07. Feature Engineering/tutorial/05. principal-component-analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "054a6fdb",
   "metadata": {
    "papermill": {
     "duration": 0.0181,
     "end_time": "2022-05-05T12:49:45.183369",
     "exception": false,
     "start_time": "2022-05-05T12:49:45.165269",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "# Introduction #\n",
    "\n",
    "In the previous lesson we looked at our first model-based method for feature engineering: clustering. In this lesson we look at our next: principal component analysis (PCA). Just like clustering is a partitioning of the dataset based on proximity, you could think of PCA as a partitioning of the variation in the data. PCA is a great tool to help you discover important relationships in the data and can also be used to create more informative features.\n",
    "\n",
    "(Technical note: PCA is typically applied to [standardized](https://www.kaggle.com/alexisbcook/scaling-and-normalization) data. With standardized data \"variation\" means \"correlation\". With unstandardized data \"variation\" means \"covariance\". All data in this course will be standardized before applying PCA.)\n",
    "\n",
    "# Principal Component Analysis #\n",
    "\n",
    "In the [*Abalone*](https://www.kaggle.com/rodolfomendes/abalone-dataset) dataset are physical measurements taken from several thousand Tasmanian abalone. (An abalone is a sea creature much like a clam or an oyster.) We'll just look at a couple features for now: the `'Height'` and `'Diameter'` of their shells.\n",
    "\n",
    "You could imagine that within this data are \"axes of variation\" that describe the ways the abalone tend to differ from one another. Pictorially, these axes appear as perpendicular lines running along the natural dimensions of the data, one axis for each original feature.\n",
    "\n",
    "<figure style=\"padding: 1em;\">\n",
    "<img src=\"https://i.imgur.com/rr8NCDy.png\" width=300, alt=\"\">\n",
    "<figcaption style=\"textalign: center; font-style: italic\"><center>\n",
    "</center></figcaption>\n",
    "</figure>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "824fdbdd",
   "metadata": {
    "papermill": {
     "duration": 0.016891,
     "end_time": "2022-05-05T12:49:45.217724",
     "exception": false,
     "start_time": "2022-05-05T12:49:45.200833",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Often, we can give names to these axes of variation. The longer axis we might call the \"Size\" component: small height and small diameter (lower left) contrasted with large height and large diameter (upper right). The shorter axis we might call the \"Shape\" component: small height and large diameter (flat shape) contrasted with large height and small diameter (round shape).\n",
    "\n",
    "Notice that instead of describing abalones by their `'Height'` and `'Diameter'`, we could just as well describe them by their `'Size'` and `'Shape'`. This, in fact, is the whole idea of PCA: instead of describing the data with the original features, we describe it with its axes of variation. The axes of variation become the new features.\n",
    "\n",
    "<figure style=\"padding: 1em;\">\n",
    "<img src=\"https://i.imgur.com/XQlRD1q.png\" width=600, alt=\"\">\n",
    "<figcaption style=\"textalign: center; font-style: italic\"><center>The principal components become the new features by a rotation of the dataset in the feature space.\n",
    "</center></figcaption>\n",
    "</figure>\n",
    "\n",
    "The new features PCA constructs are actually just linear combinations (weighted sums) of the original features:\n",
    "\n",
    "```\n",
    "df[\"Size\"] = 0.707 * X[\"Height\"] + 0.707 * X[\"Diameter\"]\n",
    "df[\"Shape\"] = 0.707 * X[\"Height\"] - 0.707 * X[\"Diameter\"]\n",
    "```\n",
    "\n",
    "These new features are called the **principal components** of the data. The weights themselves are called **loadings**. There will be as many principal components as there are features in the original dataset: if we had used ten features instead of two, we would have ended up with ten components.\n",
    "\n",
    "A component's loadings tell us what variation it expresses through signs and magnitudes:\n",
    "\n",
    "| Features \\ Components | Size (PC1) | Shape (PC2) |\n",
    "|-----------------------|------------|-------------|\n",
    "| Height                | 0.707      | 0.707       |\n",
    "| Diameter              | 0.707      | -0.707      |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb2ed9a1",
   "metadata": {
