Plotting/Confusion-Matrix-Sankey.ipynb

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    "# Daily-Dose-of-Data-Science\n",
    "\n",
    "[Daily Dose of Data Science](https://avichawla.substack.com) is a publication on Substack that brings together intriguing frameworks, libraries, technologies, and tips that make the life cycle of a Data Science project effortless. \n",
    "\n",
    "Author: Avi Chawla\n",
    "\n",
    "[Medium](https://medium.com/@avi_chawla) | [LinkedIn](https://www.linkedin.com/in/avi-chawla/)\n",
    "\n",
    "# Enrich Your Confusion Matrix With A Sankey Diagram\n",
    "\n",
    "Post Link: [Substack](https://avichawla.substack.com/p/enrich-your-confusion-matrix-with)\n",
    "\n",
    "LinkedIn Post: [LinkedIn](https://www.linkedin.com/feed/update/urn:li:ugcPost:7060539000415019008)\n",
    "\n",
    "Twitter Post: [Twitter](https://twitter.com/_avichawla/status/1654773329452990465)"
   ]
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  {
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   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from plotly import graph_objects as go"
   ]
  },
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    "RED = \"rgba(245,173,168,0.6)\"\n",
    "GREEN = \"rgba(211,255,216,0.6)\""
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    "def create_df_from_confusion_matrix(confusion_matrix, class_labels=None):\n",
    "    \n",
    "    \n",
    "    ## create a dataframe\n",
    "    if not len(class_labels):\n",
    "        ## if class labels not received, created dummy headers and index\n",
    "        df = pd.DataFrame(data=confusion_matrix, \n",
    "                          index=[f\"True Class-{i+1}\" for i in range(confusion_matrix.shape[0])],\n",
    "                          columns=[f\"Predicted Class-{i+1}\" for i in range(confusion_matrix.shape[0])])\n",
    "    else:\n",
    "        ## create headers and index using class labels\n",
    "        df = pd.DataFrame(data=confusion_matrix, \n",
    "                          index=[f\"True {i}\" for i in class_labels],\n",
    "                          columns=[f\"Predicted {i}\" for i in class_labels])\n",
    "    \n",
    "    ## unpivot dataframe and rename columns\n",
    "    df = df.stack().reset_index()\n",
    "    df.rename(columns={0:'instances', 'level_0':'actual', 'level_1':'predicted'}, inplace=True)\n",
    "    \"\"\"\n",
    "    >>> df\n",
    "            actual          predicted     instances\n",
    "          True Fraud    Predicted Fraud       10\n",
    "          True Fraud    Predicted Legit       4\n",
    "          True Legit    Predicted Fraud       2\n",
    "          True Legit    Predicted Legit       12\n",
    "    \n",
    "    \"\"\"\n",
    "    \n",
    "    ## determine classification color based on correct classification or not.\n",
    "    df[\"colour\"] = df.apply(lambda x: \n",
    "                               GREEN if x.actual.split()[1:] == x.predicted.split()[1:] \n",
    "                               else RED, axis=1)\n",
    "\n",
    "    node_labels = pd.concat([df.actual, df.predicted]).unique()\n",
    "    node_labels_indices = {label:index for index, label in enumerate(node_labels)}\n",
    "    \n",
    "    ## map actual and predicted columns to numbers\n",
    "    df =  df.assign(actual    = df.actual.apply(lambda x: node_labels_indices[x]),\n",
    "                    predicted = df.predicted.apply(lambda x: node_labels_indices[x]))\n",
    "    \n",
    "    ## determine text for hovering on connecting edges of sankey diagram\n",
    "    def get_link_text(row):\n",
    "        if row[\"colour\"] == GREEN:\n",
    "            instance_count = row[\"instances\"]\n",
    "            source_class = ' '.join(node_labels[row['actual']].split()[1:])\n",
    "            target_class = ' '.join(node_labels[row['predicted']].split()[1:])\n",
    "            return f\"{instance_count} {source_class} instances correctly classified as {target_class}\"\n",
    "        else:\n",
