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006. Logistic_Regression
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gistfile1.txt
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### `11. ML lec 5-1 Logistic Classification의 가설 함수 정의`"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Regression (HCG)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- H : Hypothesis / C : Cost Function / G : Gradient Decent\n",
"- 주어진 자료를 가지고 가설을 세우고 코스트를 점차적으로 줄여나가는 방법\n",
"- cost 는 가설과 실제값 과의 차이값\n",
"- cost의 최소값을 찾는 방법이 Gradient Decent.\n",
"- Gradient Decent에서 alpha 값은 움직이는 값"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. Hypothesis : $ H(x) = WX $\n",
"2. Cost : $ cost(W) = \\frac{1}{m}\\sum (H(x) = WX)^2 $\n",
"3. Gradicent Decent : $ W := W - \\alpha \\frac{\\sigma}{\\sigma W} cost(W) $"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Classification : 0 or 1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- Spam Detection : Spam or Ham\n",
"- Facebook feed : Show or Hide\n",
"- Credit Card Fraudulent Transaction detection : Legitimate/draud"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- 많은 자료들을 0과 1로 표현하려고 하니 문제점들이 발생.\n",
"- 너무 큰 입력값이나, 애매한 중간값을 계산하기 어려움.\n",
"- 그래서 입력값들을 0과 1사이로 정확하게 바꾸어 줄 수 있는 함수를 고민."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Sigmod : Curved in two direction"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ g(z) = \\frac{1}{(1+e^{-W^{t}X})} $$ "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- S자의 완만한 그래프가 그려짐. 값이 커지면 1에 가까워 지고, 작아지면 0에 가까워 진다.\n",
"- e로 시작하는 계산식이 0일 경우 -> 1/1이 되어서 최댓값인 1이 된다.\n",
"- e로 시작하는 계산식이 매우 클 때 -> 1/e 꼴이 되어 최소값 0이 된다.\n",
"- $WX$가 0일 경우 -> 지수가 0이 되고 결국 1/2가 되어 중간값 0.5가 된다."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"----"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### `12. ML lec 5-2 Logistic Regression의 cost 함수 설명`"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"기존 함수 : $ H(x) = Wx + b $ \n",
"<BR>\n",
"시그모이드 적용 : $ H(X) = \\frac{1}{1 + e{-W^{t}X}} $"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<img width=\"70%\" align=\"left\" src=\"img/cost_function.png\">"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- 시그모이드를 적용한 함수를 그리면 울퉁불퉁해진다.\n",
"- 이대로 최적화 함수를 적용하면 최저점을 잘 못 인식할 수 있는 문제발생.\n",
"- 일부 최저점(Local Minimum)이 아닌 전체 최저점(Global Minimum)을 구해야 한다."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### New Cost Function for Logistic"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ cost(W) = \\frac{1}{m} \\sum c(H(x), y) $$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\\begin{equation}\n",
"f(x)=\\left \\{\\begin{array}{ll}\n",
"\\ -log(H(x)) : y = 1 \\\\\n",
"\\ -log(1- H(x)) : y = 0 \\\\\n",
"\\end{array}\n",
"\\right.\n",
"\\end{equation}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ c:(H(x), y) = ylog(H(x)) - (1-y)log(1 - H(x)) $$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Minimize cost : Grdient Decent Algorithm"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import tensorflow as tf\n",
"\n",
"# cost function\n",
"cost = tf.reduce_mean(-tf.reduce_sum(Y*tf.log(hypothesis) + (1-Y)*tf.log(1-hypothesis)))\n",
"\n",
"# Minimize\n",
"a = tf.Variable(0.1) # Learning rate, alpha\n",
"optimizer = tf.train.GradientDescentOptimizer(a)\n",
"train = optimizer.minimize(cost)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"-----"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`13. ML lab 05 TensorFlow로 Logistic Classification의 구현하기 (new)`"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- Logistic Regression\n",
