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Created on Cognitive Class Labs
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a href=\"https://www.bigdatauniversity.com\"><img src = \"https://ibm.box.com/shared/static/cw2c7r3o20w9zn8gkecaeyjhgw3xdgbj.png\" width=\"400\" align=\"center\"></a>\n",
"\n",
"<h1><center>Non Linear Regression Analysis</center></h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If the data shows a curvy trend, then linear regression will not produce very accurate results when compared to a non-linear regression because, as the name implies, linear regression presumes that the data is linear. \n",
"Let's learn about non linear regressions and apply an example on python. In this notebook, we fit a non-linear model to the datapoints corrensponding to China's GDP from 1960 to 2014."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2 id=\"importing_libraries\">Importing required libraries</h2>"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Though Linear regression is very good to solve many problems, it cannot be used for all datasets. First recall how linear regression, could model a dataset. It models a linear relation between a dependent variable y and independent variable x. It had a simple equation, of degree 1, for example y = $2x$ + 3."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"##You can adjust the slope and intercept to verify the changes in the graph\n",
"y = 2*(x) + 3\n",
"y_noise = 2 * np.random.normal(size=x.size)\n",
"ydata = y + y_noise\n",
"#plt.figure(figsize=(8,6))\n",
"plt.plot(x, ydata, 'bo')\n",
"plt.plot(x,y, 'r') \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Indepdendent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Non-linear regressions are a relationship between independent variables $x$ and a dependent variable $y$ which result in a non-linear function modeled data. Essentially any relationship that is not linear can be termed as non-linear, and is usually represented by the polynomial of $k$ degrees (maximum power of $x$). \n",
"\n",
"$$ \\ y = a x^3 + b x^2 + c x + d \\ $$\n",
"\n",
"Non-linear functions can have elements like exponentials, logarithms, fractions, and others. For example: $$ y = \\log(x)$$\n",
" \n",
"Or even, more complicated such as :\n",
"$$ y = \\log(a x^3 + b x^2 + c x + d)$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's take a look at a cubic function's graph."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"##You can adjust the slope and intercept to verify the changes in the graph\n",
"y = 1*(x**3) + 1*(x**2) + 1*x + 3\n",
"y_noise = 20 * np.random.normal(size=x.size)\n",
"ydata = y + y_noise\n",
"plt.plot(x, ydata, 'bo')\n",
"plt.plot(x,y, 'r') \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Indepdendent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you can see, this function has $x^3$ and $x^2$ as independent variables. Also, the graphic of this function is not a straight line over the 2D plane. So this is a non-linear function."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Some other types of non-linear functions are:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Quadratic"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ Y = X^2 $$"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"##You can adjust the slope and intercept to verify the changes in the graph\n",
"\n",
"y = np.power(x,2)\n",
"y_noise = 2 * np.random.normal(size=x.size)\n",
"ydata = y + y_noise\n",
"plt.plot(x, ydata, 'bo')\n",
"plt.plot(x,y, 'r') \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Indepdendent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exponential"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"An exponential function with base c is defined by $$ Y = a + b c^X$$ where b ≠0, c > 0 , c ≠1, and x is any real number. The base, c, is constant and the exponent, x, is a variable. \n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"##You can adjust the slope and intercept to verify the changes in the graph\n",
"\n",
"Y= np.exp(X)\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Indepdendent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Logarithmic\n",
"\n",
"The response $y$ is a results of applying logarithmic map from input $x$'s to output variable $y$. It is one of the simplest form of __log()__: i.e. $$ y = \\log(x)$$\n",
"\n",
"Please consider that instead of $x$, we can use $X$, which can be polynomial representation of the $x$'s. In general form it would be written as \n",
"\\begin{equation}\n",
"y = \\log(X)\n",
"\\end{equation}"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/ipykernel_launcher.py:3: RuntimeWarning: invalid value encountered in log\n",
" This is separate from the ipykernel package so we can avoid doing imports until\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"Y = np.log(X)\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Indepdendent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Sigmoidal/Logistic"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ Y = a + \\frac{b}{1+ c^{(X-d)}}$$"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"\n",
