full_network

{ "cells": [ { "cell_type": "markdown", "id": "1fb2460e", "metadata": {}, "source": [ "Main Results\n", "==========" ] }, { "cell_type": "markdown", "id": "d8fe180c", "metadata": {}, "source": [ "With the data at hand and all of the preprocessing put behind we now put together our great Wikipedia network that describes how the pages references to other pages at the site. So buckle up and get ready for a crazy ride through the winding roads of academia on Wikipedia. " ] }, { "cell_type": "code", "execution_count": 64, "id": "984bb587", "metadata": { "ExecuteTime": { "end_time": "2021-12-08T22:20:47.051780Z", "start_time": "2021-12-08T22:20:47.009488Z" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " full_network\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "

\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from IPython.core.display import display, HTML\n", "display(HTML('full_network.html'))" ] }, { "cell_type": "markdown", "id": "53798961", "metadata": {}, "source": [ "So what does this network tell us about the disciplines? Well it seems that religion is not only the [opium of the of the people](https://en.wikipedia.org/wiki/Opium_of_the_people) but also for the social sciences as this it the most linked page across all disciplines. The network seemingly confirms one of many academic-stereotypes: Researches rarely care about anything outside their own field. The outlier here seems to be Sociology that makes a sympathic and honorable attempt at working as a middle-man linking knowledge from Psychology, Anthropology and Political Science. But even for sociologists the field of Economics are rather distinct except for the case of notable scholars as [Bertrand Russel](https://en.wikipedia.org/wiki/Bertrand_Russell), [John Rawls](https://en.wikipedia.org/wiki/John_Rawls) and [Daniel Kahneman](https://en.wikipedia.org/wiki/Daniel_Kahneman) whose categorisation as economists are rather dubious to say the least. Likewise, our use of the advanced statistical technique *node2vec* confirms this, and goes even further by providing evidence suggesting that the classical opponents in Social Science, Economics and Anthropology, are as expected the least connected disciplines. Besides *node2vec*, we also use a technique called *doc2vec* to create a projection of the Wiki pages text. The distance between points can be interpreted as a metric of how similar they are. These so called \"embeddings\" can be seen through `Tensorboard`:\n", "\n", "* [Document Embeddings](https://projector.tensorflow.org/?config=https://raw.githubusercontent.com/MatPiq/social-graphs-embeddings-data/main/document_config.json)\n", "* [Node Embeddings](https://projector.tensorflow.org/?config=https://raw.githubusercontent.com/MatPiq/social-graphs-embeddings-data/main/node_config.json)" ] }, { "cell_type": "markdown", "id": "ef75d94a", "metadata": {}, "source": [ "To take our analysis a bit deeper we use a *community-detection* algorithm that locates which pages tend to bundle together and form groups - so-called communites - in our network. The image below shows the 9 biggest communites found by our algorithm and the corresponding word best describing each community." ] }, { "cell_type": "code", "execution_count": 61, "id": "f9768f4a", "metadata": { "ExecuteTime": { "end_time": "2021-12-08T22:20:33.670819Z", "start_time": "2021-12-08T22:17:41.615938Z" }, "tags": [ "hide-input" ] }, "outputs": [], "source": [ "%%capture\n", "# Yep we need all the code here ...