"\n",
"$$ sigmoid: H(X) = \\frac{1}{1 + e^{-W^{t}X}} $$ <BR>\n",
"$$ cost(W) = -\\frac{1}{m}\\sum{}{}ylog(H(x)) + (1-y)(log(1 - H(x)) $$ <BR>\n",
"$$ W := W - \\alpha\\frac{\\sigma}{\\sigma W}cost(W) $$"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"import tensorflow as tf"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- 데이터 확인\n",
" - x_data는 x1, x2 형식으로 주어짐. 공부한 시간을 의미.\n",
" - y_data는 0,1로 주어짐. 1은 합격, 0은 불합격.\n",
" - [None, 2] : none은 몇 개가 들어오는 정해지지 않을때, 2는 2개씩 있다는 의미."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"x_data = [[1,2], [2,3], [3,1], [4,3], [5,3], [6,2]]\n",
"y_data = [[0], [0], [0], [1], [1], [1]]\n",
"\n",
"# placeholder for a tensor that will be always fed.\n",
"X = tf.placeholder(tf.float32, shape=[None, 2])\n",
"Y = tf.placeholder(tf.float32, shape=[None, 1])\n",
"W = tf.Variable(tf.random_normal([2, 1]), name='weight')\n",
"b = tf.Variable(tf.random_normal([1]), name='bias')"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"# Hypothesis using sigmod : tf.div(1., 1. + tf.exp(tf.matmul(X, W) + b))\n",
"hypothesis = tf.sigmoid(tf.matmul(X, W) + b)\n",
"\n",
"# cost/loss function\n",
"cost = -tf.reduce_mean(Y * tf.log(hypothesis) + (1 - Y) * tf.log(1 - hypothesi s))\n",
"\n",
"train = tf.train.GradientDescentOptimizer(learning_rate=0.01).minimize(cost)\n",
"\n",
"#Accuray Computation\n",
"# True if Hypothesis > 0.5 else False\n",
"predicted = tf.cast(hypothesis > 0.5, dtype = tf.float32)\n",
"accuracy = tf.reduce_mean(tf.cast(tf.equal(predicted, Y), dtype=tf.float32))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Train the Model"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0 2.6321828 / 200 0.672776 / 400 0.5846116 / 600 0.5382804 / 800 0.508029 / 1000 0.48489007 / 1200 0.46537724 / 1400 0.4479871 / 1600 0.43201455 / 1800 0.4171041 / 2000 0.40306374 / 2200 0.3897808 / 2400 0.377183 / 2600 0.36521864 / 2800 0.35384724 / 3000 0.34303418 / 3200 0.33274838 / 3400 0.32296112 / 3600 0.31364527 / 3800 0.304775 / 4000 0.2963256 / 4200 0.28827378 / 4400 0.2805973 / 4600 0.27327493 / 4800 0.26628685 / 5000 0.259614 / 5200 0.2532386 / 5400 0.24714382 / 5600 0.24131374 / 5800 0.23573364 / 6000 0.23038949 / 6200 0.22526823 / 6400 0.22035746 / 6600 0.21564586 / 6800 0.21112241 / 7000 0.20677702 / 7200 0.20260035 / 7400 0.19858326 / 7600 0.19471753 / 7800 0.19099534 / 8000 0.18740934 / 8200 0.18395253 / 8400 0.18061858 / 8600 0.17740141 / 8800 0.17429513 / 9000 0.17129444 / 9200 0.16839428 / 9400 0.16559003 / 9600 0.16287702 / 9800 0.16025119 / 10000 0.15770836 / \n",
"\n",
" - Hypothesis: \n",
" [[0.03426922]\n",
" [0.16337043]\n",
" [0.32133013]\n",
" [0.7739592 ]\n",
" [0.9348008 ]\n",
" [0.97858 ]] \n",
" - Correct(Y): \n",
" [[0.]\n",
" [0.]\n",
" [0.]\n",
" [1.]\n",
" [1.]\n",
" [1.]] \n",
" - Accuracy: \n",
" 1.0\n"
]
}
],
"source": [
"# Launch Graph\n",
"with tf.Session() as sess:\n",
" # Initialize TensorFlow variables\n",
" sess.run(tf.global_variables_initializer())\n",
" \n",
" for step in range(10001):\n",
" cost_val, _ = sess.run([cost, train], feed_dict={X: x_data, Y:y_data})\n",
" if step % 200 == 0:\n",
" print(step, cost_val , end=\" / \")\n",
" \n",
" # Accuracy report\n",
" h, c, a = sess.run([hypothesis, predicted, accuracy], feed_dict={X: x_data, Y:y_data})\n",
" \n",
" print(\"\\n\\n\",\" - Hypothesis: \\n\", h, \"\\n - Correct(Y): \\n\", c, \"\\n - Accuracy: \\n\", a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Classifying Diabetes\n",
"- 당뇨병 데이터\n",