    "papermill": {
     "duration": 0.014501,
     "end_time": "2022-05-05T12:49:45.246959",
     "exception": false,
     "start_time": "2022-05-05T12:49:45.232458",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "This table of loadings is telling us that in the `Size` component, `Height` and `Diameter` vary in the same direction (same sign), but in the `Shape` component they vary in opposite directions (opposite sign). In each component, the loadings are all of the same magnitude and so the features contribute equally in both.\n",
    "\n",
    "PCA also tells us the *amount* of variation in each component. We can see from the figures that there is more variation in the data along the `Size` component than along the `Shape` component. PCA makes this precise through each component's **percent of explained variance**.\n",
    "\n",
    "<figure style=\"padding: 1em;\">\n",
    "<img src=\"https://i.imgur.com/xWTvqDA.png\" width=600, alt=\"\">\n",
    "<figcaption style=\"textalign: center; font-style: italic\"><center> Size accounts for about 96% and the Shape for about 4% of the variance between Height and Diameter.\n",
    "</center></figcaption>\n",
    "</figure>\n",
    "\n",
    "The `Size` component captures the majority of the variation between `Height` and `Diameter`. It's important to remember, however, that the amount of variance in a component doesn't necessarily correspond to how good it is as a predictor: it depends on what you're trying to predict.\n",
    "\n",
    "# PCA for Feature Engineering #\n",
    "\n",
    "There are two ways you could use PCA for feature engineering.\n",
    "\n",
    "The first way is to use it as a descriptive technique. Since the components tell you about the variation, you could compute the MI scores for the components and see what kind of variation is most predictive of your target. That could give you ideas for kinds of features to create -- a product of `'Height'` and `'Diameter'` if `'Size'` is important, say, or a ratio of `'Height'` and `'Diameter'` if `Shape` is important. You could even try clustering on one or more of the high-scoring components.\n",
    "\n",
    "The second way is to use the components themselves as features. Because the components expose the variational structure of the data directly, they can often be more informative than the original features. Here are some use-cases:\n",
    "- **Dimensionality reduction**: When your features are highly redundant (*multicollinear*, specifically), PCA will partition out the redundancy into one or more near-zero variance components, which you can then drop since they will contain little or no information.\n",
    "- **Anomaly detection**: Unusual variation, not apparent from the original features, will often show up in the low-variance components. These components could be highly informative in an anomaly or outlier detection task.\n",
    "- **Noise reduction**: A collection of sensor readings will often share some common background noise. PCA can sometimes collect the (informative) signal into a smaller number of features while leaving the noise alone, thus boosting the signal-to-noise ratio.\n",
    "- **Decorrelation**: Some ML algorithms struggle with highly-correlated features. PCA transforms correlated features into uncorrelated components, which could be easier for your algorithm to work with.\n",
    "\n",
    "PCA basically gives you direct access to the correlational structure of your data. You'll no doubt come up with applications of your own!\n",
    "\n",
    "<blockquote style=\"margin-right:auto; margin-left:auto; background-color: #ebf9ff; padding: 1em; margin:24px;\">\n",
    "<strong>PCA Best Practices</strong><br>\n",
    "There are a few things to keep in mind when applying PCA:\n",
    "<ul>\n",
    "<li> PCA only works with numeric features, like continuous quantities or counts.\n",
    "<li> PCA is sensitive to scale. It's good practice to standardize your data before applying PCA, unless you know you have good reason not to.\n",
    "<li> Consider removing or constraining outliers, since they can an have an undue influence on the results.\n",
    "</ul>\n",
    "</blockquote>\n",
    "\n",
    "# Example - 1985 Automobiles #\n",
    "\n",
    "In this example, we'll return to our [*Automobile*](https://www.kaggle.com/toramky/automobile-dataset) dataset and apply PCA, using it as a descriptive technique to discover features. We'll look at other use-cases in the exercise.\n",
    "\n",
    "This hidden cell loads the data and defines the functions `plot_variance` and `make_mi_scores`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "31d8a43a",