\n", "import time\n", "import pickle\n", "import pandas as pd\n", "import community\n", "import networkx as nx\n", "from fa2 import ForceAtlas2\n", "import numpy as np\n", "from typing import List\n", "from tqdm.notebook import tqdm\n", "from collections import Counter, namedtuple, defaultdict\n", "from sklearn.linear_model import LogisticRegression\n", "\n", "import warnings\n", "warnings.filterwarnings('ignore') # Hide DeprecationWarning\n", "import matplotlib.pyplot as plt\n", "from IPython.display import set_matplotlib_formats\n", "from matplotlib import rc\n", "plt.style.use('science')\n", "set_matplotlib_formats('svg')\n", "rc(\"text\", usetex=False)\n", "\n", "from pyvis.network import Network\n", "from bokeh.io import output_notebook, show, save, output_file\n", "from bokeh.models import Range1d, Circle, ColumnDataSource, MultiLine\n", "from bokeh.plotting import from_networkx\n", "from bokeh import palettes\n", "from bokeh.layouts import row\n", "from bokeh.plotting import figure\n", "from bokeh.models import Title\n", "output_notebook()\n", "\n", "# We load in our final edgelist and model an undirected network\n", "edgelist = pd.read_pickle('https://drive.google.com/uc?export=download&id=1e3sy-VzJQXP1CozdBviCD5PYgrcWC_dw')\n", "node_attr = pd.read_pickle(\"https://drive.google.com/uc?export=download&id=1HvB-OQt4P-MXEM7X-fT47_aso9-KL_pK\")\n", "G = nx.Graph()\n", "G.add_edges_from(edgelist) \n", "nx.set_node_attributes(G, node_attr)\n", "\n", "# We extract the gcc\n", "gcc = max(nx.connected_components(G), key=len)\n", "G = G.subgraph(gcc)\n", "\n", "#Get Louvain partitions and the distribution of communites\n", "partition = community.best_partition(G, random_state = 1) # Set seed for reproducibility\n", "community_distribution = Counter(partition.values())\n", "\n", "df = pd.read_pickle('Final_df.pickle')\n", "\n", "def get_bigrams(unigram: list) -> list:\n", " \"\"\"\n", " Takes list of unigrams and converts them to bigrams\n", " \"\"\"\n", " return[\"_\".join([unigram[i], unigram[i+1]]) for i,t in enumerate(unigram) if i != len(unigram)-1]\n", "\n", "df[\"unigrams\"] = df[\"tokens\"]\n", "df[\"bigrams\"] = df[\"unigrams\"].apply(lambda x: get_bigrams(x))\n", "\n", "def create_dfm(docs:List[List], min_df:int=1, \n", " max_df:int=np.inf, idf:bool=True, \n", " return_vocab=False)->np.array:\n", " \"\"\"\n", " Creates document-feature matrix of size N (docs) x K (vocab size).\n", " args:\n", " docs(list[list]): a list of documents where a document is a list of tokens.\n", " max_df(int): maximum freq allowed for a token in a document\n", " min_df(int): minimum freq required for a token in a document\n", " idf(bool): calculate the iverse document frequency (idf) else raw count\n", " returns:\n", " dfm(np.array): the NxK dfm\n", " vocab(list): vocab of unique tokens\n", " \"\"\"\n", " #Remove very common or uncommon words\n", " if min_df != 0 or max_df != np.inf:\n", " temp = []\n", " for doc in docs:\n", " word_freq = Counter(doc)\n", " temp.append([w for w in doc if word_freq[w] >= min_df and \n", " word_freq[w] <= max_df])\n", " docs = temp\n", " \n", " #Build the vocabulary and create index for each token\n", " vocab = list(set([w for doc in docs for w in doc]))\n", " vocab_size = len(vocab)\n", " tok2idx = {w:i for i,w in enumerate(vocab)}\n", " doc_n = len(docs)\n", " \n", " #Instantiate the dfm and add counts\n", " dfm = np.zeros([doc_n, vocab_size])\n", " for i,toks in enumerate(docs):\n", " for tok in toks:\n", " tok_idx = tok2idx[tok]\n", " dfm[i, tok_idx] += 1\n", " \n", " #Calculate tf-idf\n", " if idf:\n", " dfm = dfm / dfm.sum(axis = 1)[:, None]\n", " idf = np.sign(dfm)\n", " for i in range(doc_n):\n", " idf[i] = np.log((doc_n / idf.sum(axis = 0)))\n", " dfm *= idf\n", " \n", " if return_vocab:\n", " return dfm, vocab\n", " else:\n", " return dfm\n", "\n", "#Add the corresponding community to each page in the DataFrame\n", "communites = []\n", "obs = namedtuple('Obs', 'name Louvain_Community')\n", "for n in df['title']:\n", " try:\n", " com = 'community_'+str(partition[n])\n", " except:\n", " com = np.nan\n", " communites.append(obs(n, com))\n", "df = pd.merge(df, pd.DataFrame(communites), left_on='title', right_on = 'name')\n", "\n", "#Get top9 communities\n", "top9 = ['community_'+str(c[0]) for c in community_distribution.most_common(9)]\n", "\n", "#Subset data on top 9 communities and groupby community. Extract the unigrams and bigrams.