzfFqd0kXXP9+nT9Bc7ZWn6/NbcxWl5aLq+7FOCYwTfe5gCWsYR0Nyr7CPR7w6Gnv2rvxbt+lXqnwjOHL8O7eADNIoZk=</latexit> Entropic regularization. <latexit sha1_base64="+0I5fHHSkEqsLyyCa1IqpA5OZ74=">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</latexit> Algorithms scale like O(n3)
of dimensionality: <latexit sha1_base64="hdIIwFbOeK4PwlwQnFOTa3sU+CQ=">AAAC7nicjVHLTsMwEJyGd3kVOHKJaJHgUpIKAccKLtwAiQISLyWuAatuEsUOoqr4Bm7cEFd+gCt8BuIP4C9YmyDxEAJHScazO2PvbphIobTnPRecnt6+/oHBoeLwyOjYeGlickfFWcp4g8UyTvfCQHEpIt7QQku+l6Q8aIeS74atNRPfPeepEnG0rTsJP2wHp5E4ESzQRB2X5itRxVUskFy5UrS4W9mY8xcONL/QXTJiwigvj5rzleNS2at6drk/gZ+DMvK1GZeecIAmYjBkaIMjgiYsEUDRsw8fHhLiDtElLiUkbJzjEkXSZpTFKSMgtkXfU9rt52xEe+OprJrRKZLelJQuZkkTU15K2Jzm2nhmnQ37m3fXepq7degf5l5tYjXOiP1L95H5X52pReMEK7YGQTUlljHVsdwls10xN3c/VaXJISHO4CbFU8LMKj/67FqNsrWb3gY2/mIzDWv2LM/N8GpuSQP2v4/zJ9ipVf2l6uJWrVxfzUc9iGnMYI7muYw61rGJBnlf4R4PeHQS59q5cW7fU51CrpnCl+XcvQF6O57y</latexit> n scales like O(1/precisiond) <latexit sha1_base64="H3mOTgsaL9HmzSNYU49BvmLw4p4=">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</latexit> n <latexit sha1_base64="l776QCPF7PuoZ8PQC+Wq/1Nkc0I=">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</latexit> Entropic regularization. <latexit sha1_base64="BxtDl/9kA2hNNBmwbTnXPjAyD0E=">AAAC4HicjVHLSsNAFD2Nr1pfVZfdBIvgqqQiKq5ENy5cVLAPaItMptM6NE1CMhFLceHOnbj1B9zq14h/oH/hnTEFH4hOSHLm3HvOzL3XDT0ZK8d5yVgTk1PTM9nZ3Nz8wuJSfnmlFgdJxEWVB14QNVwWC0/6oqqk8kQjjAQbuJ6ou/1DHa9fiCiWgX+qhqFoD1jPl13JmSLqLF9oKXFJutEx43076NqxYq70pBruXZ3li07JMcv+CcopKCJdlSD/jBY6CMCRYAABH4qwB4aYnibKcBAS18aIuIiQNHGBK+RIm1CWoAxGbJ++Pdo1U9anvfaMjZrTKR69ESltrJMmoLyIsD7NNvHEOGv2N++R8dR3G9LfTb0GxCqcE/uXbpz5X52uRaGLXVODpJpCw+jqeOqSmK7om9ufqlLkEBKncYfiEWFulOM+20YTm9p1b5mJv5pMzeo9T3MTvOlb0oDL38f5E9Q2S+Xt0tbJZnH/IB11FgWsYYPmuYN9HKGCKnlf4wGPeLJc68a6te4+Uq1MqlnFl2XdvwNqVZrW</latexit> Lack of stability: <latexit sha1_base64="UEW+cNittIpUv68XQ4rxvAzqcRg=">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</latexit> Mass conservation. <latexit sha1_base64="CPd0SJSu4euB6sCLGMyp/VpK1Wk=">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</latexit> Sensitivity to outliers. <latexit sha1_base64="7RkWTRd5HtHTrlFzA347j5q4iQw=">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</latexit> Unbalanced Optimal Transport. <latexit sha1_base64="+0I5fHHSkEqsLyyCa1IqpA5OZ74=">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</latexit> Algorithms scale like O(n3)
1: Entropic GW can find correspondences between a source surface (left) and a surface with similar structure, a surface with shared semantic structure, a noisy 3D point cloud, an icon, and a hand drawing. Each fuzzy map was computed using the same code. In this paper, we propose a new correspondence algorithm that minimizes distortion of long- and short-range distances alike. We study an entropically-regularized version of the Gromov-Wasserstein (GW) mapping objective function from [M´ emoli 2011] measuring of cor- ds that metric ransfer mind, at opti- ective. rtation, able to ix. We rgence tasks. frame- stance on, and Source Targets Figure 1: Entropic GW can find correspondences between a source surface (left) and a surface with similar structure, a surface with shared semantic structure, a noisy 3D point cloud, an icon, and a hand drawing. Each fuzzy map was computed using the same code. In this paper, we propose a new correspondence algorithm that minimizes distortion of long- and short-range distances alike. We study an entropically-regularized version of the Gromov-Wasserstein (GW) mapping objective function from [M´ emoli 2011] measuring <latexit 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Y <latexit 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Y <latexit 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?
