{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Trees, Trees, more Trees, oh my!!\n", "\n", "In this notebook, we demonstrate how one might use some of the learning algorithms implemented in geomstats to apply to a non-Euclidean geodesic metric space.\n", "\n", "We choose BHV space, which is the space of unrooted phylogenetic trees without pendant edges.\n", "\n", "We will then demonstrate geodesic, computation of the Fréchet mean using Sturm's algorithm, and then k-means clustering.\n", "\n", "We first will use a simulated dataset for convenience and prettiness.\n", "\n", "In a separate notebook will use a subset of a phylogenetic tree dataset to demonstrate application to real-world data.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Imports and helper functions" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from matplotlib.gridspec import GridSpec\n", "\n", "import geomstats.backend as gs\n", "from geomstats.learning.frechet_mean import FrechetMean\n", "from geomstats.learning.knn import KNearestNeighborsClassifier\n", "from geomstats.metric_geometry.bhv_space import (\n", " Tree,\n", " TreeSpace,\n", ")\n", "from geomstats.metric_geometry.trees import Split\n", "\n", "gs.random.seed(2026)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def _draw_quadrant_plot(ax, max_xy=5):\n", " ax.axhline(0, color=\"#e08020\", lw=2.0, zorder=2) # orange horizontal\n", " ax.axvline(0, color=\"#3aaa6a\", lw=2.0, zorder=2) # green vertical\n", "\n", " # Light blue background for all quadrants\n", " ax.set_facecolor(\"#dde5f5\")\n", "\n", " # Gray top-left quadrant\n", " ax.fill_betweenx([0, max_xy], -max_xy, 0, color=\"#d0d0d0\", alpha=0.85, zorder=0)\n", "\n", " # Quadrant labels\n", " font_kw = dict(fontsize=11, fontweight=\"bold\", color=\"#222\")\n", " ax.text(0.05, max_xy - 0.15, \"34|012\", va=\"top\", ha=\"left\", **font_kw)\n", " ax.text(-max_xy + 0.05, -0.05, \"04|123\", va=\"top\", ha=\"left\", **font_kw)\n", " ax.text(max_xy - 0.05, -0.05, \"01|234\", va=\"top\", ha=\"right\", **font_kw)\n", " ax.text(0.05, -max_xy + 0.15, \"23|014\", va=\"bottom\", ha=\"left\", **font_kw)\n", "\n", " ax.set_xlim(-max_xy, max_xy)\n", " ax.set_ylim(-max_xy, max_xy)\n", " ax.set_aspect(\"equal\")\n", " ax.tick_params(labelsize=9)\n", " ax.grid(False)\n", " ax.set_title(\"One Quadrant in BHV(5)\")\n", "\n", "\n", "def _draw_tree_on_quadrant(ax, tree, marker=\"o\", label=\"\", c=\"r\", ms=10):\n", " # calculate where to go on plot\n", " x, y = 0, 0\n", " for split, length in zip(tree.topology.splits, tree.lengths):\n", " small_split = split.part1 if len(split.part1) == 2 else split.part2\n", " if small_split == {0, 1}:\n", " # positive x-axis\n", " x = length\n", " elif small_split == {0, 4}:\n", " x = -length\n", " elif small_split == {3, 4}:\n", " y = length\n", " elif small_split == {2, 3}:\n", " y = -length\n", " else:\n", " print(\"Oops, this shouldn't happen\")\n", "\n", " ax.plot(x, y, marker, ms=ms, color=c, zorder=5)\n", " ax.text(x, y + 0.35, label, fontsize=8, color=c, zorder=6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Construct and visualise simulated dataset\n", "\n", "We will be working in BHV(5), which is the space of unrooted, labeled trees with five labels. This is the simplest of the spaces, which still maintains some of the interesting (ie, non-Eucliean) properties of the space, such as sticky mean (more on that later)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# BHV