\n", "top9_df = df.loc[df['Louvain_Community']\\\n", " .isin(top9)].groupby('Louvain_Community')\\\n", " .agg({'unigrams':'sum',\n", " 'bigrams':'sum'})\n", "\n", "# Token list with both unigrams and bigrams\n", "tokens = top9_df.reset_index()[\"unigrams\"] + top9_df.reset_index()[\"bigrams\"]\n", "\n", "#Create the document term frequency matrices for unigrams and bigrams. Token must appear min. 5 times\n", "tf_idf, vocab = create_dfm(tokens, idf=True, return_vocab=True, min_df=5)\n", "\n", "#Put into dataframes with vocab as colnames and community as index\n", "tfidf_df = pd.DataFrame(tf_idf, columns=vocab, index = top9_df.index)\n", "\n", "# Document feature matrix with simple counts\n", "token_count, vocab = create_dfm(tokens, idf=False, return_vocab=True, min_df=5)\n", "token_count_pd = pd.DataFrame(token_count, columns=vocab, index = top9_df.index)\n", "\n", "def multinomial_logit_margins(x:np.array=token_count_pd.values,\n", " y:np.array=token_count_pd.index.values,\n", " vocab:list=vocab, p:int=2) -> pd.DataFrame:\n", " \"\"\"\n", " Fits a multinomial logistic regression with LASSO penalty of size p.\n", " Then finds the average marginal effect for each feature for each y and append \n", " it to a DataFrame. The model fits based on a x and y both being numpy arrays. \n", " \"\"\"\n", " fitted_model = LogisticRegression(multi_class='multinomial', \n", " penalty='l1', \n", " solver = \"saga\", \n", " C= p,\n", " max_iter=10000).fit(x,y)\n", " betas = fitted_model.coef_\n", " probas = fitted_model.predict_proba(x)\n", " classes = fitted_model.classes_\n", " if len(classes) > 2:\n", " diff = betas[:,None] - np.dot(probas, betas)\n", " avg_margins = np.sum(probas * diff.T, axis=1) / probas.shape[0]\n", " avg_margins = pd.DataFrame(avg_margins, columns=classes)\n", " avg_margins[\"token\"] = vocab\n", " return avg_margins\n", "\n", "def plot_most_predictive_features(margins_df:pd.DataFrame, K:int=20):\n", " \"\"\"\n", " Based on a DataFrame with the average marginal effect for a list of \n", " features this function plots the K highest features for the different \n", " classes.\n", " \"\"\"\n", " fig, axs = plt.subplots(nrows = 3, ncols=3, figsize = (10,10), dpi = 300)\n", " fig.suptitle(\"Top 20 most predictive features for various communities\", fontsize=16)\n", " \n", " axs = axs.flat\n", " community_features = {}\n", " most_predictive_features = {}\n", " for j, c in enumerate(margins_df.drop('token', axis=1).columns):\n", " community_features[c] = {margins_df[\"token\"][i]: margins_df[c][i] for i in np.argpartition(margins_df[c],-K)[-K:]}\n", " community_features[c] = sorted(community_features[c].items(), key=lambda x: x[1], reverse=True)\n", " x = [i[0].replace('_', ' ') for i in community_features[c]]\n", " y = [i[1] for i in community_features[c]]\n", " axs[j].plot(x, y,'ko')\n", " axs[j].set_title(f\"{c.replace('_', ' ')}\", size = 10)\n", " axs[j].tick_params(axis='x', rotation=90)\n", " axs[j].tick_params(axis='x', which='minor', bottom=False, top=False)\n", " \n", " most_predictive_features[c] = x\n", " plt.tight_layout()\n", " \n", " return most_predictive_features # We return all the features as we want to use them later..