1: Entropic GW can find correspondences between a source surface (left) and a surface with similar structure, a surface with shared semantic structure, a noisy 3D point cloud, an icon, and a hand drawing. Each fuzzy map was computed using the same code. In this paper, we propose a new correspondence algorithm that minimizes distortion of long- and short-range distances alike. We study an entropically-regularized version of the Gromov-Wasserstein (GW) mapping objective function from [M´ emoli 2011] measuring of cor- ds that metric ransfer mind, at opti- ective. rtation, able to ix. We rgence tasks. frame- stance on, and Source Targets Figure 1: Entropic GW can find correspondences between a source surface (left) and a surface with similar structure, a surface with shared semantic structure, a noisy 3D point cloud, an icon, and a hand drawing. Each fuzzy map was computed using the same code. In this paper, we propose a new correspondence algorithm that minimizes distortion of long- and short-range distances alike. We study an entropically-regularized version of the Gromov-Wasserstein (GW) mapping objective function from [M´ emoli 2011] measuring <latexit 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Y <latexit 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Y <latexit 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Y <latexit 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? <latexit 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[Demetci et al 2020] <latexit 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Single-cell <latexit 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multi-omics: <latexit 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ATAC-seq <latexit 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RNA-seq <latexit 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X <latexit 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Y <latexit sha1_base64="8H4xN4xGPG5ztU4N+maxzHTbjXo=">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</latexit> dim ⇠ 103(genes) <latexit sha1_base64="NRLid9ocOcEHNQq7hjUXkZi7pNg=">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</latexit> dim ⇠ 102(peaks)
0 , X and Y are isometric. <latexit 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UGW(X, Y) is not a distance. <latexit 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UGW(X, Y) upper bounds a conic distance. <latexit 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[S´ ejourn´ e 2022] <latexit 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UGW2(X, Y) def. = <latexit sha1_base64="uRiPjVZvlHg9i6RG3FhDcDn0ALM=">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</latexit> min P>0 hQP, Pi + ⌧ KL⌦2(P1|a) + ⌧ KL⌦2(P>1|b) <latexit sha1_base64="gLZ9atfCptR3J/Fnw4H/OckXlIs=">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</latexit> KL⌦2(a0|a) def. = KL(a0a0>|aa>) <latexit sha1_base64="kIRdJ9z+ihwWnlP8Odl5kDqIjOI=">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</latexit> where <latexit sha1_base64="2yyD5IdUTxqUrtXVaNYxE1+XhCo=">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</latexit> ! Mix together unbalanced, GW and Sinkhorn!