10_neural_nets_with_keras.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 인공 신경망이란?\n",
    "지능적인 기계를 만들기위해서 인간의 뇌를 참조하여 만든 것이다.\n",
    "\n",
    "뉴런을 이요한 단순 신경망 모델 - 인공 뉴런 artificial neureon. \\\n",
    "구성 : 하나 이상의 이진 입력 + 하나의 이진 출력\n",
    "\n",
    "복잡한 논리를 표현하기 위해 A가 활성화하면 C가 작동하도록 한다거나, \\\n",
    "A, B 모두 활성화되어야 C가 작동하도록 한다거나 \\\n",
    "A or B 가 활성화되면 C가 작동되도록 하는 등 ... 다양한 네트워크로 연결하여 표현하였다.\n",
    "\n",
    "## 1.3 퍼셉트론\n",
    "- 간단한 AN(인공 신경망)\n",
    "- input, output : 숫자 타입\n",
    "- input 네트워크 - 가중치 존재\n",
    "- 조금 다른 형태의 TLU or LTU 인공 뉴런 기반\n",
    "- 하나의 TLU로 구성\n",
    "\n",
    "TLU\n",
    "- input 가중치 sum -> 계단 함수(헤비사이드 계단 함수) 적용 -> output\n",
    "- 간단한 선형 이진 분류 문제에 사용\n",
    "- input, linear을 이용한 임곗값 지정\n",
    "- 임곗값을 기준으로 output 결정\n",
    "- input layer : input neureon 으로 구성\n",
    "- 인공 뉴런마다 1개 편향이 붙음\n",
    "- input layer + 편향(항상 1을 출력) 으로 진행\n",
    "- 편향 : 편향 뉴런 bias neureon으로 표현\n",
    "- 활성화 함수(input*weight+편향)\n",
    "- weight_update = weight + learning_rate(y - y_hat)*input\n",
    "\n",
    "퍼셉트론 수렴 이론 : dataset이 선형적으로 구분할 수 있다면 퍼셉트론 알고리즘이 정답에 수렴한다.\n",
    "\n",
    "아래는 scikit-learn의 Perceptron class를 이용한 TLU network 구현이다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2023-02-28 23:45:36.911962: I tensorflow/core/platform/cpu_feature_guard.cc:193] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations:  AVX2 FMA\n",
      "To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.\n"
     ]
    }
   ],
   "source": [
    "# Python ≥3.5 is required\n",
    "import sys\n",
    "assert sys.version_info >= (3, 5)\n",
    "\n",
    "# Scikit-Learn ≥0.20 is required\n",
    "import sklearn\n",
    "assert sklearn.__version__ >= \"0.20\"\n",
    "\n",
    "try:\n",
    "    # %tensorflow_version only exists in Colab.\n",
    "    %tensorflow_version 2.x\n",
    "except Exception:\n",
    "    pass\n",
    "\n",
    "# TensorFlow ≥2.0 is required\n",
    "import tensorflow as tf\n",
    "assert tf.__version__ >= \"2.0\"\n",
    "\n",
    "# Common imports\n",
    "import numpy as np\n",
    "import os\n",
    "\n",
    "# to make this notebook's output stable across runs\n",
    "np.random.seed(42)\n",
    "\n",
    "# To plot pretty figures\n",
    "%matplotlib inline\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "mpl.rc('axes', labelsize=14)\n",
    "mpl.rc('xtick', labelsize=12)\n",
    "mpl.rc('ytick', labelsize=12)\n",
    "\n",
    "# Where to save the figures\n",
    "PROJECT_ROOT_DIR = \".\"\n",
    "CHAPTER_ID = \"ann\"\n",
    "IMAGES_PATH = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID)\n",
    "os.makedirs(IMAGES_PATH, exist_ok=True)\n",
    "\n",
    "def save_fig(fig_id, tight_layout=True, fig_extension=\"png\", resolution=300):\n",