\n", "# Prettyfying and uniforming names in the df and graph\n", "\n", "# We fit the multinomial_logit_margins() on our raw counts and plot our results\n", "margins_pd = multinomial_logit_margins()\n", "most_predictive_features = plot_most_predictive_features(margins_pd)\n", "\n", "def change_node_names(node):\n", " \"\"\"\n", " Replaces \"_\" to \" \" in node names.\n", " \"\"\"\n", " return \" \".join(node.split(\"_\"))\n", "G = nx.relabel_nodes(G, change_node_names)\n", "df[\"title\"] = df[\"title\"].apply(lambda x: \" \".join(x.split(\"_\")))\n", "\n", "# Setting colours\n", "def get_colors_palette_from_parent(G: nx.Graph) -> dict:\n", " \"\"\"\n", " Creates a color palette given the parent attribute of the \n", " nodes in a network.\n", " \"\"\"\n", " disciplines = set([G.nodes[node][\"parent\"] for node in G.nodes()])\n", " col_pal = palettes.viridis(len(disciplines))\n", " col_pal = {parent: col_pal[key] for key, parent in enumerate(disciplines)}\n", " return col_pal\n", "\n", "col_pal = get_colors_palette_from_parent(G)\n", "\n", "def get_color_list_from_palette(G: nx.Graph, col_pal: dict=col_pal) -> list:\n", " \"\"\"\n", " Creates a list of colors given the parent attribute of a node\n", " and its color defined in the color palette.\n", " \"\"\"\n", " return [col_pal[G.nodes[i][\"parent\"]] for i in G.nodes]\n", "\n", "# Creates dictionary of subgraphs for each community\n", "community_graphs = {}\n", "for c in top9_df.index.tolist():\n", " community_nodes = [x for x, y in G.nodes(data=True) \n", " if x in df[df[\"Louvain_Community\"] == c][\"title\"].tolist()]\n", " community_graphs[c] = G.subgraph(community_nodes)\n", " \n", "# Specifies positioning algorithm\n", "forceatlas2 = ForceAtlas2(gravity=1)\n", "\n", "# Create and store a graph plot for each community\n", "graphs = {}\n", "for i, k in enumerate(community_graphs.keys()):\n", " G = community_graphs[k]\n", " title = f'Community: {k.split(\"_\")[1]}'\n", " HOVER_TOOLTIPS = [(\"Page\", \"@index\"),\n", " (\"Discipline\", \"@parent\")]\n", " \n", " #Create a plot\n", " graphs[k] = figure(tooltips = HOVER_TOOLTIPS,\n", " width=333, plot_height=333,\n", " tools=\"pan,wheel_zoom,save,reset\", active_scroll='wheel_zoom', \n", " x_range=Range1d(-250, 250),\n", " y_range=Range1d(-250, 250))\n", " \n", " # Add title and subtitle\n", " graphs[k].add_layout(Title(text= f'{most_predictive_features[k][0:5]}', text_font_style=\"italic\"), 'above')\n", " graphs[k].add_layout(Title(text=f'Community: {k.split(\"_\")[1]}', text_font_size=\"16pt\"), 'above')\n", " \n", " # Hide grid and axs\n", " graphs[k].axis.visible = False\n", " graphs[k].grid.grid_line_color = None\n", " \n", " #Set positions, node size and color\n", " positions = forceatlas2.forceatlas2_networkx_layout(G, pos=None, iterations=2000)\n", " G_interactive = from_networkx(G, positions, scale=1, center=(0, 0))\n", " G_interactive.node_renderer.data_source.data['node_sizes'] = [G.degree(node) * 0.25 for node in tqdm(G.nodes())]\n", " G_interactive.node_renderer.data_source.data['node_colour'] = get_color_list_from_palette(G)\n", " G_interactive.node_renderer.data_source.data['alpha'] = [0.75 for node in G.nodes()]\n", " G_interactive.node_renderer.glyph = Circle(\n", " size=\"node_sizes\",\n", " fill_color=\"node_colour\",\n", " fill_alpha = \"alpha\")\n", " \n", " #Set edge opacity and width\n", " G_interactive.edge_renderer.glyph = MultiLine(line_alpha=0.8, line_width=0.1)\n", " graphs[k].renderers.append(G_interactive)" ] }, { "cell_type": "code", "execution_count": 63, "id": "b2074f1b", "metadata": { "ExecuteTime": { "end_time": "2021-12-08T22:20:38.585605Z", "start_time": "2021-12-08T22:20:37.695717Z" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "\n", "