"- 숫자들은 당뇨에 관련된 데이터들\n",
"- 마지막 컬럼에서 1이 당뇨병이 있는 거, 0이 없는 거"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
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" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>-0.294118</th>\n",
" <th>0.487437</th>\n",
" <th>0.180328</th>\n",
" <th>-0.292929</th>\n",
" <th>0</th>\n",
" <th>0.00149028</th>\n",
" <th>-0.53117</th>\n",
" <th>-0.0333333</th>\n",
" <th>0.1</th>\n",
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" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
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" <td>-0.145729</td>\n",
" <td>0.081967</td>\n",
" <td>-0.414141</td>\n",
" <td>0.000000</td>\n",
" <td>-0.207153</td>\n",
" <td>-0.766866</td>\n",
" <td>-0.666667</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>-0.058824</td>\n",
" <td>0.839196</td>\n",
" <td>0.049180</td>\n",
" <td>0.000000</td>\n",
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" <td>0.081967</td>\n",
" <td>-0.535354</td>\n",
" <td>-0.777778</td>\n",
" <td>-0.162444</td>\n",
" <td>-0.923997</td>\n",
" <td>0.000000</td>\n",
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],
"text/plain": [
" -0.294118 0.487437 0.180328 -0.292929 0 0.00149028 -0.53117 \\\n",
"0 -0.882353 -0.145729 0.081967 -0.414141 0.000000 -0.207153 -0.766866 \n",
"1 -0.058824 0.839196 0.049180 0.000000 0.000000 -0.305514 -0.492741 \n",
"2 -0.882353 -0.105528 0.081967 -0.535354 -0.777778 -0.162444 -0.923997 \n",
"\n",
" -0.0333333 0.1 \n",
"0 -0.666667 1 \n",
"1 -0.633333 0 \n",
"2 0.000000 1 "
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import pandas as pd\n",
"\n",
"df = pd.read_csv('Data/data-03-diabetes.csv')\n",
"df.head(3)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"\n",
"xy = np.loadtxt('Data/data-03-diabetes.csv', delimiter=',', dtype=np.float32)\n",
"x_data = xy[:, 0:-1]\n",
"y_data = xy[:, [-1]]"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [],
"source": [
"# placeholder for a tensor that will be always fed.\n",
"X = tf.placeholder(tf.float32, shape=[None, 8])\n",
"Y = tf.placeholder(tf.float32, shape=[None, 1])\n",
"W = tf.Variable(tf.random_normal([8, 1]), name='weight')\n",
"b = tf.Variable(tf.random_normal([1]), name='bias')"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [],
"source": [
"# Hypothesis using sigmod : tf.div(1., 1. + tf.exp(tf.matmul(X, W) + b))\n",
"hypothesis = tf.sigmoid(tf.matmul(X, W) + b)\n",
"\n",
"# cost/loss function\n",
"cost = -tf.reduce_mean(Y * tf.log(hypothesis) + (1 - Y) * tf.log(1 - hypothesis))\n",
"train = tf.train.GradientDescentOptimizer(learning_rate=0.01).minimize(cost)\n",
"\n",
"#Accuray Computation\n",
"# True if Hypothesis > 0.5 else False\n",
"predicted = tf.cast(hypothesis > 0.5, dtype = tf.float32)\n",
"accuracy = tf.reduce_mean(tf.cast(tf.equal(predicted, Y), dtype=tf.float32))"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0 0.9145897 / 200 0.6217353 / 400 0.5711805 / 600 0.5571511 / 800 0.54969805 / 1000 0.54386365 / 1200 0.53870153 / 1400 0.53399694 / 1600 0.5296793 / 1800 0.52570844 / 2000 0.5220531 / 2200 0.51868516 / 2400 0.51558 / 2600 0.51271427 / 2800 0.5100674 / 3000 0.50762063 / 3200 0.50535667 / 3400 0.5032599 / 3600 0.5013163 / 3800 0.49951324 / 4000 0.49783888 / 4200 0.4962824 / 4400 0.49483478 / 4600 0.49348676 / 4800 0.49223068 / 5000 0.49105918 / 5200 0.48996592 / 5400 0.48894438 / 5600 0.48798954 / 5800 0.4870961 / 6000 0.4862596 / 6200 0.48547593 / 6400 0.48474097 / 6600 0.4840514 / 6800 0.48340395 / 7000 0.48279542 / 7200 0.48222357 / 7400 0.48168546 / 7600 0.48117882 / 7800 0.4807017 / 8000 0.48025212 / 8200 0.47982812 / 8400 0.47942802 / 8600 0.47905034 / 8800 0.47869363 / 9000 0.47835648 / 9200 0.47803774 / 9400 0.47773623 / 9600 0.47745106 / 9800 0.47718093 / 10000 0.47692513 / \n",