"Y = 1-4/(1+np.power(3, X-2))\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Indepdendent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a id=\"ref2\"></a>\n",
"# Non-Linear Regression example"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For an example, we're going to try and fit a non-linear model to the datapoints corresponding to China's GDP from 1960 to 2014. We download a dataset with two columns, the first, a year between 1960 and 2014, the second, China's corresponding annual gross domestic income in US dollars for that year. "
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2020-01-15 18:50:00 URL:https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/china_gdp.csv [1218/1218] -> \"china_gdp.csv\" [1]\n"
]
},
{
"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",
" vertical-align: top;\n",
" }\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>Year</th>\n",
" <th>Value</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1960</td>\n",
" <td>5.918412e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>1961</td>\n",
" <td>4.955705e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>1962</td>\n",
" <td>4.668518e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>1963</td>\n",
" <td>5.009730e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>1964</td>\n",
" <td>5.906225e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>1965</td>\n",
" <td>6.970915e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>1966</td>\n",
" <td>7.587943e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>1967</td>\n",
" <td>7.205703e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>1968</td>\n",
" <td>6.999350e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>1969</td>\n",
" <td>7.871882e+10</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Year Value\n",
"0 1960 5.918412e+10\n",
"1 1961 4.955705e+10\n",
"2 1962 4.668518e+10\n",
"3 1963 5.009730e+10\n",
"4 1964 5.906225e+10\n",
"5 1965 6.970915e+10\n",
"6 1966 7.587943e+10\n",
"7 1967 7.205703e+10\n",
"8 1968 6.999350e+10\n",
"9 1969 7.871882e+10"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"\n",
"#downloading dataset\n",
"!wget -nv -O china_gdp.csv https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/china_gdp.csv\n",
" \n",
"df = pd.read_csv(\"china_gdp.csv\")\n",
"df.head(10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__Did you know?__ When it comes to Machine Learning, you will likely be working with large datasets. As a business, where can you host your data? IBM is offering a unique opportunity for businesses, with 10 Tb of IBM Cloud Object Storage: [Sign up now for free](http://cocl.us/ML0101EN-IBM-Offer-CC)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plotting the Dataset ###\n",
"This is what the datapoints look like. It kind of looks like an either logistic or exponential function. The growth starts off slow, then from 2005 on forward, the growth is very significant. And finally, it decelerate slightly in the 2010s."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(8,5))\n",
"x_data, y_data = (df[\"Year\"].values, df[\"Value\"].values)\n",
"plt.plot(x_data, y_data, 'ro')\n",
"plt.ylabel('GDP')\n",
"plt.xlabel('Year')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Choosing a model ###\n",
"\n",
"From an initial look at the plot, we determine that the logistic function could be a good approximation,\n",
"since it has the property of starting with a slow growth, increasing growth in the middle, and then decreasing again at the end; as illustrated below:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"Y = 1.0 / (1.0 + np.exp(-X))\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Indepdendent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"The formula for the logistic function is the following:\n",
"\n",
"$$ \\hat{Y} = \\frac1{1+e^{\\beta_1(X-\\beta_2)}}$$\n",
"\n",
"$\\beta_1$: Controls the curve's steepness,\n",
"\n",
"$\\beta_2$: Slides the curve on the x-axis."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Building The Model ###\n",
"Now, let's build our regression model and initialize its parameters. "
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"def sigmoid(x, Beta_1, Beta_2):\n",
" y = 1 / (1 + np.exp(-Beta_1*(x-Beta_2)))\n",
" return y"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets look at a sample sigmoid line that might fit with the data:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f4f2a23e630>]"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"beta_1 = 0.10\n",
"beta_2 = 1990.0\n",
"\n",
"#logistic function\n",
"Y_pred = sigmoid(x_data, beta_1 , beta_2)\n",
"\n",
"#plot initial prediction against datapoints\n",
"plt.plot(x_data, Y_pred*15000000000000.)\n",
"plt.plot(x_data, y_data, 'ro')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our task here is to find the best parameters for our model. Lets first normalize our x and y:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"# Lets normalize our data\n",
"xdata =x_data/max(x_data)\n",
"ydata =y_data/max(y_data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### How we find the best parameters for our fit line?\n",
