P4DS4D2_14_ Reducing_Dimensionality.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Understanding SVD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Looking for dimensionality reduction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 3 4]\n",
      " [2 3 5]\n",
      " [1 2 3]\n",
      " [5 4 6]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "A = np.array([[1, 3, 4], [2, 3, 5], [1, 2, 3], [5, 4, 6]])\n",
    "print(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4, 3) (3,) (3, 3)\n",
      "[12.26362747  2.11085464  0.38436189]\n"
     ]
    }
   ],
   "source": [
    "U, s, Vh = np.linalg.svd(A, full_matrices=False)\n",
    "print(np.shape(U), np.shape(s), np.shape(Vh))\n",
    "print(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 3. 4.]\n",
      " [2. 3. 5.]\n",
      " [1. 2. 3.]\n",
      " [5. 4. 6.]]\n"
     ]
    }
   ],
   "source": [
    "print(np.dot(np.dot(U, np.diag(s)), Vh)) # Full matrix reconstruction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.  2.8 4.1]\n",
      " [2.  3.2 4.8]\n",
      " [1.  2.  3. ]\n",
      " [5.  3.9 6. ]]\n"
     ]
    }
   ],
   "source": [
    "print(np.round(np.dot(np.dot(U[:,:2], np.diag(s[:2])),\n",
    "                      Vh[:2,:]),1)) # k=2 reconstruction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2.1 2.5 3.7]\n",
      " [2.6 3.1 4.6]\n",
      " [1.6 1.8 2.8]\n",
      " [3.7 4.3 6.5]]\n"
     ]
    }
   ],
   "source": [
    "print(np.round(np.dot(np.dot(U[:,:1], np.diag(s[:1])), \n",
    "                      Vh[:1,:]),1)) # k=1 reconstruction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Performing Factor Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Looking for hidden factors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn.decomposition import FactorAnalysis\n",
    "iris = load_iris()\n",
    "X = iris.data\n",
    "Y = iris.target\n",
    "cols = [s[:12].strip() for s in iris.feature_names]\n",
    "factor = FactorAnalysis(n_components=4).fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   sepal length  sepal width  petal length  petal width\n",
      "0      0.707227    -0.153147      1.653151     0.701569\n",
      "1      0.114676     0.159763     -0.045604    -0.014052\n",
      "2     -0.000000     0.000000      0.000000     0.000000\n",
      "3     -0.000000     0.000000      0.000000    -0.000000\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "print(pd.DataFrame(factor.components_, columns=cols))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Achieving dimensionality reduction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Explained variance by each component: [0.92461621 0.05301557 0.01718514 0.00518309]\n",
      "   sepal length  sepal width  petal length  petal width\n",
      "0      0.361590    -0.082269      0.856572     0.358844\n",
      "1      0.656540     0.729712     -0.175767    -0.074706\n",
      "2     -0.580997     0.596418      0.072524     0.549061\n",
      "3      0.317255    -0.324094     -0.479719     0.751121\n"
     ]
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "import pandas as pd\n",
    "pca = PCA().fit(X)\n",
    "print('Explained variance by each component: %s' \n",
    "      % pca.explained_variance_ratio_)\n",
    "print(pd.DataFrame(pca.components_, columns=cols))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Squeezing information with t-SNE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "digits = load_digits()\n",
    "X = digits.data\n",
    "ground_truth = digits.target\n",
    "\n",
    "from sklearn.manifold import TSNE\n",
    "tsne = TSNE(n_components=2, \n",
    "            init='pca', \n",
    "            random_state=0,\n",
    "            perplexity=50, \n",
    "            early_exaggeration=25,\n",
    "            n_iter=300)\n",
    "Tx = tsne.fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.xticks([], [])\n",
    "plt.yticks([], [])\n",
    "for target in np.unique(ground_truth):\n",
    "    selection = ground_truth==target\n",
    "    X1, X2 = Tx[selection, 0], Tx[selection, 1]\n",
    "    c1, c2 = np.median(X1), np.median(X2)\n",
    "    plt.plot(X1, X2, 'o', ms=5)\n",