   "metadata": {
    "_kg_hide-input": true,
    "execution": {
     "iopub.execute_input": "2022-05-05T12:49:45.278566Z",
     "iopub.status.busy": "2022-05-05T12:49:45.277735Z",
     "iopub.status.idle": "2022-05-05T12:49:46.582467Z",
     "shell.execute_reply": "2022-05-05T12:49:46.581670Z"
    },
    "papermill": {
     "duration": 1.323219,
     "end_time": "2022-05-05T12:49:46.584939",
     "exception": false,
     "start_time": "2022-05-05T12:49:45.261720",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "from IPython.display import display\n",
    "from sklearn.feature_selection import mutual_info_regression\n",
    "\n",
    "\n",
    "plt.style.use(\"seaborn-whitegrid\")\n",
    "plt.rc(\"figure\", autolayout=True)\n",
    "plt.rc(\n",
    "    \"axes\",\n",
    "    labelweight=\"bold\",\n",
    "    labelsize=\"large\",\n",
    "    titleweight=\"bold\",\n",
    "    titlesize=14,\n",
    "    titlepad=10,\n",
    ")\n",
    "\n",
    "\n",
    "def plot_variance(pca, width=8, dpi=100):\n",
    "    # Create figure\n",
    "    fig, axs = plt.subplots(1, 2)\n",
    "    n = pca.n_components_\n",
    "    grid = np.arange(1, n + 1)\n",
    "    # Explained variance\n",
    "    evr = pca.explained_variance_ratio_\n",
    "    axs[0].bar(grid, evr)\n",
    "    axs[0].set(\n",
    "        xlabel=\"Component\", title=\"% Explained Variance\", ylim=(0.0, 1.0)\n",
    "    )\n",
    "    # Cumulative Variance\n",
    "    cv = np.cumsum(evr)\n",
    "    axs[1].plot(np.r_[0, grid], np.r_[0, cv], \"o-\")\n",
    "    axs[1].set(\n",
    "        xlabel=\"Component\", title=\"% Cumulative Variance\", ylim=(0.0, 1.0)\n",
    "    )\n",
    "    # Set up figure\n",
    "    fig.set(figwidth=8, dpi=100)\n",
    "    return axs\n",
    "\n",
    "def make_mi_scores(X, y, discrete_features):\n",
    "    mi_scores = mutual_info_regression(X, y, discrete_features=discrete_features)\n",
    "    mi_scores = pd.Series(mi_scores, name=\"MI Scores\", index=X.columns)\n",
    "    mi_scores = mi_scores.sort_values(ascending=False)\n",
    "    return mi_scores\n",
    "\n",
    "\n",
    "df = pd.read_csv(\"../input/fe-course-data/autos.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "394b6d72",
   "metadata": {
    "papermill": {
     "duration": 0.01504,
     "end_time": "2022-05-05T12:49:46.615461",
     "exception": false,
     "start_time": "2022-05-05T12:49:46.600421",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "We've selected four features that cover a range of properties. Each of these features also has a high MI score with the target, `price`. We'll standardize the data since these features aren't naturally on the same scale."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a98516dd",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-05-05T12:49:46.647083Z",
     "iopub.status.busy": "2022-05-05T12:49:46.646788Z",
     "iopub.status.idle": "2022-05-05T12:49:46.664288Z",
     "shell.execute_reply": "2022-05-05T12:49:46.663716Z"
    },
    "papermill": {
     "duration": 0.035551,
     "end_time": "2022-05-05T12:49:46.666102",
     "exception": false,
     "start_time": "2022-05-05T12:49:46.630551",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "features = [\"highway_mpg\", \"engine_size\", \"horsepower\", \"curb_weight\"]\n",
    "\n",
    "X = df.copy()\n",
    "y = X.pop('price')\n",
    "X = X.loc[:, features]\n",
    "\n",
    "# Standardize\n",
    "X_scaled = (X - X.mean(axis=0)) / X.std(axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fafdef45",
   "metadata": {
    "papermill": {
     "duration": 0.015511,
     "end_time": "2022-05-05T12:49:46.696707",
     "exception": false,
     "start_time": "2022-05-05T12:49:46.681196",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Now we can fit scikit-learn's `PCA` estimator and create the principal components. You can see here the first few rows of the transformed dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e022f816",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-05-05T12:49:46.728396Z",
     "iopub.status.busy": "2022-05-05T12:49:46.728114Z",
     "iopub.status.idle": "2022-05-05T12:49:46.761080Z",
     "shell.execute_reply": "2022-05-05T12:49:46.760309Z"
    },
    "papermill": {
     "duration": 0.051213,
     "end_time": "2022-05-05T12:49:46.763195",
     "exception": false,
     "start_time": "2022-05-05T12:49:46.711982",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PC1</th>\n",
       "      <th>PC2</th>\n",
