Word2Vec.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "gpuClass": "standard"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/jansoe/AICA/blob/main/Word2Vec.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RX02S6Aq8OxF"
      },
      "source": [
        "# Wortvektoren"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c6sSUrDuDXkX",
        "cellView": "form"
      },
      "source": [
        "#@title \n",
        "#@markdown Importieren von Extrafunktionalität (insbesondere Gensim)\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import nltk\n",
        "import gensim\n",
        "from pprint import pprint\n",
        "from sklearn.metrics.pairwise import cosine_similarity\n",
        "\n",
        "#Die Bibliothek `gensim` ist etwas veraltet und gibt eine Menge Warnungen aus. \n",
        "# Wir können diese aber erstmal getrost ignorieren und deren Ausgabe wie folgt verhindern.\n",
        "import warnings\n",
        "warnings.filterwarnings('ignore')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UWH2te0GpahO"
      },
      "source": [
        "Mit dem `gensim.downloader` können wir vortrainierte Wortvektoren herunterladen."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0KspB4YAtT0t",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "24eb5487-58dc-43ef-993a-0c92e5d379c1"
      },
      "source": [
        "import gensim.downloader as api\n",
        "api.info()['models'].keys()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "dict_keys(['fasttext-wiki-news-subwords-300', 'conceptnet-numberbatch-17-06-300', 'word2vec-ruscorpora-300', 'word2vec-google-news-300', 'glove-wiki-gigaword-50', 'glove-wiki-gigaword-100', 'glove-wiki-gigaword-200', 'glove-wiki-gigaword-300', 'glove-twitter-25', 'glove-twitter-50', 'glove-twitter-100', 'glove-twitter-200', '__testing_word2vec-matrix-synopsis'])"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ddSifIOVXLGS",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "58e921ee-3fd3-4733-944b-bc75ddcd5498"
      },
      "source": [
        "model = api.load('glove-wiki-gigaword-300')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[=================================================-] 99.9% 375.9/376.1MB downloaded\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Visualisiern von Wortvektoren"
      ],
      "metadata": {
        "id": "1QuJ-8tnLBBD"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title\n",
        "#@markdown Funktion zum Visualisieren\n",
        "\n",
        "def plot_vector(v):\n",
        "    plt.subplots(figsize=(15,1))\n",
        "    plt.imshow(v.reshape(1,-1), aspect='auto', cmap=plt.cm.Spectral, vmin=-.3, vmax=.3)\n",
        "    _ = plt.colorbar()\n",
        "    plt.yticks([])\n",
        "    plt.xlabel('Dimension')"
      ],
      "metadata": {
        "id": "erzLauumL1DM",
        "cellView": "form"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KU7-j75qtt9C",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 157
        },
        "outputId": "dfa323a0-ca0c-4ea8-a5b4-d55cca2f9c9b"
      },
      "source": [
        "word_vector1 = model.get_vector('noodles', norm=True)\n",
        "plot_vector(word_vector1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x100 with 2 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Wortähnlichkeiten"
      ],
      "metadata": {
        "id": "_WelWGM61RBz"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Wir können natürlich auch Wortvektoren vergleichen"
      ],
      "metadata": {
        "id": "y66jPGvEqaas"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "word1 = 'pasta'\n",
        "word2 = 'noodles'\n",
        "\n",
        "word_vector1 = model.get_vector(word1, norm=True)\n",
        "plot_vector(word_vector1)\n",
        "plt.ylabel(word1)\n",
        "\n",
        "word_vector2 = model.get_vector(word2, norm=True)\n",
        "plot_vector(word_vector2)\n",
        "plt.ylabel(word2)\n",
        "\n",
        "difference = word_vector1 - word_vector2 \n",
        "plot_vector(difference)\n",
        "plt.ylabel(f'{word1}-{word2}')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 454
        },
        "id": "YF_f8YZWWAor",
        "outputId": "3eb0948a-2ab5-401f-b00e-3b2e7231e83c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'pasta-noodles')"
            ]
          },
          "metadata": {},
          "execution_count": 48
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x100 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x100 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x100 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Die Ähnlichkeit von 2 Vekoren können wir nicht nur über ihre Differenz sondern auch über den Winkel dazwischen bestimmen:"
