LogisticRegression.ipynb

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  "metadata": {
    "colab": {
      "name": "LogisticRegression.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyMaVGqJ/zkqQ6gEah1C0vpc",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/symaeng98/Artificial_Intelligence/blob/main/LogisticRegression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wMtlxq-frqb1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "outputId": "822fe65c-d1f4-4a6d-8f51-8e567b5950ee"
      },
      "source": [
        "import pandas as pd\n",
        "fish = pd.read_csv('https://bit.ly/fish_csv_data')\n",
        "fish.head() #5개만 출력"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
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              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Species</th>\n",
              "      <th>Weight</th>\n",
              "      <th>Length</th>\n",
              "      <th>Diagonal</th>\n",
              "      <th>Height</th>\n",
              "      <th>Width</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Bream</td>\n",
              "      <td>242.0</td>\n",
              "      <td>25.4</td>\n",
              "      <td>30.0</td>\n",
              "      <td>11.5200</td>\n",
              "      <td>4.0200</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Bream</td>\n",
              "      <td>290.0</td>\n",
              "      <td>26.3</td>\n",
              "      <td>31.2</td>\n",
              "      <td>12.4800</td>\n",
              "      <td>4.3056</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Bream</td>\n",
              "      <td>340.0</td>\n",
              "      <td>26.5</td>\n",
              "      <td>31.1</td>\n",
              "      <td>12.3778</td>\n",
              "      <td>4.6961</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Bream</td>\n",
              "      <td>363.0</td>\n",
              "      <td>29.0</td>\n",
              "      <td>33.5</td>\n",
              "      <td>12.7300</td>\n",
              "      <td>4.4555</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Bream</td>\n",
              "      <td>430.0</td>\n",
              "      <td>29.0</td>\n",
              "      <td>34.0</td>\n",
              "      <td>12.4440</td>\n",
              "      <td>5.1340</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "  Species  Weight  Length  Diagonal   Height   Width\n",
              "0   Bream   242.0    25.4      30.0  11.5200  4.0200\n",
              "1   Bream   290.0    26.3      31.2  12.4800  4.3056\n",
              "2   Bream   340.0    26.5      31.1  12.3778  4.6961\n",
              "3   Bream   363.0    29.0      33.5  12.7300  4.4555\n",
              "4   Bream   430.0    29.0      34.0  12.4440  5.1340"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 1
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HTJiQRAiGj2A",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "26a4d91a-5fe7-4339-9927-288189467842"
      },
      "source": [
        "print(pd.unique(fish['Species'])) #Species열의 값들 출력"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "['Bream' 'Roach' 'Whitefish' 'Parkki' 'Perch' 'Pike' 'Smelt']\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S37idxDiHwSN",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "dfc981e6-40ce-4ed9-9b99-c62e7a17ccda"
      },
      "source": [
        "fish_input = fish[['Weight', 'Length', 'Diagonal','Height','Width']].to_numpy() #fish_input 변수에 여러 열들을 선택하여 넘파이 배열로 반환\n",
        "fish_target = fish['Species'].to_numpy()\n",
        "print(fish_input[:5])"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[242.      25.4     30.      11.52     4.02  ]\n",
            " [290.      26.3     31.2     12.48     4.3056]\n",
            " [340.      26.5     31.1     12.3778   4.6961]\n",
            " [363.      29.      33.5     12.73     4.4555]\n",
            " [430.      29.      34.      12.444    5.134 ]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jI_wyE2EITs3",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "114c4693-4b4b-4fca-f4b2-acbd40ba44ee"
