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    "# 混淆矩阵(confusion matrix)\n",
    "\n",
    "混淆矩阵是用来总结一个分类器结果的矩阵。对于k元分类，其实它就是一个$k \\times k$的表格，用来记录分类器的预测结果。\n",
    "\n",
    "对于最常见的二元分类来说，它的混淆矩阵是2乘2的，如下\n",
    "![confusion_matrix1](images/confusion_matrix1.png)\n",
    "\n",
    "* `TP` = True Postive = 真阳性\n",
    "* `FP` = False Positive = 假阳性\n",
    "* `FN` = False Negative = 假阴性\n",
    "* `TN` = True Negative = 真阴性\n",
    "\n",
    "你要的例子来了。。。比如我们一个模型对15个样本进行预测，然后结果如下。\n",
    "\n",
    "* 预测值：1    1    1    1    1    0    0    0    0    0    1    1    1    0    1\n",
    "* 真实值：0    1    1    0    1    1    0    0    1    0    1    0    1    0    0\n",
    "\n",
    "![confusion_matrix2](images/confusion_matrix2.png)\n",
    "\n",
    "\n",
    "这个就是混淆矩阵。混淆矩阵中的这四个数值，经常被用来定义其他一些度量。\n",
    "\n",
    "\n",
    "### 准确度\n",
    "```\n",
    "Accuracy = (TP+TN) / (TP+TN+FN+TN)\n",
    "```\n",
    "\n",
    "在上面的例子中，准确度 = (5+4) / 15 = 0.6\n",
    "\n",
    "\n",
    "\n",
    "### 精度(precision, 或者PPV, positive predictive value) \n",
    "```\n",
    "precision = TP / (TP + FP)\n",
    "```\n",
    "在上面的例子中，精度 = 5 / (5+4) = 0.556\n",
    "\n",
    "\n",
    "\n",
    "### 召回(recall, 或者敏感度，sensitivity，真阳性率，TPR，True Positive Rate) \n",
    "\n",
    "```\n",
    "recall = TP / (TP + FN)\n",
    "```\n",
    "\n",
    "在上面的例子中，召回 = 5 / (5+2) = 0.714\n",
    "\n",
    "\n",
    "\n",
    "### 特异度(specificity，或者真阴性率，TNR，True Negative Rate)\n",
    "```\n",
    "specificity = TN / (TN + FP)\n",
    "```\n",
    "\n",
    "在上面的例子中，特异度 = 4 / (4+2) = 0.667\n",
    "\n",
    "\n",
    "\n",
    "### F1-值(F1-score) \n",
    "```\n",
    "F1 = 2*TP / (2*TP+FP+FN) \n",
    "```\n",
    "在上面的例子中，F1-值 = 2*5 / (2*5+4+2) = 0.625\n",
    "\n",
    "\n"
   ]
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