space only defined with N >= 4\n", "bhv5 = TreeSpace(n_labels=5)\n", "\n", "# This is the star tree, with no interior splits\n", "star_tree = Tree((), [], n_labels=5)\n", "\n", "# Let's make 7 more random trees\n", "N_RANDOM_TREES = 7\n", "random_trees = bhv5.random_point(N_RANDOM_TREES)\n", "\n", "trees = [star_tree] + random_trees\n", "\n", "fig, axes = plt.subplots(2, N_RANDOM_TREES // 2 + 1, figsize=(6, 4))\n", "axes = axes.flatten()\n", "for i, tree in enumerate(trees):\n", " # root_id is just for visualisation, so we know how to hang the tree\n", " tree.plot(root_id=0, ax=axes[i])\n", "plt.suptitle(f\"Star tree and {N_RANDOM_TREES} random trees in BHV(5)\")\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Geodesic\n", "\n", "Here is a nice website to visualise how three orthants are related https://plewis.github.io/applets/bhvspace/ and how points in those orthants are connected by geodesics (distance-minimising paths). The star tree is located at the origin.\n", "\n", "In BHV(5) there are four different types of geodesics:\n", "- inner-orthant, meaning just interior split lengths change, but no splits are created and none are destroyed. This is the same as a straight line in Euclidean space\n", "- edge-ending, meaning the geodesic ends on a lower-dimensional stratum, here a line or point. This means a split was destroyed (mutatis mutandum edge-starting geodesics start on a lower-dimensional stratum and enter a higher-dimensional one, creating a split)\n", "- \"straight\" intra-orthant, in here a split is destroyed and another is created, and the geodesic traverses from a higher-dimensional plane, through the lower-dimensional stratum, and to another higher-dimensional stratum, but the line is straight (in BHV(5): 2d->1d->2d)\n", "- \"bent\" intra-orthant, in this one, the shortest path one passes through the origin (star tree)! and looks like a bent line. Here all interior splits dissapear and then new ones are created (in BHV(5): 2d->0d->2d)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Inner-orthant geodesic" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "top_quadrant_topology = (Split({3, 4}, {0, 1, 2}), Split({0, 1}, {2, 3, 4}))\n", "\n", "top_tree = Tree(top_quadrant_topology, [3, 1])\n", "top_tree_shifted = Tree(top_quadrant_topology, [1, 4])\n", "\n", "top_trees = [top_tree, top_tree_shifted]" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(4, 6), facecolor=\"white\")\n", "grid = GridSpec(\n", " 2, max(2, 1), figure=fig, height_ratios=[1, 2.2], hspace=0.35, wspace=0.3\n", ")\n", "\n", "top_trees = [top_tree, top_tree_shifted]\n", "labels = [\"start\", \"end\"]\n", "for i, tree in enumerate(top_trees):\n", " ax = fig.add_subplot(grid[0, i])\n", " tree.plot(root_id=0, show_edge_weights=True, ax=ax)\n", " ax.set_title(labels[i])\n", "\n", "ax_quad = fig.add_subplot(grid[1, :])\n", "_draw_quadrant_plot(ax_quad, max_xy=5)\n", "colors = [\"red\", \"green\"]\n", "for i, tree in enumerate(top_trees):\n", " _draw_tree_on_quadrant(ax_quad, tree, c=colors[i], label=labels[i])\n", " _draw_tree_on_quadrant(ax_quad, tree, c=colors[i], label=labels[i])\n", "\n", "plt.suptitle(\"Trees in top quadrant of online BHV(5) visualisation\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Geodesic same quadrant\n", "geodesic = bhv5.metric.geodesic(top_trees[0], top_trees[-1])\n", "beginning = geodesic(0)[0]\n", "tenth = geodesic(0.1)[0]\n", "halfway = geodesic(0.5)[0]\n", "three_quarters = geodesic(0.75)[0]\n", "end = geodesic(1)[0]\n", "\n", "geodesic_trees = [beginning, tenth, halfway, three_quarters, end]\n", "labels = [\"start\", \"tenth\", \"half\", \"3/4\", \"end\"]\n", "colors = [\"red\", \"orangered\", \"orange\", \"yellow\", \"green\"]\n", "\n", "# Let's draw the geodesic!!