      },
      "source": [
        "print(fish_target)"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "['Bream' 'Bream' 'Bream' 'Bream' 'Bream' 'Bream' 'Bream' 'Bream' 'Bream'\n",
            " 'Bream' 'Bream' 'Bream' 'Bream' 'Bream' 'Bream' 'Bream' 'Bream' 'Bream'\n",
            " 'Bream' 'Bream' 'Bream' 'Bream' 'Bream' 'Bream' 'Bream' 'Bream' 'Bream'\n",
            " 'Bream' 'Bream' 'Bream' 'Bream' 'Bream' 'Bream' 'Bream' 'Bream' 'Roach'\n",
            " 'Roach' 'Roach' 'Roach' 'Roach' 'Roach' 'Roach' 'Roach' 'Roach' 'Roach'\n",
            " 'Roach' 'Roach' 'Roach' 'Roach' 'Roach' 'Roach' 'Roach' 'Roach' 'Roach'\n",
            " 'Roach' 'Whitefish' 'Whitefish' 'Whitefish' 'Whitefish' 'Whitefish'\n",
            " 'Whitefish' 'Parkki' 'Parkki' 'Parkki' 'Parkki' 'Parkki' 'Parkki'\n",
            " 'Parkki' 'Parkki' 'Parkki' 'Parkki' 'Parkki' 'Perch' 'Perch' 'Perch'\n",
            " 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch'\n",
            " 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch'\n",
            " 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch'\n",
            " 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch'\n",
            " 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch'\n",
            " 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Perch' 'Pike'\n",
            " 'Pike' 'Pike' 'Pike' 'Pike' 'Pike' 'Pike' 'Pike' 'Pike' 'Pike' 'Pike'\n",
            " 'Pike' 'Pike' 'Pike' 'Pike' 'Pike' 'Pike' 'Smelt' 'Smelt' 'Smelt' 'Smelt'\n",
            " 'Smelt' 'Smelt' 'Smelt' 'Smelt' 'Smelt' 'Smelt' 'Smelt' 'Smelt' 'Smelt'\n",
            " 'Smelt']\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ykn-wTsPMiJM"
      },
      "source": [
        "from sklearn.model_selection import train_test_split\n",
        "train_input, test_input, train_target, test_target = train_test_split(fish_input, fish_target, random_state = 42)\n",
        "\n",
        "from sklearn.preprocessing import StandardScaler #표준화 전처리\n",
        "ss = StandardScaler()\n",
        "ss.fit(train_input)\n",
        "train_scaled = ss.transform(train_input)\n",
        "test_scaled = ss.transform(test_input)"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6fEfZVsFQIvM",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "34b2de98-44b0-4ff7-840a-737e2f9f72a1"
      },
      "source": [
        "from sklearn.neighbors import KNeighborsClassifier\n",
        "kn = KNeighborsClassifier(n_neighbors=3)\n",
        "kn.fit(train_scaled, train_target)\n",
        "print(kn.score(train_scaled, train_target))\n",
        "print(kn.score(test_scaled, test_target))"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.8907563025210085\n",
            "0.85\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VbwcloXnMbyw"
      },
      "source": [
        "타깃 데이터에 2개 이상의 클래스가 포함된 문제를 **다중 분류(multiclass classification)**라고 부른다. 사이킷런에서는 문자열로 된 타깃값을 그대로 사용할 수 있다. 하지만 타깃값을 그대로 사이킷런 모델에 전달하면 순서가 자동으로 알파벳 순으로 매겨지므로 주의해야한다."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bVUjXF8UMJxi",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d8c1dfc0-4d89-487a-de43-7dbe91021e19"
      },
      "source": [
        "print(kn.classes_) #정렬된 타깃 값"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "['Bream' 'Parkki' 'Perch' 'Pike' 'Roach' 'Smelt' 'Whitefish']\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mM6Gh-5RM8iE",
        "outputId": "dcf02c61-c1fe-4c98-b6d5-a2eb8ab97fa9"
      },
      "source": [
        "print(kn.predict(test_scaled[:5]))"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "['Perch' 'Smelt' 'Pike' 'Perch' 'Perch']\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SByLbNoaiAW1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "876d477b-261f-4c6e-afca-4f243e2e8725"
      },
      "source": [
        "import numpy as np\n",
        "proba = kn.predict_proba(test_scaled[:5])\n",
        "print(np.round(proba, decimals = 4)) #소수점 네번째 자리까지 표기 --> 다섯번째 자리에서 반올림, 원래 round()는 소수점 첫째자리에서 반올림한다."