    "            instance_count = row[\"instances\"]\n",
    "            source_class = ' '.join(node_labels[row['actual']].split()[1:])\n",
    "            target_class = ' '.join(node_labels[row['predicted']].split()[1:])\n",
    "            return f\"{instance_count} {source_class} instances incorrectly classified as {target_class}\"\n",
    "        \n",
    "    df[\"link_text\"] = df.apply(get_link_text, axis = 1)\n",
    "    return df, node_labels\n",
    "    \n",
    "\n",
    "def plot_confusion_matrix_as_sankey(confusion_matrix,  class_labels = None):\n",
    "    \n",
    "    \"\"\"\n",
    "    plots sankey diagram from confusion matrix and class labels\n",
    "    \n",
    "    The function acceps:\n",
    "        - confusion_matrix\n",
    "                [[TP, FN]\n",
    "                 [FP, TN]]\n",
    "        - class_labels:\n",
    "            class_labels[0]: Label for positive class\n",
    "            class_labels[1]: Label for negative class\n",
    "        \n",
    "    \"\"\"\n",
    "    \n",
    "    df, labels = create_df_from_confusion_matrix(confusion_matrix,  class_labels)\n",
    "    \n",
    "    fig = go.Figure(data=[go.Sankey(\n",
    "    \n",
    "    node = dict(\n",
    "      pad = 20,\n",
    "      thickness = 20,\n",
    "      line = dict(color = \"gray\", width = 1.0),\n",
    "      label = labels,\n",
    "      hovertemplate = \"%{label} has total %{value:d} instances<extra></extra>\"\n",
    "    ),\n",
    "    link = dict(\n",
    "      source = df.actual, \n",
    "      target = df.predicted,\n",
    "      value = df.instances,\n",
    "      color = df.colour,\n",
    "      customdata = df['link_text'], \n",
    "      hovertemplate = \"%{customdata}<extra></extra>\"  \n",
    "    ))])\n",
    "\n",
    "    fig.update_layout(title_text=\"Confusion Matrix Sankey Diagram\", font_size=15,\n",
    "                      width=500, height=400)\n",
    "    \n",
    "    return fig"
   ]
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   "source": [
    "confusion_matrix = np.array([[10, 4],\n",
    "                             [2, 20]])\n",
    "\n",
    "plot_confusion_matrix_as_sankey(confusion_matrix,  ['Fraud', 'Legit'])"
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  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9a07f896",
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   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Define the confusion matrix\n",
    "confusion_matrix = np.array([[10, 4], [2, 20]])\n",
    "\n",
    "# Define the class labels\n",
    "class_names = ['Negative', 'Positive']\n",
    "\n",
    "# Create the figure and axes objects\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Create the heatmap of the confusion matrix\n",
    "im = ax.imshow(confusion_matrix, cmap='viridis')\n",
    "\n",
    "# Add colorbar\n",
    "cbar = ax.figure.colorbar(im, ax=ax)\n",
    "\n",
    "# Show all ticks\n",
    "ax.set_xticks(np.arange(len(class_names)))\n",
    "ax.set_yticks(np.arange(len(class_names)))\n",
    "\n",
    "# Label ticks with the respective class names\n",
    "ax.set_xticklabels(class_names)\n",
    "ax.set_yticklabels(class_names)\n",
    "\n",
    "# Set axis labels and title\n",
    "ax.set_xlabel('Predicted label')\n",
    "ax.set_ylabel('True label')\n",
    "ax.set_title('Confusion Matrix')\n",
    "\n",
    "# Loop over the data and add text annotations\n",
    "for i in range(len(class_names)):\n",
    "    for j in range(len(class_names)):\n",
    "        text = ax.text(j, i, confusion_matrix[i, j],\n",
    "                       ha='center', va='center', color='white')\n",
    "\n",
    "# Show the figure\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c02338f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10,  4],\n",
       "       [ 2, 20]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "confusion_matrix"
   ]
  }
 ],
 "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": "3.9.12"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}