DiffusionMap.ipynb

diffusionmap.ipynb

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      "name": "DiffusionMap.ipynb",
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        "id": "view-in-github",
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      "source": [
        "<a href=\"https://colab.research.google.com/gist/rahulrajpl/36a5724d0c261b915292182b1d741393/diffusionmap.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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        "id": "JpOnmegjEOUr",
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      "source": [
        "# Diffusion Map implementation\n",
        "\n",
        "\n",
        "**Author**: Rahul Raj (twitter.com/rahulrajpl)\n",
        "\n",
        "License: MIT License 2020 Rahul Raj\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "nsHBKoawDfue",
        "colab": {}
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import random\n",
        "import pandas as pd\n",
        "from sklearn.metrics.pairwise import euclidean_distances\n",
        "from scipy.linalg import eigh\n",
        "import plotly.graph_objs as go\n",
        "from plotly.subplots import make_subplots\n",
        "import warnings\n",
        "warnings.filterwarnings('ignore')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kpt_wsF-2vmf",
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      "source": [
        "def find_diffusion_matrix(X=None, alpha=0.15):\n",
        "    \"\"\"Function to find the diffusion matrix P\n",
        "        \n",
        "        >Parameters:\n",
        "        alpha - to be used for gaussian kernel function\n",
        "        X - feature matrix as numpy array\n",
        "        \n",
        "        >Returns:\n",
        "        P_prime, P, Di, K, D_left\n",
        "    \"\"\"\n",
        "    alpha = alpha\n",
        "        \n",
        "    dists = euclidean_distances(X, X)\n",
        "    K = np.exp(-dists**2 / alpha)\n",
        "    \n",
        "    r = np.sum(K, axis=0)\n",
        "    Di = np.diag(1/r)\n",
        "    P = np.matmul(Di, K)\n",
        "    \n",
        "    D_right = np.diag((r)**0.5)\n",
        "    D_left = np.diag((r)**-0.5)\n",
        "    P_prime = np.matmul(D_right, np.matmul(P,D_left))\n",
        "\n",
        "    return P_prime, P, Di, K, D_left"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PX_cJkmL2vmr",
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      "source": [
        "def find_diffusion_map(P_prime, D_left, n_eign=3):\n",
        "    \"\"\"Function to find the diffusion coordinates in the diffusion space\n",
        "        \n",
        "        >Parameters:\n",
        "        P_prime - Symmetrized version of Diffusion Matrix P\n",
        "        D_left - D^{-1/2} matrix\n",
        "        n_eigen - Number of eigen vectors to return. This is effectively \n",
        "                    the dimensions to keep in diffusion space.\n",
        "        \n",
        "        >Returns:\n",
        "        Diffusion_map as np.array object\n",
        "    \"\"\"   \n",
        "    n_eign = n_eign\n",
        "    \n",
        "    eigenValues, eigenVectors = eigh(P_prime)\n",
        "    idx = eigenValues.argsort()[::-1]\n",
        "    eigenValues = eigenValues[idx]\n",
        "    eigenVectors = eigenVectors[:,idx]\n",
        "    \n",
        "    diffusion_coordinates = np.matmul(D_left, eigenVectors)\n",
        "    \n",
        "    return diffusion_coordinates[:,:n_eign]"
      ],
      "execution_count": 0,
      "outputs": []
    },
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      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "1Sil2FeYDfuy",
        "colab": {}
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      "source": [
        "# Reference: https://scikit-learn.org/stable/auto_examples/manifold/plot_compare_methods.html#\n",
        "def make_plot(N=1000, rseed=42):\n",
        "    # Make a plot with \"HELLO\" text; save as PNG\n",
        "    fig, ax = plt.subplots(figsize=(4, 1))\n",
        "    fig.subplots_adjust(left=0, right=1, bottom=0, top=1)\n",
        "    ax.axis('off')\n",
        "    ax.text(0.5, 0.4, 'S', va='center', ha='center', size=85)\n",
        "    fig.savefig('plot.png')\n",
        "    plt.close(fig)\n",
        "    fig.show()\n",
        "    # Open this PNG and draw random points from it\n",
        "    from matplotlib.image import imread\n",
        "    data = imread('plot.png')[::-1, :, 0].T\n",
        "    rng = np.random.RandomState(rseed)\n",
        "    X = rng.rand(5 * N, 2)\n",
        "    i, j = (X * data.shape).astype(int).T\n",
        "    mask = (data[i, j] < 1)\n",
        "    X = X[mask]\n",
        "    X[:, 0] *= (data.shape[0] / data.shape[1])\n",
        "    X = X[:N]\n",
        "    return X[np.argsort(X[:, 0])]"
      ],
      "execution_count": 0,
      "outputs": []
    },
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      "cell_type": "code",
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        "id": "e0xk6Azz2vm8",
        "colab_type": "code",
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        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 417
        }
      },
      "source": [
        "# Generate shape\n",
        "X = make_plot(3000)\n",
        "data=go.Scatter(x=X[:, 0], y=X[:, 1], mode='markers', marker=dict(\n",
        "        size=3,color=X[:,1],opacity=1,colorscale='Viridis'))\n",
        "layout=go.Layout(title_text=\"Original shape\", title_x=0.5, title_y=0.8,title_font_size=12)\n",
        "fig = go.Figure(data=[data], layout=layout)\n",
        "fig.update_layout(height=400, width=400,showlegend=False)\n",
        "fig.update_xaxes(showticklabels=False)\n",
        "fig.update_yaxes(showticklabels=False)\n",
