Machine Learning/PCA-Dimensions-Hyperparameter.ipynb

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   "source": [
    "# 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",
    "# How Many Dimensions Should You Reduce Your Data To When Using PCA?\n",
    "\n",
    "Post Link: [Substack](https://avichawla.substack.com/p/how-many-dimensions-should-you-reduce)\n",
    "\n",
    "LinkedIn Post: [LinkedIn](https://www.linkedin.com/feed/update/urn:li:share:7054019408293240832/)"
   ]
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  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "07110daf",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import matplotlib.ticker as mtick\n",
    "\n",
    "from sklearn.decomposition import PCA\n",
    "from matplotlib_inline.backend_inline import set_matplotlib_formats\n",
    "\n",
    "set_matplotlib_formats('svg')\n",
    "plt.style.use(\"seaborn-darkgrid\")\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "20407923",
   "metadata": {},
   "outputs": [],
   "source": [
    "def percent_formatter(x, pos):\n",
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  {
   "cell_type": "markdown",
   "id": "400fc90b",
   "metadata": {},
   "source": [
    "## Dummy data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f4208866",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Mean values for the 10 dimensions\n",
    "init_dimensions = 10\n",
    "\n",
    "mean = np.zeros(init_dimensions)\n",
    "\n",
    "# Variances for the 10 dimensions\n",
    "variances = np.array([10, 8, 6, 4, 2, 1, 0.5, 0.4, 0.3, 0.2])\n",
    "\n",
    "# Covariance matrix\n",
    "cov_matrix = np.diag(variances)\n",
    "\n",
    "# Generate the 10-dimensional dataset (1000 samples)\n",
    "data = np.random.multivariate_normal(mean, cov_matrix, size=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1d76ab7",
   "metadata": {},
   "source": [
    "## Apply PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e78c3803",
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "PCA()"
      ]
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     "execution_count": 4,
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   "source": [
    "pca = PCA()\n",
    "pca.fit(data)"
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   "source": [
    "exp_var = pca.explained_variance_ratio_ ## variance of individual component \n",
    "\n",
    "cumulative_explained_variance = np.cumsum(exp_var) ## cumulative variance"
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   "id": "d66acf57",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
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     "output_type": "display_data"
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   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "## add individual variance bars\n",
    "plt.bar(range(1, init_dimensions+1), exp_var, align='center',\n",
    "        label='Individual Component Variance', color = 'lightsalmon')\n",
    "\n",
    "## add cumulative variance line\n",
    "plt.plot(range(1, init_dimensions+1), cumulative_explained_variance, marker=\"o\",\n",
    "         label='Cumulative Variance', color='#00B9FF')\n",
    "\n",
    "## add cumulative variance annotation\n",
    "for x, y in zip(range(1, init_dimensions+1), cumulative_explained_variance):\n",
    "    ax.annotate(f\"{round(y * 100):.0f}%\", (x - 0.3, y + 0.03))\n",
    "\n",
    "## add label, title, ticks\n",
    "plt.xlabel('Principal Component Number')\n",
    "plt.ylabel('Explained Variance')\n",
    "plt.title('Cumulative Explained Variance Plot\\nfor PCA', fontsize=19, fontweight=\"bold\", pad=20)\n",
    "plt.xticks(range(1, init_dimensions+1))\n",
    "\n",
    "## format y-axis\n",
    "ax.yaxis.set_major_formatter(mtick.FuncFormatter(percent_formatter))\n",
    "\n",
    "## legend location\n",
    "plt.legend(loc='best')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5be91917",
   "metadata": {},
   "outputs": [],
   "source": []
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