\n", "fig, ax = plt.subplots(1, 1, figsize=(4, 4), facecolor=\"white\")\n", "_draw_quadrant_plot(ax, max_xy=5)\n", "for i, tree in enumerate(geodesic_trees):\n", " _draw_tree_on_quadrant(ax, tree, c=colors[i], label=labels[i])\n", " _draw_tree_on_quadrant(ax, tree, c=colors[i], label=labels[i])\n", "\n", "plt.suptitle(\"Trees in top quadrant of online BHV(5) visualisation\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Intra-orthant \"straight\" geodesic" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bottom_right_quadrant_topology = (Split({2, 3}, {0, 1, 4}), Split({0, 1}, {2, 3, 4}))\n", "\n", "top_tree = Tree(top_quadrant_topology, [1, 4])\n", "bottom_tree = Tree(bottom_right_quadrant_topology, [3, 1])\n", "\n", "trees = [top_tree, bottom_tree]\n", "\n", "fig = plt.figure(figsize=(4, 6), facecolor=\"white\")\n", "grid = GridSpec(\n", " 2, max(2, 1), figure=fig, height_ratios=[1, 2.2], hspace=0.35, wspace=0.3\n", ")\n", "\n", "labels = [\"start\", \"end\"]\n", "for i, tree in enumerate(trees):\n", " ax = fig.add_subplot(grid[0, i])\n", " tree.plot(root_id=0, show_edge_weights=True, ax=ax)\n", " ax.set_title(labels[i])\n", "\n", "ax_quad = fig.add_subplot(grid[1, :])\n", "_draw_quadrant_plot(ax_quad, max_xy=5)\n", "colors = [\"red\", \"green\"]\n", "for i, tree in enumerate(trees):\n", " _draw_tree_on_quadrant(ax_quad, tree, c=colors[i], label=labels[i])\n", " _draw_tree_on_quadrant(ax_quad, tree, c=colors[i], label=labels[i])\n", "\n", "### ADD GEODESIC TREES\n", "geodesic = bhv5.metric.geodesic(top_tree, bottom_tree)\n", "for i in range(1, 5):\n", " tree = geodesic(i / 5)[0]\n", " _draw_tree_on_quadrant(ax_quad, tree, ms=5, c=\"grey\", label=str(i / 5))\n", "\n", "plt.suptitle(\"Trees in top and bottom quadrant of online BHV(5) visualisation\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Intra-orthant \"bent\" geodesic" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bottom_left_quadrant_topology = (Split({2, 3}, {0, 1, 4}), Split({0, 4}, {1, 2, 3}))\n", "\n", "top_tree = Tree(top_quadrant_topology, [3, 0.5])\n", "bottom_tree = Tree(bottom_left_quadrant_topology, [2, 4])\n", "\n", "trees = [top_tree, bottom_tree]\n", "\n", "fig = plt.figure(figsize=(4, 6), facecolor=\"white\")\n", "grid = GridSpec(\n", " 2, max(2, 1), figure=fig, height_ratios=[1, 2.2], hspace=0.35, wspace=0.3\n", ")\n", "\n", "labels = [\"start\", \"end\"]\n", "for i, tree in enumerate(trees):\n", " ax = fig.add_subplot(grid[0, i])\n", " tree.plot(root_id=0, show_edge_weights=True, ax=ax)\n", " ax.set_title(labels[i])\n", "\n", "ax_quad = fig.add_subplot(grid[1, :])\n", "_draw_quadrant_plot(ax_quad, max_xy=5)\n", "colors = [\"red\", \"green\"]\n", "for i, tree in enumerate(trees):\n", " _draw_tree_on_quadrant(ax_quad, tree, c=colors[i], label=labels[i])\n", " _draw_tree_on_quadrant(ax_quad, tree, c=colors[i], label=labels[i])\n", "\n", "### ADD GEODESIC TREES\n", "geodesic = bhv5.metric.geodesic(top_tree, bottom_tree)\n", "n_examples = 7\n", "for i in range(1, n_examples):\n", " tree = geodesic(i / n_examples)[0]\n", " _draw_tree_on_quadrant(\n", " ax_quad, tree, ms=5, c=\"grey\", label=f\"{(i / n_examples):.2f}\"\n", " )\n", "\n", "plt.suptitle(\"Bent geodesic in BHV(5) visualisation\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Mean\n", "\n", "Fréchet mean is computed in geodesic metric spaces (like BHV) via Sturm's algorithm. Since we do not have an `exp` in this space (undefined at origin), we can not use the typical gradient-descent approach. Instead, we use an iterative approach, which samples a point, computes the geodesic between that and the current mean estimate, walks a decreasing amount down that geodesic, rinses, and repeats. Since BHV is a CAT(0) (non-positively-curved) space, there are nice convergence guarantees.\n", "\n", "Let's sample some random trees until we find ten in our three quadrants that we have decided to visualize!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Mean of two random samples\n", "Should be the same as 0.5 geodesic" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Half geodesic tree:\t (({0, 3}|{1, 2, 4}, {0, 3, 4}|{1, 2});[0.45475402 1.76129826])\n", "Frechet mean tree:\t (({0, 3}|{1, 2, 4}, {0, 3, 4}|{1, 2});[0.4552997 1.7604958])\n", "Distance between: 0.0009704139815367815\n" ] } ], "source": [ "random_trees = bhv5.random_point(2)\n", "geodesic = bhv5.metric.geodesic(random_trees[0], random_trees[-1])\n", "half_geodesic_tree = geodesic(0.5)[0]\n", "print(\"Half geodesic tree:\\t\", half_geodesic_tree)\n", "\n", "## Compute the mean!!\n", "# Will be Sturm's algorithm by default for bhv space\n", "mean_estimator = FrechetMean(bhv5, sample_method=\"cyclic\", max_iter=10000, epsilon=1e-3)\n", "mean_estimator = mean_estimator.fit(random_trees)\n", "mean_tree = mean_estimator.estimate_\n", "print(\"Frechet mean tree:\\t\", mean_tree)\n", "\n", "print(\"Distance between:\", bhv5.metric.dist(half_geodesic_tree, mean_tree))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Mean with 10 random samples" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "valid_trees = []\n", "while len(valid_trees) < 10:\n", " random_tree = bhv5.random_point()\n", " tree_good = True\n", " for split in random_tree.topology.splits:\n", " small_split = split.part1 if len(split.part1) == 2 else split.part2\n", " if small_split not in ({0, 1}, {0, 4}, {3, 4}, {2, 3}):\n", " tree_good = False\n", "\n", " if tree_good:\n", " random_tree.lengths = 3 * random_tree.lengths\n", " valid_trees.append(random_tree)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "mean_estimator = FrechetMean(\n", " bhv5, sample_method=\"stochastic\", max_iter=10000, epsilon=1e-3\n", ")\n", "mean_estimator = mean_estimator.fit(valid_trees)\n", "mean = mean_estimator.estimate_" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Visualise with the mean as a gold star lol\n", "fig = plt.figure(figsize=(6, 8), facecolor=\"white\")\n", "grid = GridSpec(\n", " 2, len(valid_trees) + 1, figure=fig, height_ratios=[1, 2.7], hspace=0.35, wspace=0.3\n", ")\n", "\n", "ax = fig.add_subplot(grid[0, 0])\n", "mean.plot(root_id=0, ax=ax)\n", "ax.set_title(\"mean\")\n", "\n", "for i, tree in enumerate(valid_trees):\n", " ax = fig.add_subplot(grid[0, i + 1])\n", " tree.plot(root_id=0, show_edge_weights=False, ax=ax)\n", "\n", "ax_quad = fig.add_subplot(grid[1, :])\n", "_draw_quadrant_plot(ax_quad, max_xy=5)\n", "for i, tree in enumerate(valid_trees):\n", " _draw_tree_on_quadrant(ax_quad, tree, c=\"pink\")\n", "\n", "_draw_tree_on_quadrant(ax_quad, mean, marker=\"*\", ms=25, c=\"yellow\")\n", "\n", "plt.suptitle(\"Random