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0.     0.     1.     0.     0.     0.     0.    ]\n",
            " [0.     0.     0.     0.     0.     1.     0.    ]\n",
            " [0.     0.     0.     1.     0.     0.     0.    ]\n",
            " [0.     0.     0.6667 0.     0.3333 0.     0.    ]\n",
            " [0.     0.     0.6667 0.     0.3333 0.     0.    ]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1CtZouxH7nuT",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1dd5b372-f026-4c29-997a-b2fad52f8d12"
      },
      "source": [
        "distance, indexes = kn.kneighbors(test_scaled[3:4]) #kneighbors()의 입력은 2차원 배열이어야 하는데, 슬라이싱 연산자를 이용하면 하나의 샘플만 선택해도 항상 2차원 배열이 만들어진다.\n",
        "print(train_target[indexes])"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[['Roach' 'Perch' 'Perch']]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p25-4qgT_Qnh"
      },
      "source": [
        "로지스틱 회귀는 이름은 회귀이지만 분류 모델이다.\n",
        "\n",
        "z = a * (Weight) + b * (Length) + c * (Diagonal) + d * (Height) + e * (Width) + f\n",
        "\n",
        "위 식에서 z는 어떤 값도 가능한데, 확률이 되려면 0 ~ 1 혹은 0 ~ 100% 사이 값이 되어야한다. z가 아주 큰 양수일 때 1, 아주 큰 음수일 때 0으로 바꿀 방법이 없을까?\n",
        "\n",
        "이럴 때 **시그모이드 함수(sigmoid function)** 혹은 **로지스틱 함수(logistic function)**을 사용한다.\n",
        "\n",
        "넘파이를 사용하여 그래프를 그려보자."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "Sme6xNFmAjm6",
        "outputId": "cdd52fd8-e08d-4350-a346-0c9e22d6c77e"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "z = np.arange(-5,5,0.1) #-5와 5사이에 0.1간격으로 배열 z를 만든다.\n",
        "phi = 1 / (1 + np.exp(-z)) #시그모이드 함수 형태를 phi에 넣어준다. 1/(1 + e ^ (-z)) 꼴\n",
        "plt.plot(z, phi)\n",
        "plt.xlabel('z')\n",
        "plt.ylabel('phi')\n",
        "plt.show()"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0bZ4WeFLHWFg",
        "outputId": "6355520d-90a9-4272-80e4-68bf31fb9602"
      },
      "source": [
        "bream_smelt_indexes = (train_target == 'Bream') | (train_target == 'Smelt')\n",
        "train_bream_smelt = train_scaled[bream_smelt_indexes]\n",
        "target_bream_smelt = train_target[bream_smelt_indexes]\n",
        "\n",
        "from sklearn.linear_model import LogisticRegression\n",
        "lr = LogisticRegression()\n",
        "lr.fit(train_bream_smelt, target_bream_smelt)\n",
        "print(lr.predict(train_bream_smelt[:5]))"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "['Bream' 'Smelt' 'Bream' 'Bream' 'Bream']\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gZUIFWrKVBbN",
        "outputId": "54f33086-643f-438a-ba68-fd549ffabfc4"
      },
      "source": [
        "print(lr.predict_proba(train_bream_smelt[:5]))"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0.99759855 0.00240145]\n",
            " [0.02735183 0.97264817]\n",
            " [0.99486072 0.00513928]\n",
            " [0.98584202 0.01415798]\n",
            " [0.99767269 0.00232731]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "axBB9KSsVKfq",
        "outputId": "70a2c9f1-f513-4c02-e9d3-9c30757818ce"
      },
      "source": [
        "print(lr.classes_) #출력값에서 Bream이 음성 클래스 Smelt가 양성 클래스임을 확인할 수 있다."
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "['Bream' 'Smelt']\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ie8Dk_PbY4kv"
      },
      "source": [
        "print(lr.coef_, lr.intercept_)#수식의 계수들"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "W5RIZH_AY9Db"
      },
      "source": [
        "decisions = lr.decision_function(train_bream_smelt[:5]) #수식에서 z값을 출력해준다. 이 z값을 시그모이드 함수에 통과시키면 확률을 얻을 수 있다.\n",
        "print(decisions)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "C3kF4BruZWsY",
        "outputId": "23f9b94c-9139-479a-da76-05b460d7f553"
      },
      "source": [
        "from scipy.special import expit\n",
        "print(expit(decisions)) #출력값이 predict_proba의 두번째 열의 값과 동일하다. 즉 decision_function()은 양성 클래스에 대한 z값을 반환한다."