      ],
      "metadata": {
        "id": "WKkgZY56sFrx"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "cosine_similarity(\n",
        "    word_vector1.reshape(1, -1), \n",
        "    word_vector2.reshape(1, -1)\n",
        ")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FKZd0wk4XLmR",
        "outputId": "bbbbfd38-8113-4477-d7a2-5620379da011"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.63435376]], dtype=float32)"
            ]
          },
          "metadata": {},
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E_uQgFLEZaJ1"
      },
      "source": [
        "Wir können somit auch  diejenigen Wörter aus dem Korpus heraussuchen, die im latenten Raum am nahesten liegen und somit eine verwandte Bedeutung aufweisen:"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "model.most_similar('noodles', topn=5)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dhvC6GotVUb8",
        "outputId": "b9ff9c41-68e5-4670-c054-1ef93cfcd758"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[('noodle', 0.6829882264137268),\n",
              " ('pasta', 0.634353756904602),\n",
              " ('vermicelli', 0.6315168738365173),\n",
              " ('tofu', 0.6053614616394043),\n",
              " ('cooked', 0.6040924787521362)]"
            ]
          },
          "metadata": {},
          "execution_count": 50
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7ZxJkZdzD5PB",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b14d2dbd-5ca2-492f-d5fe-26bbbb8968f3"
      },
      "source": [
        "model.most_similar('shoe', topn=5)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[('shoes', 0.7242045402526855),\n",
              " ('footwear', 0.5965994000434875),\n",
              " ('sneaker', 0.5847949981689453),\n",
              " ('sneakers', 0.5435681343078613),\n",
              " ('clothing', 0.5319083333015442)]"
            ]
          },
          "metadata": {},
          "execution_count": 51
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wVWQITrgpOLF"
      },
      "source": [
        "### Analogien im Nachbarschaftsraum\n",
        "\n",
        "Dank der Vektorrepräsentation eines Word2Vec-Modells lässt sich auch leicht nach analogen Verwandtschaftsbeziehungen suchen. Z.B. können wir folgende Aufgabe stellen:\n",
        "\n",
        "`berlin` verhält sich zu `germany` wie `???` zu `italy`\n",
        "\n",
        "Die besten Kandidaten für die Lösung dieser Aufgabe können wir heraussuchen, indem wir uns im Vektorraum zu einem entsprechenden Punkt bewegen (`berlin - germany + italy`) und dort die nahesten Begriffe identifizieren: "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XWkCHwbX6ElZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "bc5360e9-da29-472d-cd2a-a10d6cf75673"
      },
      "source": [
        "model.most_similar(positive=['berlin', 'italy'], negative=['germany'], topn=1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[('rome', 0.7019403576850891)]"
            ]
          },
          "metadata": {},
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5MpCWK-e0NE_",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c4a0bc4e-b74d-402d-df49-b5cbc1f30e69"
      },
      "source": [
        "model.most_similar(positive=['munich', 'italy'], negative=['germany'], topn=1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[('milan', 0.6967077255249023)]"
            ]
          },
          "metadata": {},
          "execution_count": 53
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vGm2nzKOu9l6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f52eaf2d-860b-42bf-e02f-27ee4fba977f"
      },
      "source": [
        "model.most_similar(positive=['beer', 'italy'], negative=['germany'], topn=1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[('wine', 0.5321523547172546)]"
            ]
          },
          "metadata": {},
          "execution_count": 54
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-OSz3WiA1RTk",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ffd16c18-632d-4873-9fb2-3784cc8f08d1"
      },
      "source": [
        "model.most_similar(positive=['beer', 'russia'], negative=['germany'], topn=1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[('vodka', 0.5345780849456787)]"
            ]
          },
          "metadata": {},
          "execution_count": 55
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IJVn3PIFgG1F"
      },
      "source": [
        "### Visualisierung der Wortverwandtschaft mit TSNE\n",
