Data projection (数据降维实例）.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "X = np.empty((100, 2))\n",
    "X[:,0] = np.random.uniform(0., 100., size=100)\n",
    "X[:,1] = 0.75 * X[:,0] + 3. + np.random.normal(0, 10., size=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from PCA import PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca = PCA(n_components=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(n_components=2)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.78512414,  0.61933842],\n",
       "       [ 0.61934297, -0.78512055]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.components_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 降维"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca_1 = PCA(n_components=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(n_components=1)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_1.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.78512419,  0.61933836]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_1.components_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_reduction = pca_1.transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 1)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_reduction.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_inverse = pca_1.inverse_transform(X_reduction)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 2)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_inverse.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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zN4GHrlTQ8Uqh9htIXlANPV4d1U9vv739WnI8ddcEatFHauVVbTs0Ix/n5z+H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\nYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:,0],X[:,1],marker=\"*\",color=\"r\")\n",
    "plt.scatter(X_inverse[:,0],X_inverse[:,1],marker = \"+\",color=\"b\",alpha = 0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## scikit-learn中的PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca_sklearn = PCA(n_components=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=1, random_state=None,\n",
       "  svd_solver='auto', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_sklearn.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.78512421,  0.61933833]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_sklearn.components_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca_trans_sklean = pca_sklearn.transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 1)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_trans_sklean.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca_inv_sklearn = pca_sklearn.inverse_transform(pca_trans_sklean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 2)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_inv_sklearn.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VNnYyYYIL5NOnu2PVleeMcugiRa7LevJoXnruXHjnHfjgg+w2JHZXInAbYUSvCzl/HyDq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\nRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:,0],X[:,1],marker=\"*\",color=\"r\")\n",
    "plt.scatter(pca_inv_sklearn[:,0],pca_inv_sklearn[:,1],marker = \"+\",color=\"b\",alpha = 0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}