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0.00240145 0.97264817 0.00513928 0.01415798 0.00232731]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Nwah_aHzZqfi",
        "outputId": "08116e86-6bec-45f7-fef1-982c4c5a870e"
      },
      "source": [
        "lr = LogisticRegression(C = 20, max_iter = 1000)\n",
        "lr.fit(train_scaled, train_target)\n",
        "print(lr.score(train_scaled, train_target))\n",
        "print(lr.score(test_scaled, test_target))"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.9327731092436975\n",
            "0.925\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zDEFH5ZhNEOr",
        "outputId": "c05c997f-585c-4b3a-89d2-1ac805f335f5"
      },
      "source": [
        "print(lr.predict(test_scaled[:5]))"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "['Perch' 'Smelt' 'Pike' 'Roach' 'Perch']\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mYAd6nHNOtp9",
        "outputId": "6ca0301b-d584-49c7-a400-a1363b1b9d36"
      },
      "source": [
        "proba = lr.predict_proba(test_scaled[:5]) #이진 분류는 샘플마다 2개의 확률을 출력하고 다중 분류는 샘플마다 클래스 개수만큼 확률을 출력한다.\n",
        "print(np.round(proba, decimals=3)) "
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0.    0.014 0.841 0.    0.136 0.007 0.003]\n",
            " [0.    0.003 0.044 0.    0.007 0.946 0.   ]\n",
            " [0.    0.    0.034 0.935 0.015 0.016 0.   ]\n",
            " [0.011 0.034 0.306 0.007 0.567 0.    0.076]\n",
            " [0.    0.    0.904 0.002 0.089 0.002 0.001]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8VpIvUQNsYWL"
      },
      "source": [
        "이진 분류에서는 시그모이드 함수를 사용해 z를 0과 1 사이의 값으로 변환한다. 반면에 다중 분류는 **소프트맥스 함수**를 사용하여 여러개의 z값을 확률로 변환해준다. 또한 여러개의 선형 방정식의 출력값을 0~1 사이로 압축하고 전체 합이 1이 되도록 만든다. 이를 위해서 지수함수를 사용하므로 **정규화된 지수 함수**라고도 한다.\n",
        "\n",
        "e_sum = e^z1 + e^z2 + ...\n",
        "\n",
        "S1 = e^z1 / e_sum, S2 = e^z2 / e_sum, ...\n",
        "\n",
        "위 식에서 모든 S들의 합은 1이된다.\n",
        "\n",
        "시그모이드 함수와 소프트맥스 함수는 나중에 신경망을 배울 때 다시 등장하니 자세히 익혀두자."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0ft09mt0Pg2V",
        "outputId": "ffb0a3e4-d57f-4bfc-d8c6-acbe58e6342a"
      },
      "source": [
        "decision = lr.decision_function(test_scaled[:5]) # z1 ~ z7의 값\n",
        "print(np.round(decision, decimals = 2))"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[ -6.5    1.03   5.16  -2.73   3.34   0.33  -0.63]\n",
            " [-10.86   1.93   4.77  -2.4    2.98   7.84  -4.26]\n",
            " [ -4.34  -6.23   3.17   6.49   2.36   2.42  -3.87]\n",
            " [ -0.68   0.45   2.65  -1.19   3.26  -5.75   1.26]\n",
            " [ -6.4   -1.99   5.82  -0.11   3.5   -0.11  -0.71]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7OrAi1r-vP-l",
        "outputId": "01ad6a84-64a0-44d3-9f84-90fc24f0f426"
      },
      "source": [
        "from scipy.special import softmax\n",
        "proba = softmax(decision, axis=1) #axis = 1이면 각 행,즉 각 샘플에 대해 계산해준다. 설정하지 않으면 배열 전체에 대해 계산한다.\n",
        "print(np.round(proba, decimals = 3))"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0.    0.014 0.841 0.    0.136 0.007 0.003]\n",
            " [0.    0.003 0.044 0.    0.007 0.946 0.   ]\n",
            " [0.    0.    0.034 0.935 0.015 0.016 0.   ]\n",
            " [0.011 0.034 0.306 0.007 0.567 0.    0.076]\n",
            " [0.    0.    0.904 0.002 0.089 0.002 0.001]]\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}