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Now let's take a look at the network. Generally speaking the pattern from our previous network is confirmed: The editors of disciplines' pages on Wikipedia do really not like to link to pages from other disciplines! But it also reveals that the disciplines pages might not be as uniform as first anticipated. Community 1, 10 and 15 are rather unambigous communities of the Political Science category but they serve as a great example of the discipline's heterogenity. On the one hand Community 15 illustrates the modern study of politics at the universities using scientific methods, whereas community 1 and 10 are two pages of a another subcategory we could label \"ideology\". And even though they both revolve around political ideologies, they are widely different as one describes far-left/socialist tendencies whereas the other deals with far-right/libertarian pages. Our detection of communites therefore adds nuances to the painting of the social science landscape: Yes, they do not like to interact, but even within their own disciplinary most like to stay together in their small community of like-minded pages. " ] }, { "cell_type": "markdown", "id": "51e58dbd", "metadata": {}, "source": [ "## Okay.. So the discipline are different, but there must be some similiarites, right?" ] }, { "cell_type": "markdown", "id": "4b80854e", "metadata": {}, "source": [ "Paradoxically, a rather famous and widely applied theory in social science [*Social identity theory*](https://en.wikipedia.org/wiki/Social_identity_theory) can help us understand why all of the disciplines seem to think within the box. Originally put forward by [Henri Tajfel](https://en.wikipedia.org/wiki/Henri_Tajfel) and his apprentice [John Turner](https://en.wikipedia.org/wiki/John_Turner_(psychologist)) the theory explains how members of a group favorize persons similar to themselves, say sociologists, at the expense of the out-group members, say economists. Interestingly, the theory propose that one way to build bridge between people of different groups is by exposure to one another to discover their many similarities. A lesson we believe the editors of Wikipedia could learn a bit from.\n", "\n", "Instead of only looking at how the Wikipeda pages were connected we decided to also look at their actual content. For this we ran a *topic-model*, a model similar to our community detection, but instead of relying on the networks structure it tries to partition the pages into different topics based on the pages' *text*." ] }, { "cell_type": "markdown", "id": "2bdf3846", "metadata": { "ExecuteTime": { "end_time": "2021-12-08T20:03:28.428736Z", "start_time": "2021-12-08T20:03:28.255126Z" } }, "source": [ "![](topic_models.svg)\n" ] }, { "cell_type": "markdown", "id": "c2cb6550", "metadata": {}, "source": [ "The funny thing about these topics is, that although some clearly relates to only one disciplines, most of them are constituted by words of pages from more than one discipline. The most clear example of this is the topic we have decided to label *statistical methods*. When we qualitatively asses the pages of this topic we find a remarkable diversity in the discipline represented [hSBM Topic Modelling](explainer_topic_model). As this topic relates to the (statistical) methods used to genereate new knowledge it might suggest, that although the theory of the discplines might vary a bit, the ways they explore the world are fairly similar. What we are trying to say with this is that despite the disciplines cluster together on Wikipedia and stick to intra-disciplinary referencing, they are actually not that different from eatch other. Maybe we could all learn from Tajfel and Turner and enrichen our perspectives by seeing things from other angels." ] } ], "metadata": { "celltoolbar": "Edit Metadata", "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.8.8" } }, "nbformat": 4, "nbformat_minor": 5 }