       "      <th>PC3</th>\n",
       "      <th>PC4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.382486</td>\n",
       "      <td>-0.400222</td>\n",
       "      <td>0.124122</td>\n",
       "      <td>0.169539</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.382486</td>\n",
       "      <td>-0.400222</td>\n",
       "      <td>0.124122</td>\n",
       "      <td>0.169539</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.550890</td>\n",
       "      <td>-0.107175</td>\n",
       "      <td>0.598361</td>\n",
       "      <td>-0.256081</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.408859</td>\n",
       "      <td>-0.425947</td>\n",
       "      <td>0.243335</td>\n",
       "      <td>0.013920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.132749</td>\n",
       "      <td>-0.814565</td>\n",
       "      <td>-0.202885</td>\n",
       "      <td>0.224138</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        PC1       PC2       PC3       PC4\n",
       "0  0.382486 -0.400222  0.124122  0.169539\n",
       "1  0.382486 -0.400222  0.124122  0.169539\n",
       "2  1.550890 -0.107175  0.598361 -0.256081\n",
       "3 -0.408859 -0.425947  0.243335  0.013920\n",
       "4  1.132749 -0.814565 -0.202885  0.224138"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "# Create principal components\n",
    "pca = PCA()\n",
    "X_pca = pca.fit_transform(X_scaled)\n",
    "\n",
    "# Convert to dataframe\n",
    "component_names = [f\"PC{i+1}\" for i in range(X_pca.shape[1])]\n",
    "X_pca = pd.DataFrame(X_pca, columns=component_names)\n",
    "\n",
    "X_pca.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06869302",
   "metadata": {
    "papermill": {
     "duration": 0.015572,
     "end_time": "2022-05-05T12:49:46.795341",
     "exception": false,
     "start_time": "2022-05-05T12:49:46.779769",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "After fitting, the `PCA` instance contains the loadings in its `components_` attribute. (Terminology for PCA is inconsistent, unfortunately. We're following the convention that calls the transformed columns in `X_pca` the *components*, which otherwise don't have a name.) We'll wrap the loadings up in a dataframe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "43a585dd",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-05-05T12:49:46.828643Z",
     "iopub.status.busy": "2022-05-05T12:49:46.828182Z",
     "iopub.status.idle": "2022-05-05T12:49:46.838395Z",
     "shell.execute_reply": "2022-05-05T12:49:46.837856Z"
    },
    "papermill": {
     "duration": 0.029057,
     "end_time": "2022-05-05T12:49:46.840222",
     "exception": false,
     "start_time": "2022-05-05T12:49:46.811165",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PC1</th>\n",
       "      <th>PC2</th>\n",
       "      <th>PC3</th>\n",
       "      <th>PC4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>highway_mpg</th>\n",
       "      <td>-0.492347</td>\n",
       "      <td>0.770892</td>\n",
       "      <td>0.070142</td>\n",
       "      <td>-0.397996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine_size</th>\n",
       "      <td>0.503859</td>\n",
       "      <td>0.626709</td>\n",
       "      <td>0.019960</td>\n",
       "      <td>0.594107</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.500448</td>\n",
       "      <td>0.013788</td>\n",
       "      <td>0.731093</td>\n",
       "      <td>-0.463534</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>curb_weight</th>\n",
       "      <td>0.503262</td>\n",
       "      <td>0.113008</td>\n",
       "      <td>-0.678369</td>\n",
       "      <td>-0.523232</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  PC1       PC2       PC3       PC4\n",
       "highway_mpg -0.492347  0.770892  0.070142 -0.397996\n",
       "engine_size  0.503859  0.626709  0.019960  0.594107\n",
       "horsepower   0.500448  0.013788  0.731093 -0.463534\n",
       "curb_weight  0.503262  0.113008 -0.678369 -0.523232"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loadings = pd.DataFrame(\n",
    "    pca.components_.T,  # transpose the matrix of loadings\n",
    "    columns=component_names,  # so the columns are the principal components\n",
    "    index=X.columns,  # and the rows are the original features\n",
    ")\n",
    "loadings"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad6ba9fa",
   "metadata": {
    "papermill": {
     "duration": 0.016302,
     "end_time": "2022-05-05T12:49:46.873199",
     "exception": false,