trees for mean BHV(5) visualisation\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Weighted mean" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3/4 geodesic tree:\t (({0, 2, 3}|{1, 4}, {0, 3}|{1, 2, 4});[2.11471919 0.04378198])\n", "Weighted Frechet mean tree:\t (({0, 2, 3}|{1, 4}, {0, 3}|{1, 2, 4});[2.1205068 0.0438576])\n", "Distance between: 0.005788097109810386\n" ] } ], "source": [ "random_trees = bhv5.random_point(2)\n", "geodesic = bhv5.metric.geodesic(random_trees[0], random_trees[-1])\n", "half_geodesic_tree = geodesic(0.75)[0]\n", "print(\"3/4 geodesic tree:\\t\", half_geodesic_tree)\n", "\n", "## Compute the mean!!\n", "# Will be Sturm's algorithm by default for bhv space\n", "# Must use stochastic sample method bc cyclic is broken.\n", "mean_estimator = FrechetMean(\n", " bhv5, sample_method=\"stochastic\", max_iter=10000, epsilon=1e-3\n", ")\n", "mean_estimator = mean_estimator.fit(random_trees, weights=[0.25, 0.75])\n", "mean_tree = mean_estimator.estimate_\n", "print(\"Weighted Frechet mean tree:\\t\", mean_tree)\n", "\n", "print(\"Distance between:\", bhv5.metric.dist(half_geodesic_tree, mean_tree))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. KNN Classification" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Predictions: [0 2 2 1 0]\n", "Labels: [0 2 2 1 0]\n" ] } ], "source": [ "# create fake data that is VERY easily separable\n", "# in 3 quadrants in BHV space\n", "quadrant_1_topology = (Split({3, 4}, {0, 1, 2}), Split({0, 1}, {2, 3, 4}))\n", "quadrant_2_topology = (Split({2, 3}, {0, 1, 4}), Split({0, 1}, {2, 3, 4}))\n", "quadrant_3_topology = (Split({0, 4}, {1, 2, 3}), Split({2, 3}, {0, 1, 4}))\n", "topologies = [quadrant_1_topology, quadrant_2_topology, quadrant_3_topology]\n", "lengths = gs.array([3, 1])\n", "\n", "X, y = [], []\n", "n_of_each = 5\n", "for i in range(3):\n", " X.extend([Tree(topologies[i], lengths + 0.1 * x) for x in range(n_of_each)])\n", " y.extend([i] * n_of_each)\n", "X = gs.array(X)\n", "y = gs.array(y)\n", "\n", "indices = np.arange(len(X))\n", "np.random.shuffle(indices)\n", "\n", "n_train = (len(X) * 2) // 3\n", "X_train, X_test = X[indices[:n_train]], X[indices[n_train:]]\n", "y_train, y_test = y[indices[:n_train]], y[indices[n_train:]]\n", "\n", "knn = KNearestNeighborsClassifier(bhv5, n_neighbors=3)\n", "knn = knn.fit(X_train, y_train)\n", "predictions = knn.predict(X_test)\n", "print(\"Predictions:\", predictions)\n", "print(\"Labels:\", y_test)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Visualise\n", "fig = plt.figure(figsize=(6, 8), facecolor=\"white\")\n", "grid = GridSpec(2, 3, figure=fig, height_ratios=[1, 2.7], hspace=0.35, wspace=0.3)\n", "\n", "for i, tree in enumerate(X[::n_of_each]):\n", " ax = fig.add_subplot(grid[0, i])\n", " tree.plot(root_id=0, show_edge_weights=False, ax=ax)\n", "\n", "ax_quad = fig.add_subplot(grid[1, :])\n", "_draw_quadrant_plot(ax_quad, max_xy=5)\n", "colors = [\"red\", \"blue\", \"green\"]\n", "for i, (tree, pred_label) in enumerate(zip(X, knn.predict(X))):\n", " _draw_tree_on_quadrant(ax_quad, tree, c=colors[pred_label])\n", "\n", "plt.suptitle(\"Trees for KNN BHV(5) visualisation\")\n", "plt.show()" ] } ], "metadata": { "backends": [ "numpy" ], "kernelspec": { "display_name": "geomstats", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.14.0" } }, "nbformat": 4, "nbformat_minor": 2 }