        "Zuerst visualisieren wir die Verwandtschaftsbeziehungen der Wortvektoren mit TSNE. Dazu lassen wir uns die 200 Wörter heraussuchen, die dem Wort `pasta` am nächsten stehen, und erstellen uns eine Liste von deren Vektoren."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iw1nuS2rY6E4"
      },
      "source": [
        "top_similarity = model.most_similar(positive=['pasta'], topn=200)\n",
        "selected_words = [word for word, similarity in top_similarity]\n",
        "vectors = np.array([model.get_vector(word) for word in selected_words])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gu9AAyCE6xrp"
      },
      "source": [
        "Jetzt können wir wieder TSNE verwenden, um die hochdimensionalen Vektoren in einem zweidimensionalen Raum zu platzieren und dabei deren lokale Verwandtschaftsbeziehungen beizubehalten."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_qr3uySrY_S0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        },
        "outputId": "fac52d34-3f5f-499c-ee90-96c8515b913b"
      },
      "source": [
        "import plotly.express as px\n",
        "import pandas as pd\n",
        "from sklearn.manifold import TSNE\n",
        "\n",
        "tsne = TSNE(\n",
        "    n_components = 2,\n",
        "    perplexity = 20 # ~Anzahl der Nachbarn zu die der Abstand möglichst genau approximiert werden soll \n",
        ")\n",
        "vectors_2D = tsne.fit_transform(vectors)\n",
        "\n",
        "to_plot = pd.DataFrame(vectors_2D, columns=['x', 'y'])\n",
        "to_plot['labels'] = selected_words\n",
        "\n",
        "px.scatter(to_plot, x='x', y='y', hover_name='labels')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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          "metadata": {}
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      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "##### Aufgabe: Was beobachten Sie wenn Sie den Parameter Perplexity ändern?"
      ],
      "metadata": {
        "id": "yjOe4GbY4MUg"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oBRo8vSppcPO"
      },
      "source": [
        "### Visualisierung der Wortverwandtschaften mit PCA"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hL0lJ6GL6o3L"
      },
      "source": [
        "words_to_vis = [\n",
        "    'germany', 'italy', 'france', 'spain', 'uk', 'poland', 'russia', 'austria',\n",
        "    'berlin', 'rome', 'paris', 'madrid', 'london', 'warsaw', 'moscow', 'vienna', \n",
        "]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-bCNyEkMpjJX"
      },
      "source": [
        "Wir errechnen zunächst wieder die Wortvektoren der ausgewählten Wörter."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FikqqY_7v1Vj"
      },
      "source": [
        "vectors = [model.get_vector(word, norm=True) for word in words_to_vis]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ipJ1MOQ3pvZ0"
      },
      "source": [
        "Nun visualisieren wir diese wir in einem 2D-Raum. Anders als zuvor verwenden wir nun jedoch die Methode `PCA`, denn im Gegensatz zu TSNE versucht PCA auch Beziehungen von weit voneinander entfernten Punkten mit abzubilden. Bei wenigen Punkte ist das vorteilhaft, jedoch geht dieser Vorteil bei vielen Punkten schnell verloren, da deren komplexe Nachbarschaftsbeziehungen im hochdimensionalen Raum nicht adäquat in 2D abgebildet werden können."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ihK8vVqMw8Fp"
      },
      "source": [
        "from sklearn.decomposition import PCA\n",
        "import plotly.express as px\n",
        "import pandas as pd"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H_2q6bWDv2XY"
      },
      "source": [
        "pca = PCA(n_components=2)\n",
        "vectors_2D = pca.fit_transform(vectors)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "viQDxmP0weWH",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        },
        "outputId": "90b2259b-f76f-4f71-bed7-7bcb84429de1"
      },
      "source": [
        "to_plot = pd.DataFrame(vectors_2D, columns=['x', 'y'])\n",
        "to_plot['labels'] = words_to_vis\n",
        "\n",
        "px.scatter(to_plot, x='x', y='y', hover_name='labels')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CyRiOFrKcLnc"
      },
      "source": [
        "#### Aufgabe: Visualierung anderer Begriffe"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Ändern sie die Begriffe in der Variable `words_to_vis` und führen Sie alle nachfolgenden Zellen nochmals aus. Sind die visuelle Darstellung der Wordvektoren und ihre Nachbarschaftsbeziehungen intuitiv nachvollziehbar? Können Sie Eigenschaften identifizieren, die im Zusammenhang mit der X- und/oder Y-Achse stehen? "
      ],
      "metadata": {
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