PCA_R2.ipynb

{
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  {
   "cell_type": "code",
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   "source": [
    "from pandas import DataFrame\n",
    "from sklearn import datasets\n",
    "from sklearn.pipeline import make_pipeline, Pipeline\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_inertia(matrix):\n",
    "    return (matrix ** 2).sum().sum()\n",
    "\n",
    "\n",
    "def sum_of_squared_errors(true, pred):\n",
    "    \"\"\"Residual sum of squares\"\"\"\n",
    "    return ((true - pred)**2).sum().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_r2(pipeline: Pipeline, data, components_n=10):\n",
    "    \"\"\"Assumes that the PCA is the last step of the pipeline.\"\"\"\n",
    "    result = []\n",
    "\n",
    "    pipeline.fit(data)\n",
    "\n",
    "    pca = pipeline.steps[-1][1]\n",
    "    components_fitted = pca.n_components_\n",
    "\n",
    "    preprocessing_pipeline = Pipeline(pipeline.steps[:-1])\n",
    "    preprocessing_pipeline.fit(data)\n",
    "\n",
    "    x_processed = preprocessing_pipeline.transform(data)\n",
    "    total_inertia = calc_inertia(x_processed)\n",
    "\n",
    "    scores = pipeline.transform(data)\n",
    "    loadings = pca.components_\n",
    "\n",
    "    components_n = min(components_n, components_fitted)\n",
    "\n",
    "    for k in range(1, components_n + 1):\n",
    "        x_hat = scores[:, :k] @ loadings[:k, :]\n",
    "\n",
    "        # REsidual Sum of Squares\n",
    "        ress = sum_of_squared_errors(x_processed, x_hat)\n",
    "        explained = calc_inertia(x_hat)\n",
    "\n",
    "        result.append({\n",
    "            'n': k,\n",
    "            'r2_ratio': explained / total_inertia,\n",
    "            'r2_ress': 1 - ress / total_inertia,\n",
    "            'r2_sklearn': sum(pca.explained_variance_ratio_[:k])\n",
    "        })\n",
    "\n",
    "    return DataFrame(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "iris = datasets.load_iris()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "pipeline = make_pipeline(StandardScaler(), PCA())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>n</th>\n",
       "      <th>r2_ratio</th>\n",
       "      <th>r2_ress</th>\n",
       "      <th>r2_sklearn</th>\n",
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       "      <td>0.729624</td>\n",
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       "      <th>2</th>\n",
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      "text/plain": [
       "   n  r2_ratio   r2_ress  r2_sklearn\n",
       "0  1  0.729624  0.729624    0.729624\n",
       "1  2  0.958132  0.958132    0.958132\n",
       "2  3  0.994821  0.994821    0.994821\n",
       "3  4  1.000000  1.000000    1.000000"
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   ],
   "source": [
    "pca_r2 = calc_r2(pipeline, iris.data)\n",
    "pca_r2"
   ]
  }
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