    "    plt.text(c1, c2, target, fontsize=18)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Understanding Some Applications"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Recognizing faces with PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import fetch_olivetti_faces\n",
    "dataset = fetch_olivetti_faces(shuffle=True, \n",
    "                               random_state=101)\n",
    "train_faces = dataset.data[:350,:]\n",
    "test_faces  = dataset.data[350:,:]\n",
    "train_answers = dataset.target[:350]\n",
    "test_answers = dataset.target[350:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Modified Olivetti faces dataset.\n",
      "\n",
      "The original database was available from\n",
      "\n",
      "    http://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html\n",
      "\n",
      "The version retrieved here comes in MATLAB format from the personal\n",
      "web page of Sam Roweis:\n",
      "\n",
      "    http://www.cs.nyu.edu/~roweis/\n",
      "\n",
      "There are ten different images of each of 40 distinct subjects. For some\n",
      "subjects, the images were taken at different times, varying the lighting,\n",
      "facial expressions (open / closed eyes, smiling / not smiling) and facial\n",
      "details (glasses / no glasses). All the images were taken against a dark\n",
      "homogeneous background with the subjects in an upright, frontal position (with\n",
      "tolerance for some side movement).\n",
      "\n",
      "The original dataset consisted of 92 x 112, while the Roweis version\n",
      "consists of 64x64 images.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(dataset.DESCR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Explained variance by 25 components: 0.794\n"
     ]
    }
   ],
   "source": [
    "from sklearn.decomposition import RandomizedPCA\n",
    "n_components = 25\n",
    "Rpca = PCA(svd_solver='randomized', \n",
    "           n_components=n_components, \n",
    "           whiten=True)\n",
    "Rpca.fit(train_faces)\n",
    "print('Explained variance by %i components: %0.3f' \n",
    "      % (n_components, np.sum(Rpca.explained_variance_ratio_)))\n",
    "compressed_train_faces = Rpca.transform(train_faces)\n",
    "compressed_test_faces  = Rpca.transform(test_faces)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The represented person is subject 34\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "photo = 17\n",
    "print('The represented person is subject %i' \n",
    "      % test_answers[photo])\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.axis('off')\n",
    "plt.title('Unknown photo '+str(photo)+' in test set')\n",
    "plt.imshow(test_faces[photo].reshape(64,64), \n",
    "           cmap=plt.cm.gray, interpolation='nearest')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best resembling subject in training set: 34\n"
     ]
    }
   ],
   "source": [
    "mask = compressed_test_faces[photo,] \n",
    "squared_errors = np.sum((compressed_train_faces \n",
    "                         - mask)**2, axis=1)\n",
    "minimum_error_face = np.argmin(squared_errors)\n",
    "most_resembling = list(np.where(squared_errors < 20)[0])\n",
    "print('Best resembling subject in training set: %i' \n",
    "      % train_answers[minimum_error_face])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.subplot(2, 2, 1)\n",
    "plt.axis('off')\n",
    "plt.title('Unknown face '+str(photo)+' in test set')\n",
    "plt.imshow(test_faces[photo].reshape(64, 64), \n",
    "           cmap=plt.cm.gray, \n",
    "           interpolation='nearest')\n",
    "for k,m in enumerate(most_resembling[:3]):\n",
    "    plt.subplot(2, 2, 2+k)\n",
    "    plt.title('Match in train set no. '+str(m))\n",
    "    plt.axis('off')\n",
    "    plt.imshow(train_faces[m].reshape(64, 64), \n",
    "               cmap=plt.cm.gray, \n",
    "               interpolation='nearest')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Extracting topics with NMF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Posts: 585\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import fetch_20newsgroups\n",
    "dataset = fetch_20newsgroups(shuffle=True, \n",
    "                             categories = ['misc.forsale'], \n",
    "                             remove=('headers', 'footers', 'quotes'), \n",
    "                             random_state=101)\n",