"\n",
" - Hypothesis: \n",
" [[0.37795937]\n",
" [0.93710846]\n",
" [0.2772684 ]\n",
" [0.94427884]\n",
" [0.08024111]\n",
" [0.8161948 ]\n",
" [0.93239474]\n",
" [0.5422459 ]\n",
" [0.26880753]\n",
" [0.5600177 ]\n",
" [0.73212385]\n",
" [0.15082034]\n",
" [0.2643727 ]\n",
" [0.25788882]\n",
" [0.7307969 ]\n",
" [0.37741715]\n",
" [0.7592269 ]\n",
" [0.7322997 ]\n",
" [0.8136358 ]\n",
" [0.5986698 ]\n",
" [0.64691615]\n",
" [0.10534783]\n",
" [0.701169 ]\n",
" [0.6604219 ]\n",
" [0.3165895 ]\n",
" [0.9538011 ]\n",
" [0.6144037 ]\n",
" [0.6854153 ]\n",
" [0.6379973 ]\n",
" [0.4849738 ]\n",
" [0.95931435]\n",
" [0.9331794 ]\n",
" [0.60776037]\n",
" [0.8443987 ]\n",
" [0.36229703]\n",
" [0.6154204 ]\n",
" [0.79683864]\n",
" [0.46518764]\n",
" [0.46110174]\n",
" [0.33292928]\n",
" [0.8835323 ]\n",
" [0.13436048]\n",
" [0.43114787]\n",
" [0.03980754]\n",
" [0.5946765 ]\n",
" [0.9426602 ]\n",
" [0.6372723 ]\n",
" [0.6930083 ]\n",
" [0.9666622 ]\n",
" [0.9395554 ]\n",
" [0.94415545]\n",
" [0.24174732]\n",
" [0.31210196]\n",
" [0.9628792 ]\n",
" [0.17701541]\n",
" [0.39859533]\n",
" [0.0988318 ]\n",
" [0.6342522 ]\n",
" [0.8446446 ]\n",
" [0.49572718]\n",
" [0.9523375 ]\n",
" [0.7556712 ]\n",
" [0.63299966]\n",
" [0.8689161 ]\n",
" [0.6120836 ]\n",
" [0.52707195]\n",
" [0.97274303]\n",
" [0.7715598 ]\n",
" [0.8486615 ]\n",
" [0.70004165]\n",
" [0.20912507]\n",
" [0.75264645]\n",
" [0.92826045]\n",
" [0.9342586 ]\n",
" [0.8759662 ]\n",
" [0.76235896]\n",
" [0.31451526]\n",
" [0.89634657]\n",
" [0.9071251 ]\n",
" [0.91639215]\n",
" [0.8765216 ]\n",
" [0.8530673 ]\n",
" [0.34343988]\n",
" [0.82991475]\n",
" [0.45937157]\n",
" [0.85160947]\n",
" [0.33583802]\n",
" [0.920775 ]\n",
" [0.9528135 ]\n",
" [0.79035646]\n",
" [0.7167408 ]\n",
" [0.7116038 ]\n",
" [0.7822815 ]\n",
" [0.56358117]\n",
" [0.9039538 ]\n",
" [0.98123646]\n",
" [0.88511926]\n",
" [0.536103 ]\n",
" [0.22637509]\n",
" [0.71892756]\n",
" [0.73735535]\n",
" [0.9696666 ]\n",
" [0.71954125]\n",
" [0.7444778 ]\n",
" [0.95869905]\n",
" [0.68527675]\n",
" [0.91050303]\n",
" [0.81628585]\n",
" [0.53486943]\n",
" [0.28905788]\n",
" [0.9457995 ]\n",
" [0.86101824]\n",
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" [0.68219376]\n",
" [0.71421254]\n",
" [0.8614742 ]\n",
" [0.717938 ]\n",
" [0.9099425 ]] \n",
" - Correct(Y): \n",
" [[0.]\n",
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" [1.]] \n",
" - Accuracy: \n",
" 0.77338606\n"
]
}
],
"source": [
"# Launch Graph\n",
"with tf.Session() as sess:\n",
" # Initialize TensorFlow variables\n",
" sess.run(tf.global_variables_initializer())\n",
" \n",
" feed = {X: x_data, Y:y_data}\n",
" for step in range(10001):\n",
" cost_val, _ = sess.run([cost, train], feed_dict=feed)\n",
" if step % 200 == 0:\n",
" print(step, cost_val , end=\" / \")\n",
" \n",
" # Accuracy report\n",
" h, c, a = sess.run([hypothesis, predicted, accuracy], feed_dict=feed)\n",
" \n",
" print(\"\\n\\n\",\" - Hypothesis: \\n\", h, \"\\n - Correct(Y): \\n\", c, \"\\n - Accuracy: \\n\", a)\n",
" \n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "python3.5",
"language": "python",
"name": "python3.5"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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