正定値性を満たすように変換して精度が変わるかの確認

positive_definite_kernel.ipynb

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   "source": [
    "import numpy as np\n",
    "from sklearn import datasets, metrics, model_selection, svm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "np.random.seed(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def convert_add_lmd(mat, eps=0.0001):\n",
    "    \"\"\"\n",
    "    K' = K + \\lmd I\n",
    "    \\lmd is decided as all eigen values are larger than 0\n",
    "    \"\"\"\n",
    "    mat_positive_definite = np.copy(mat)\n",
    "    eigen_values = np.linalg.eigvals(mat)\n",
    "    min_eigen_values = np.min(eigen_values)\n",
    "    if min_eigen_values < 0:\n",
    "        lmd = -min_eigen_values + eps  # new eigen values are larger than 0\n",
    "        mat_positive_definite += lmd * np.eye(mat.shape[0])\n",
    "    return mat_positive_definite"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
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   "source": [
    "def convert_with_decomposition(mat, eps=0.0001):\n",
    "    \"\"\"\n",
    "    K' = P D' P^T\n",
    "    P: eigen vectors matrix\n",
    "    D: diag eigen values matrix\n",
    "    D': negative eigen values of D are \\epsilon\n",
    "    \"\"\"\n",
    "    eigen_values, eigen_vectors_mat = np.linalg.eig(mat)\n",
    "    eigen_values[eigen_values <= 0] = eps\n",
    "    # K' = P D' P^T\n",
    "    mat_positive_definite = eigen_vectors_mat.dot(np.diag(eigen_values)).dot(eigen_vectors_mat.T)\n",
    "    return mat_positive_definite"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X, ys = datasets.make_classification(n_samples=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "kf = model_selection.StratifiedKFold(n_splits=5, shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# sigmoid kernel is not positive definite\n",
    "K = metrics.pairwise.sigmoid_kernel(X, gamma=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def acc_evaluation(K):\n",
    "    acc_scores = []\n",
    "    for train_index, test_index in kf.split(K, ys):\n",
    "        K_train, K_test = K[train_index][:, train_index], K[test_index][:, train_index]\n",
    "        ys_train, ys_test = ys[train_index], ys[test_index]\n",
    "        clf = svm.SVC(kernel=\"precomputed\")\n",
    "        clf.fit(K_train, ys_train)\n",
    "        acc_score = metrics.accuracy_score(ys_test, clf.predict(K_test))\n",
    "        acc_scores.append(acc_score)\n",
    "    return np.mean(acc_scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.830021625541\n"
     ]
    }
   ],
   "source": [
    "# without convert to positive definite\n",
    "print(acc_evaluation(K))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.930993624841\n"
     ]
    }
   ],
   "source": [
    "# with adding lmd * I\n",
    "K_added_lmd = convert_add_lmd(K)\n",
    "print(acc_evaluation(K_added_lmd))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.951983974599\n"
     ]
    }
   ],
   "source": [
    "# with decomposition\n",
    "K_with_decomposition = convert_with_decomposition(K)\n",
    "print(acc_evaluation(K_with_decomposition))"
   ]
  }
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