    "    path = os.path.join(IMAGES_PATH, fig_id + \".\" + fig_extension)\n",
    "    print(\"Saving figure\", fig_id)\n",
    "    if tight_layout:\n",
    "        plt.tight_layout()\n",
    "    plt.savefig(path, format=fig_extension, dpi=resolution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/0s/knzc6bzs1l9dgw6x4k24t9740000gn/T/ipykernel_6780/367974035.py:7: DeprecationWarning: `np.int` is a deprecated alias for the builtin `int`. To silence this warning, use `int` by itself. Doing this will not modify any behavior and is safe. When replacing `np.int`, you may wish to use e.g. `np.int64` or `np.int32` to specify the precision. If you wish to review your current use, check the release note link for additional information.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  y = (iris.target == 0).astype(np.int)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([1])"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.linear_model import Perceptron\n",
    "\n",
    "iris = load_iris()\n",
    "X = iris.data[:, (2, 3)]  # petal length, petal width\n",
    "y = (iris.target == 0).astype(np.int)\n",
    "\n",
    "per_clf = Perceptron(max_iter=1000, tol=1e-3, random_state=42)\n",
    "per_clf.fit(X, y)\n",
    "\n",
    "y_pred = per_clf.predict([[2, 0.5]])\n",
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure perceptron_iris_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = -per_clf.coef_[0][0] / per_clf.coef_[0][1]\n",
    "b = -per_clf.intercept_ / per_clf.coef_[0][1]\n",
    "\n",
    "axes = [0, 5, 0, 2]\n",
    "\n",
    "x0, x1 = np.meshgrid(\n",
    "        np.linspace(axes[0], axes[1], 500).reshape(-1, 1),\n",
    "        np.linspace(axes[2], axes[3], 200).reshape(-1, 1),\n",
    "    )\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "y_predict = per_clf.predict(X_new)\n",
    "zz = y_predict.reshape(x0.shape)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y==0, 0], X[y==0, 1], \"bs\", label=\"Not Iris-Setosa\")\n",
    "plt.plot(X[y==1, 0], X[y==1, 1], \"yo\", label=\"Iris-Setosa\")\n",
    "\n",
    "plt.plot([axes[0], axes[1]], [a * axes[0] + b, a * axes[1] + b], \"k-\", linewidth=3)\n",
    "from matplotlib.colors import ListedColormap\n",
    "custom_cmap = ListedColormap(['#9898ff', '#fafab0'])\n",
    "\n",
    "plt.contourf(x0, x1, zz, cmap=custom_cmap)\n",
    "plt.xlabel(\"Petal length\", fontsize=14)\n",
    "plt.ylabel(\"Petal width\", fontsize=14)\n",
    "plt.legend(loc=\"lower right\", fontsize=14)\n",
    "plt.axis(axes)\n",
    "\n",
    "save_fig(\"perceptron_iris_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "퍼셉트론의 한계 : XOR 문제 못품 \\\n",
    "해결법 : 여러개 쌓아올려 다층 퍼셉트론을 이용해 XOR 문제를 푼다.\n",
    "\n",
    "## 1.4 다층 퍼셉트론과 역전파\n",
    "다층 퍼셉트론 구조 = 1개 input layer + 1개 이상 hidden layer + 1개 output layer \\\n",