        "fig.show()"
      ],
      "execution_count": 5,
      "outputs": [
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          "metadata": {
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    {
      "cell_type": "code",
      "metadata": {
        "id": "CUpJEGDU2vnG",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Adding new dimension to the original geometric structure\n",
        "newX = pd.DataFrame(X)\n",
        "newX['dimension1'] = [random.uniform(0.1,0.5) for _ in range(len(X))]\n",
        "newX = np.asarray(newX)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hBHTmZCL2vnM",
        "colab_type": "code",
        "colab": {}
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        "def plot_3Dfigure(newX, title='Datapoints'):\n",
        "    data = go.Scatter3d(x=newX[:,0], y=newX[:,1], z=newX[:,2], mode='markers', marker=dict(\n",
        "            size=2,color=newX[:,1],opacity=0.7,colorscale='Viridis'))\n",
        "    layout = go.Layout(title_text=title,title_x=0.5,title_y=0.8,title_font_size=12)\n",
        "    fig = go.Figure(data=[data], layout=layout)\n",
        "    fig.update_layout(showlegend=False)\n",
        "    fig.update_xaxes(showticklabels=False)\n",
        "    fig.update_yaxes(showticklabels=False)\n",
        "    fig.update_layout(scene = dict(\n",
        "                    xaxis = dict(title= '', ticks= '', showticklabels= False,),\n",
        "                    yaxis = dict(title= '', ticks= '', showticklabels= False,),\n",
        "                    zaxis = dict(title= '', ticks= '', showticklabels= False,),\n",
        "                    ))\n",
        "                  \n",
        "    fig.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "P9mdGJ_52vnS",
        "colab_type": "code",
        "outputId": "679b48d3-110d-4d32-8c7a-bbc440e9ce7f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        }
      },
      "source": [
        "plot_3Dfigure(newX, title='Synthetic 3D Datapoints')"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
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        "def plot_2Dsub_figures(d_map, alpha_values, title='Diffused points'):\n",
        "    subplot_titles=[f'α={round(a,4)}' for a in alpha_values]\n",
        "    fig = make_subplots(rows=2, cols=5,subplot_titles=subplot_titles)\n",
        "    for i in range(1,3):\n",
        "        for j in range(1,6):\n",
        "            dmap_idx = i+j-1\n",
        "            fig.add_trace(\n",
        "                go.Scatter(x=d_map[dmap_idx][:,0], y=d_map[dmap_idx][:,1], mode='markers', marker=dict(\n",
        "                size=3,color=d_map[dmap_idx][:,1],opacity=0.8,colorscale='Viridis')),row=i, col=j)\n",
        "\n",
        "    fig.update_layout(title_text=title, title_x=0.5)\n",
        "    fig.update_xaxes(showticklabels=False)\n",
        "    fig.update_yaxes(showticklabels=False)\n",
        "    fig.update_layout(height=500, width=1000, showlegend=False)\n",
        "    fig.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-0o65Uy92vnv",
        "colab_type": "code",
        "colab": {}
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      "source": [
        "def apply_diffusions(alpha_start=0.001, alpha_end= 0.009, title='Diffused points'):\n",
        "    d_maps = []\n",
        "    alpha_values = np.linspace(alpha_start, alpha_end, 10)\n",
        "    for alpha in alpha_values:\n",
        "        P_prime, P, Di, K, D_left = find_diffusion_matrix(newX, alpha=alpha)\n",
        "        d_maps.append(find_diffusion_map(P_prime, D_left, n_eign=2))\n",
        "    return d_maps, alpha_values"
      ],
      "execution_count": 0,
      "outputs": []
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    {
      "cell_type": "code",
      "metadata": {
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        "colab_type": "code",
        "outputId": "2f56cf04-3f4c-44a7-8ebd-1fa06c823224",
        "colab": {
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          "height": 517
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      "source": [
        "d_maps, alpha_values = apply_diffusions(0.001, 0.009)\n",
        "plot_2Dsub_figures(d_maps,alpha_values)"
      ],
      "execution_count": 11,
      "outputs": [
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    {
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      "source": [
        "d_maps, alpha_values = apply_diffusions(0.01, 0.09)\n",
        "plot_2Dsub_figures(d_maps,alpha_values)"
      ],
      "execution_count": 12,
      "outputs": [
        {
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              "                        [{\"marker\": {\"color\": [0.007509588712984552, -0.0033447505881739024, 0.0075417200674111826, -0.0033905561951260263, -0.0036687508824933073, 0.007545057973341132, 0.007511219348541352, -0.0034642214273993325, -0.003743349820522875, 0.0075116399407837205, -0.003305212182783729, -0.0038217236318333872, -0.0032688987911056945, 0.007544013533377012, -0.0037885429981030973, 0.007530451485588356, -0.003189688975160533, 0.0075219811212110105, 0.007517519056299597, 0.007524252210856195, 0.007536751888630314, -0.003258372078946923, 0.007481649250144677, -0.003391225815810798, -0.0040091915893462554, -0.003333734769121821, -0.0031973284807600803, -0.004069530045668236, 0.007513544548526679, 0.007525350886823239, 0.007488772122154056, -0.003775035831144367, -0.004015862844153112, -0.003980961232813489, -0.003535336156828299, 0.007499180655404191, 0.007466927676424638, 0.0075159755659705806, 0.007497838257980409, 0.007507691398385734, 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diffusion_coordinates = np.matmul(D_left, eigenVectors)
why not diffusion_coordinates = np.matmul(eigenValues, eigenVectors)?