docs/tutorials/hierarchy/ward.ipynb

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  {
   "cell_type": "markdown",
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   "source": [
    "# Ward"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook illustrates the hierarchical clustering of graphs by the [Ward method](https://scikit-network.readthedocs.io/en/latest/reference/hierarchy.html), after embedding in a space of low dimension."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import SVG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "pycharm": {
     "is_executing": false
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "pycharm": {
     "is_executing": false,
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    }
   },
   "outputs": [],
   "source": [
    "from sknetwork.data import karate_club, painters, movie_actor\n",
    "from sknetwork.embedding import Spectral\n",
    "from sknetwork.hierarchy import Ward, cut_straight, dasgupta_score, tree_sampling_divergence\n",
    "from sknetwork.visualization import svg_graph, svg_digraph, svg_bigraph, svg_dendrogram"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "pycharm": {
     "is_executing": false
    }
   },
   "outputs": [],
   "source": [
    "graph = karate_club(metadata=True)\n",
    "adjacency = graph.adjacency\n",
    "position = graph.position"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "pycharm": {
     "is_executing": false
    }
   },
   "outputs": [],
   "source": [
    "# hierarchical clustering\n",
    "ward = Ward()\n",
    "dendrogram = ward.fit_transform(adjacency)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "pycharm": {
     "is_executing": false
    }
   },
   "outputs": [],
   "source": [
    "image = svg_dendrogram(dendrogram)\n",
    "SVG(image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "pycharm": {
     "is_executing": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0]\n"
     ]
    }
   ],
   "source": [
    "# cuts\n",
    "labels = cut_straight(dendrogram)\n",
    "print(labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "pycharm": {
     "is_executing": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 1 1 1 3 3 3 1 0 0 3 1 1 1 2 2 3 1 2 1 2 1 2 0 0 0 0 0 0 2 2 0 0 0]\n"
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   ],
   "source": [
    "n_clusters = 4\n",
    "labels, dendrogram_aggregate = cut_straight(dendrogram, n_clusters, return_dendrogram=True)\n",
    "print(labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "_, counts = np.unique(labels, return_counts=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# aggregate dendrogram\n",
    "image = svg_dendrogram(dendrogram_aggregate, names=counts, rotate_names=False)\n",
    "SVG(image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "pycharm": {
     "is_executing": false
    }
   },
   "outputs": [],
   "source": [
    "# clustering\n",
    "image = svg_graph(adjacency, position, labels=labels)\n",
    "SVG(image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "pycharm": {
     "is_executing": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.583710407239819"
      ]
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     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# metrics\n",
    "dasgupta_score(adjacency, dendrogram)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "pycharm": {
     "is_executing": false
    }
   },
   "outputs": [],
   "source": [
    "# other embedding\n",
    "ward = Ward(embedding_method=Spectral(4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Directed graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "pycharm": {
     "is_executing": false
    }
   },
   "outputs": [],
   "source": [
    "graph = painters(metadata=True)\n",
    "adjacency = graph.adjacency\n",
    "position = graph.position\n",
    "names = graph.names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "pycharm": {
     "is_executing": false
    }
   },
   "outputs": [],
   "source": [
    "# hierarchical clustering\n",
    "ward = Ward()\n",
    "dendrogram = ward.fit_transform(adjacency)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "pycharm": {
     "is_executing": false
    }
   },
   "outputs": [],
   "source": [
    "image = svg_dendrogram(dendrogram, names, n_clusters=3, rotate=True)\n",
    "SVG(image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "pycharm": {
     "is_executing": false
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    "scrolled": true
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 1 0 1 1 2 0 0 1 0 0 0 2]\n"
     ]
    }
   ],
   "source": [
    "# cut with 3 clusters\n",
    "labels = cut_straight(dendrogram, n_clusters = 3)\n",
    "print(labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "pycharm": {
     "is_executing": false
    }
   },
   "outputs": [],
   "source": [
    "image = svg_digraph(adjacency, position, names=names, labels=labels)\n",
    "SVG(image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "pycharm": {
     "is_executing": false
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.49857142857142855"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# metrics\n",
    "dasgupta_score(adjacency, dendrogram)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bipartite graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "graph = movie_actor(metadata=True)\n",
    "biadjacency = graph.biadjacency\n",
    "names_row = graph.names_row\n",
    "names_col = graph.names_col"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BiWard(embedding_method=GSVD(n_components=10, regularization=None, relative_regularization=True, factor_row=0.5, factor_col=0.5, factor_singular=0.0, normalized=True, solver=LanczosSVD()), cluster_row=True, cluster_col=True, cluster_both=True)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# hierarchical clustering\n",
    "ward = Ward(co_cluster = True)\n",
    "ward.fit(biadjacency)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "dendrogram_row = ward.dendrogram_row_\n",
    "dendrogram_col = ward.dendrogram_col_\n",
    "dendrogram_full = ward.dendrogram_full_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "image = svg_dendrogram(dendrogram_row, names_row, n_clusters=4, rotate=True)\n",
    "SVG(image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "image = svg_dendrogram(dendrogram_col, names_col, n_clusters=4, rotate=True)\n",
    "SVG(image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# cuts\n",
    "labels = cut_straight(dendrogram_full, n_clusters = 4)\n",
    "n_row = biadjacency.shape[0]\n",
    "labels_row = labels[:n_row]\n",
    "labels_col = labels[n_row:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "image = svg_bigraph(biadjacency, names_row, names_col, labels_row, labels_col)\n",
    "SVG(image)"
   ]
  }
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