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Fixed Pablo's comments
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Patrick Nicodemus committed Jan 9, 2025
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"id": "c303cd48-48ba-4b05-93b6-d230bb8ce64f",
"metadata": {},
"source": [
"We first compute the intracellular distance matrices and the Gromov-Wasserstein distance between each pair of neurons, as described in Tutorial 1. This process may take approximately 30 minutes, depending on your computer."
"We first compute the intracellular distance matrices and the Gromov-Wasserstein distance between each pair of neurons, as described in Tutorial 1."
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"\n",
"\\- Hao, Y. et al. [Integrated analysis of multimodal single-cell data.](https://www.sciencedirect.com/science/article/pii/S0092867421005833) Cell 184, 3573-3587 (2021).\n",
"\n",
"The relative influence of each of the three spaces in the consolidated space varies throughout the space and is locally biased at any point toward the spaces that are contributing more information in a neighborhood of that point. Because the WNN algorithm was designed for Euclidean spaces, CAJAL represents the Gromov-Wasserstein space as a metric subspace of a Euclidean subspace of the same intrinsic dimension of the data using the Isomap embedding and the Manifold-Adaptive Dimension Estimation (MADA) (Farahmand et al. IMLS 2007).\n",
"The relative influence of each of the three spaces in the consolidated space varies throughout the space and is locally biased at any point toward the spaces that are contributing more information in a neighborhood of that point. Because the WNN algorithm was designed for Euclidean spaces, CAJAL represents the Gromov-Wasserstein space as a metric subspace of a Euclidean space of the same intrinsic dimension of the data using the Isomap embedding and the Manifold-Adaptive Dimension Estimation (MADA) (Farahmand et al. IMLS 2007).\n",
"\n",
"Before introducing WNN, let us look at the morphology space and the transcriptomic space separately. We build the gene expression latent space using [Scanpy](https://scanpy.readthedocs.io/en/stable/). For this purpose, we perform log(1 + c CPM) normalization and build a PCA space using the top 2,000 variable genes and 50 principal components."
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