    "print('Posts: %i' % len(dataset.data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.feature_extraction.text import TfidfVectorizer\n",
    "from sklearn.decomposition import NMF\n",
    "\n",
    "vectorizer = TfidfVectorizer(max_df=0.95, min_df=2, \n",
    "                             stop_words='english')\n",
    "tfidf = vectorizer.fit_transform(dataset.data)\n",
    "\n",
    "n_topics = 5\n",
    "nmf = NMF(n_components=n_topics, \n",
    "          random_state=101).fit(tfidf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Topic #1:\n",
      "condition excellent asking offer best car old new sale 10 miles 000 tape cd power\n",
      "Topic #2:\n",
      "00 50 dos 20 10 15 cover 1st new 25 price man 40 shipping comics\n",
      "Topic #3:\n",
      "drive hard card floppy monitor meg ram disk motherboard vga modem brand scsi color internal\n",
      "Topic #4:\n",
      "email looking game games send interested mail thanks like edu good want package price list\n",
      "Topic #5:\n",
      "shipping vcr works stereo obo included amp plus great volume unc mathes gibbs radley remotes\n"
     ]
    }
   ],
   "source": [
    "feature_names = vectorizer.get_feature_names()\n",
    "n_top_words = 15\n",
    "for topic_idx, topic in enumerate(nmf.components_):\n",
    "    print('Topic #%d:' % (topic_idx+1),)\n",
    "    topics = topic.argsort()[:-n_top_words - 1:-1]\n",
    "    print(' '.join([feature_names[i] for i in topics]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1075 1459  632 2463  740  888 2476 2415 2987   10 2305    1 3349  923\n",
      " 2680]\n"
     ]
    }
   ],
   "source": [
    "print(nmf.components_[0,:].argsort()[:-n_top_words-1:-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "offer\n"
     ]
    }
   ],
   "source": [
    "word_index = 2463\n",
    "print(vectorizer.get_feature_names()[word_index])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Recommending movies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Luca\\Dropbox\\Wiley\\Wiley_Python_data_science\\text_2nd\\Chapter 14 Reducing Dimensionality\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "print(os.getcwd())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from scipy.sparse import csr_matrix\n",
    "users = pd.read_table('ml-1m/users.dat', sep='::', \n",
    "        header=None, names=['user_id', 'gender', \n",
    "        'age', 'occupation', 'zip'], engine='python')\n",
    "ratings = pd.read_table('ml-1m/ratings.dat', sep='::', \n",
    "          header=None, names=['user_id', 'movie_id', \n",
    "          'rating', 'timestamp'], engine='python')\n",
    "movies = pd.read_table('ml-1m/movies.dat', sep='::', \n",
    "         header=None, names=['movie_id', 'title', \n",
    "         'genres'], engine='python')\n",
    "MovieLens = pd.merge(pd.merge(ratings, users), movies)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "ratings_mtx_df = MovieLens.pivot_table(values='rating', \n",
    "        index='user_id', columns='title', fill_value=0)\n",
    "movie_index = ratings_mtx_df.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import TruncatedSVD\n",
    "recom = TruncatedSVD(n_components=15, random_state=101)\n",
    "R = recom.fit_transform(ratings_mtx_df.values.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "movie index: 3154\n",
      "[184.72254552 -17.77612872  47.33450866  51.4664494   47.92058216\n",
      "  17.65033116  14.3574635  -12.82219207  17.51347857   5.46888807\n",
      "   7.5430805   -0.57117869 -30.74032355   2.4088565  -22.50368497]\n"
     ]
    }
   ],
   "source": [
    "movie = 'Star Wars: Episode V \\\n",
    "- The Empire Strikes Back (1980)'\n",
    "movie_idx = list(movie_index).index(movie)\n",
    "print(\"movie index: %i\" %movie_idx)\n",
    "print(R[movie_idx])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Raiders of the Lost Ark (1981)', 'Star Wars: Episode IV - A New Hope (1977)', 'Star Wars: Episode V - The Empire Strikes Back (1980)', 'Star Wars: Episode VI - Return of the Jedi (1983)', 'Terminator, The (1984)']\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "correlation_matrix = np.corrcoef(R)\n",
    "P = correlation_matrix[movie_idx]\n",
    "print(list(movie_index[(P > 0.95) & (P < 1.0)]))"
   ]
  }
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