     "start_time": "2022-05-05T12:49:46.856897",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Recall that the signs and magnitudes of a component's loadings tell us what kind of variation it's captured. The first component (`PC1`) shows a contrast between large, powerful vehicles with poor gas milage, and smaller, more economical vehicles with good gas milage. We might call this the \"Luxury/Economy\" axis. The next figure shows that our four chosen features mostly vary along the Luxury/Economy axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "151b5ee9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-05-05T12:49:46.908080Z",
     "iopub.status.busy": "2022-05-05T12:49:46.907642Z",
     "iopub.status.idle": "2022-05-05T12:49:47.320432Z",
     "shell.execute_reply": "2022-05-05T12:49:47.319579Z"
    },
    "papermill": {
     "duration": 0.433004,
     "end_time": "2022-05-05T12:49:47.322790",
     "exception": false,
     "start_time": "2022-05-05T12:49:46.889786",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Look at explained variance\n",
    "plot_variance(pca);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "413a67ef",
   "metadata": {
    "papermill": {
     "duration": 0.017582,
     "end_time": "2022-05-05T12:49:47.358508",
     "exception": false,
     "start_time": "2022-05-05T12:49:47.340926",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Let's also look at the MI scores of the components. Not surprisingly, `PC1` is highly informative, though the remaining components, despite their small variance, still have a significant relationship with `price`. Examining those components could be worthwhile to find relationships not captured by the main Luxury/Economy axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "581a80e1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-05-05T12:49:47.396146Z",
     "iopub.status.busy": "2022-05-05T12:49:47.395543Z",
     "iopub.status.idle": "2022-05-05T12:49:47.413757Z",
     "shell.execute_reply": "2022-05-05T12:49:47.412980Z"
    },
    "papermill": {
     "duration": 0.039265,
     "end_time": "2022-05-05T12:49:47.415742",
     "exception": false,
     "start_time": "2022-05-05T12:49:47.376477",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PC1    1.013364\n",
       "PC2    0.379388\n",
       "PC3    0.306872\n",
       "PC4    0.205228\n",
       "Name: MI Scores, dtype: float64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mi_scores = make_mi_scores(X_pca, y, discrete_features=False)\n",
    "mi_scores"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2bdcb63",
   "metadata": {
    "papermill": {
     "duration": 0.018317,
     "end_time": "2022-05-05T12:49:47.452791",
     "exception": false,
     "start_time": "2022-05-05T12:49:47.434474",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "The third component shows a contrast between `horsepower` and `curb_weight` -- sports cars vs. wagons, it seems."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "197325af",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-05-05T12:49:47.491879Z",
     "iopub.status.busy": "2022-05-05T12:49:47.491276Z",
     "iopub.status.idle": "2022-05-05T12:49:47.506653Z",
     "shell.execute_reply": "2022-05-05T12:49:47.505873Z"
    },
    "papermill": {
     "duration": 0.037243,
     "end_time": "2022-05-05T12:49:47.508601",
     "exception": false,
     "start_time": "2022-05-05T12:49:47.471358",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>make</th>\n",
       "      <th>body_style</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>curb_weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>118</th>\n",
       "      <td>porsche</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>207</td>\n",
       "      <td>2756</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>117</th>\n",
       "      <td>porsche</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>207</td>\n",
       "      <td>2756</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>119</th>\n",
       "      <td>porsche</td>\n",
       "      <td>convertible</td>\n",
       "      <td>207</td>\n",
       "      <td>2800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>jaguar</td>\n",
       "      <td>sedan</td>\n",
       "      <td>262</td>\n",
       "      <td>3950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>nissan</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>200</td>\n",
       "      <td>3139</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>mercedes-benz</td>\n",
       "      <td>wagon</td>\n",
       "      <td>123</td>\n",