    "input layer, hidden layer 모든 층은 편향 뉴런을 포함한다. \\\n",
    "다음 층과 완전히 연결됨 \n",
    "\n",
    "심층 신경망 DNN (Deep Neural Network) : 은닉층을 여러 개 쌓아 올린 것 \\\n",
    "딥러닝이란 연산이 연속하여 길게 연결된 모델 \\\n",
    "다층 퍼셉트론을 딥러닝으로 훈련할 방법 -> 역전파 훈련 알고리즘 이용\n",
    "\n",
    "**역전파 훈련 알고리즘**\n",
    "- 후진 모드 자동 미분\n",
    "- gradient 자동 계산(자동 미분) 경사 하강법\n",
    "- 네트워크 두 번 (정방향 한번, 역방향 한 번)통과하여 모든 모델 파라미터의 네트워크 오차 gradient 계산 \n",
    "- 각 가중치의 편향값 조절위한 계산 가능\n",
    "- gradient 확정 후 경사 하강법 실행\n",
    "\n",
    "1. 정방향 계산(예측을 만들고)\n",
    "mini batch 이동 구조 : input layer -> 1st hidden layer -> all hidden layer(모든 뉴런의 출력 계산) -> output layer\n",
    "2. 알고리즘(손실 함수)을 사용하여 네트워크 출력 오차값 return\n",
    "3. 역방향 계산(오차에 기여한 정도 계산)\n",
    "각 출력 연결이 오차에 기여하는 정도 계산 - 연쇄 법칙 chain rule 사용 \n",
    "\n",
    "**연쇄 법칙이란?**\n",
    "이전 층의 연결 가중치가 오차에 어느정도 기여했는지 측정. \\\n",
    "output layer에서 input layer 방향으로 - 역방향 - 측정한다.\n",
    "\n",
    "4. 경사 하강법 단계(오차가 감소하도록 가중치 조정)\n",
    "\n",
    "**주의점**\n",
    "hidden layer의 weight 초기값을 모두 0으로 지정한다면 역방향 계산시 모든 hidden layer의 가중치 값을 똑같은 값으로 수정하게 된다. 그러면 모든 뉴런이 하나의 뉴런처럼 작동하게 되고 제대로된 문제를 풀기 힘들게된다.\n",
    "가중치값을 랜덤값으로 주어지게 되면 대칭성이 깨지고, 역전파를 이용해 다양한 값으로 훈련이 가능하다.\n",
    "\n",
    "역전파 훈련 알고리즘이 잘 작동하고자 **다층 퍼셉트론 구조**에 변화를 주게된다.\n",
    "- 계단 함수를 로지스틱 함수로 변경하여 사용하기 시작했다. \n",
    "- 로지스틱(시그모이드) 함수 $\\sigma$(z)=1/(1+exp(-z))\n",
    "- 계단 함수에는 수평선만 있어서 계산할 gradient가 없다.\n",
    "- 로지스틱 함수는 gradient가 잘 정의되어 있다.\n",
    "- 계단 함수, 로지스틱 함수 외 다른 활성화 함수도 사용 가능하다.\n",
    "- 기타 함수 : 하이퍼볼릭 탄젠트 함수(-1~1값, 빠른 수렴을 도와줌), ReLU 함수(0에서 미분 불가)\n",
    "\n",
    "**활성화 함수 필요성**\n",
    "선형 변환 *여러개 = 선형 변환 \\\n",
    "\"f(x)=2x+5 , g(x)=9x \\\n",
    "f(x)+g(x)=11x+5\" => 하나의 층\n",
    "\n",
    "선형 * 비선형성 = 연속 함수로 근사 가능 \n",
    "\n",
    "## 1.5 회귀를 위한 다층 퍼셉트론\n",
    "다변량 회귀(동시에 여러 값 예측) - 각 ouput 차원마다 output neureon 필요. \\\n",
    "- ex) 이미지에서 물체의 중심 : 2D좌표 예측, 출력 뉴런 2개 필요 \\\n",
    "Bounding Box : 뉴런 4개 필요\n",
    "- output layer에 활성화 함수를 사용x, 범위의 값 출력\n",
    "- output이 항상 양수 -> output layer에 ReLU, softplus(ReLU 변종) 활성화 함수 사용 가능\n",
    "\n",
    "softplus(z)=log(1+exp(z)), z<0 이면 0에 수렴, z가 큰양수이면 z에 수렴\n",
    "\n",
    "- 범위안의 값 예측 - 로지스틱 함수(0~1 범위), 하이퍼볼릭 탄젠트 함수(-1~1 범위) + 레이블의 스케일 범위 조정\n",
    "\n",
    "## 1.6 분류를 위한 다층 퍼셉트론\n",
    "- 로지스틱 활성화 함수를 가진 1개의 output neuron만 필요\n",
    "- output 범위 : 0 ~ 1\n",
    "- 음성 클래스 예측 확률 = 1 - 양성 클래스 예측 확률\n",
    "\n",
    "다중 레이블 이진 분류 \\\n",
    "ex) 스팸 메일 유무, 긴급 메일 분류 - 로지스틱 활성화 함수를 가진 2개 output neuron 필요 \\\n",
    "-> n개 클래스로 분류시 n개 output neuron 필요 \n",
    "\n",
    "- output layer에 softmax(확률 0 ~ 1범위, 모두 더하면 1로 만듦) 활성화 함수 사용\n",
    "(활성화 함수에 따라서 모두 더했을때 1이 될수도 아닐수도 있다.)\n",
    "- 확률 분포 예측 - 손실 함수로 cross entropy loss(log loss) 선택\n"
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