"we can use __curve_fit__ which uses non-linear least squares to fit our sigmoid function, to data. Optimal values for the parameters so that the sum of the squared residuals of sigmoid(xdata, *popt) - ydata is minimized.\n",
"\n",
"popt are our optimized parameters."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" beta_1 = 690.447527, beta_2 = 0.997207\n"
]
}
],
"source": [
"from scipy.optimize import curve_fit\n",
"popt, pcov = curve_fit(sigmoid, xdata, ydata)\n",
"#print the final parameters\n",
"print(\" beta_1 = %f, beta_2 = %f\" % (popt[0], popt[1]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we plot our resulting regression model."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x = np.linspace(1960, 2015, 55)\n",
"x = x/max(x)\n",
"plt.figure(figsize=(8,5))\n",
"y = sigmoid(x, *popt)\n",
"plt.plot(xdata, ydata, 'ro', label='data')\n",
"plt.plot(x,y, linewidth=3.0, label='fit')\n",
"plt.legend(loc='best')\n",
"plt.ylabel('GDP')\n",
"plt.xlabel('Year')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Practice\n",
"Can you calculate what is the accuracy of our model?"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mean absolute error is: 0.02\n",
"Residual sum of squares is: 0.00\n",
"R2-score is: 0.97\n"
]
}
],
"source": [
"# write your code here\n",
"from sklearn.metrics import r2_score\n",
"\n",
"print(\"Mean absolute error is: %.02f\" % np.absolute(np.mean(y - ydata)))\n",
"print(\"Residual sum of squares is: %.02f\" % np.mean((y - ydata)**2))\n",
"print(\"R2-score is: %.02f\" % r2_score(ydata, y))\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click __here__ for the solution.\n",
"\n",
"<!-- Your answer is below:\n",
" \n",
"# split data into train/test\n",
"msk = np.random.rand(len(df)) < 0.8\n",
"train_x = xdata[msk]\n",
"test_x = xdata[~msk]\n",
"train_y = ydata[msk]\n",
"test_y = ydata[~msk]\n",
"\n",
"# build the model using train set\n",
"popt, pcov = curve_fit(sigmoid, train_x, train_y)\n",
"\n",
"# predict using test set\n",
"y_hat = sigmoid(test_x, *popt)\n",
"\n",
"# evaluation\n",
"print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(y_hat - test_y)))\n",
"print(\"Residual sum of squares (MSE): %.2f\" % np.mean((y_hat - test_y) ** 2))\n",
"from sklearn.metrics import r2_score\n",
"print(\"R2-score: %.2f\" % r2_score(y_hat , test_y) )\n",
"\n",
"-->"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click __here__ for the solution.\n",
"\n",
"<!-- Your answer is below:\n",
" \n",
"# split data into train/test\n",
"msk = np.random.rand(len(df)) < 0.8\n",
"train_x = xdata[msk]\n",
"test_x = xdata[~msk]\n",
"train_y = ydata[msk]\n",
"test_y = ydata[~msk]\n",
"\n",
"# build the model using train set\n",
"popt, pcov = curve_fit(sigmoid, train_x, train_y)\n",
"\n",
"# predict using test set\n",
"y_hat = sigmoid(test_x, *popt)\n",
"\n",
"# evaluation\n",
"print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(y_hat - test_y)))\n",
"print(\"Residual sum of squares (MSE): %.2f\" % np.mean((y_hat - test_y) ** 2))\n",
"from sklearn.metrics import r2_score\n",
"print(\"R2-score: %.2f\" % r2_score(y_hat , test_y) )\n",
"\n",
"-->"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Want to learn more?</h2>\n",
"\n",
"IBM SPSS Modeler is a comprehensive analytics platform that has many machine learning algorithms. It has been designed to bring predictive intelligence to decisions made by individuals, by groups, by systems – by your enterprise as a whole. A free trial is available through this course, available here: <a href=\"http://cocl.us/ML0101EN-SPSSModeler\">SPSS Modeler</a>\n",
"\n",
"Also, you can use Watson Studio to run these notebooks faster with bigger datasets. Watson Studio is IBM's leading cloud solution for data scientists, built by data scientists. With Jupyter notebooks, RStudio, Apache Spark and popular libraries pre-packaged in the cloud, Watson Studio enables data scientists to collaborate on their projects without having to install anything. Join the fast-growing community of Watson Studio users today with a free account at <a href=\"https://cocl.us/ML0101EN_DSX\">Watson Studio</a>\n",
"\n",
"<h3>Thanks for completing this lesson!</h3>\n",
"\n",
"<h4>Author: <a href=\"https://ca.linkedin.com/in/saeedaghabozorgi\">Saeed Aghabozorgi</a></h4>\n",
"<p><a href=\"https://ca.linkedin.com/in/saeedaghabozorgi\">Saeed Aghabozorgi</a>, PhD is a Data Scientist in IBM with a track record of developing enterprise level applications that substantially increases clients’ ability to turn data into actionable knowledge. He is a researcher in data mining field and expert in developing advanced analytic methods like machine learning and statistical modelling on large datasets.</p>\n",
"\n",
"<hr>\n",
"\n",
"<p>Copyright &copy; 2018 <a href=\"https://cocl.us/DX0108EN_CC\">Cognitive Class</a>. This notebook and its source code are released under the terms of the <a href=\"https://bigdatauniversity.com/mit-license/\">MIT License</a>.</p>"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python",
"language": "python",
"name": "conda-env-python-py"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.7"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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