       "      <td>3750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61</th>\n",
       "      <td>mercedes-benz</td>\n",
       "      <td>sedan</td>\n",
       "      <td>123</td>\n",
       "      <td>3770</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>101</th>\n",
       "      <td>peugot</td>\n",
       "      <td>wagon</td>\n",
       "      <td>95</td>\n",
       "      <td>3430</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>105</th>\n",
       "      <td>peugot</td>\n",
       "      <td>wagon</td>\n",
       "      <td>95</td>\n",
       "      <td>3485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>143</th>\n",
       "      <td>toyota</td>\n",
       "      <td>wagon</td>\n",
       "      <td>62</td>\n",
       "      <td>3110</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>193 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              make   body_style  horsepower  curb_weight\n",
       "118        porsche      hardtop         207         2756\n",
       "117        porsche      hardtop         207         2756\n",
       "119        porsche  convertible         207         2800\n",
       "45          jaguar        sedan         262         3950\n",
       "96          nissan    hatchback         200         3139\n",
       "..             ...          ...         ...          ...\n",
       "59   mercedes-benz        wagon         123         3750\n",
       "61   mercedes-benz        sedan         123         3770\n",
       "101         peugot        wagon          95         3430\n",
       "105         peugot        wagon          95         3485\n",
       "143         toyota        wagon          62         3110\n",
       "\n",
       "[193 rows x 4 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Show dataframe sorted by PC3\n",
    "idx = X_pca[\"PC3\"].sort_values(ascending=False).index\n",
    "cols = [\"make\", \"body_style\", \"horsepower\", \"curb_weight\"]\n",
    "df.loc[idx, cols]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "564435ce",
   "metadata": {
    "papermill": {
     "duration": 0.021296,
     "end_time": "2022-05-05T12:49:47.549301",
     "exception": false,
     "start_time": "2022-05-05T12:49:47.528005",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "To express this contrast, let's create a new ratio feature:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "5749c093",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-05-05T12:49:47.589786Z",
     "iopub.status.busy": "2022-05-05T12:49:47.589302Z",
     "iopub.status.idle": "2022-05-05T12:49:48.062774Z",
     "shell.execute_reply": "2022-05-05T12:49:48.062012Z"
    },
    "papermill": {
     "duration": 0.496519,
     "end_time": "2022-05-05T12:49:48.065399",
     "exception": false,
     "start_time": "2022-05-05T12:49:47.568880",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[\"sports_or_wagon\"] = X.curb_weight / X.horsepower\n",
    "sns.regplot(x=\"sports_or_wagon\", y='price', data=df, order=2);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35fc3d6c",
   "metadata": {
    "papermill": {
     "duration": 0.020915,
     "end_time": "2022-05-05T12:49:48.107472",
     "exception": false,
     "start_time": "2022-05-05T12:49:48.086557",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "# Your Turn #\n",
    "\n",
    "[**Improve your feature set**](https://www.kaggle.com/kernels/fork/14393921) by decomposing the variation in *Ames Housing* and use principal components to detect outliers."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f7105e7",
   "metadata": {
    "papermill": {
     "duration": 0.020783,
     "end_time": "2022-05-05T12:49:48.149555",
     "exception": false,
     "start_time": "2022-05-05T12:49:48.128772",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "---\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "*Have questions or comments? Visit the [course discussion forum](https://www.kaggle.com/learn/feature-engineering/discussion) to chat with other learners.*"
   ]
  }
 ],
 "metadata": {
  "jupytext": {
   "cell_metadata_filter": "-all",
   "formats": "ipynb"
  },
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.12"
  },
  "papermill": {
   "default_parameters": {},
   "duration": 13.21069,
   "end_time": "2022-05-05T12:49:48.891034",
   "environment_variables": {},
   "exception": null,
   "input_path": "__notebook__.ipynb",
   "output_path": "__notebook__.ipynb",
   "parameters": {},
   "start_time": "2022-05-05T12:49:35.680344",
   "version": "2.3.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}