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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 2: Classification"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we have learned in the previous chapter *classification* belongs to the field of *supervised learning*. In such problems the aim is to predict a category. Such categories can be \n",
"\n",
"- ok/not ok\n",
"- good / bad / dont't know\n",
"- digit 0 ... / digit 9\n",
"- etc \n",
"\n",
"In this chapter we introduce the core concepts of classification."
]
},
{
"cell_type": "markdown",
"metadata": {},
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## How could we build a simple classifier ?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Geometrical interpretation of feature vectors\n",
"\n",
"\n",
"If you take the values of an input-feature vector you can imagine it as a point in a d-dimensional space.\n",
"\n",
"\n",
"E.g. if a data set consists of feature vectors of length 2, you can interpret the first feature value as a x-coordinate and the second value as a y-coordinate.\n",
"\n",
"Labeled features then group such points to different point clouds.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example\n",
"\n",
"For sake of simplicity we restrict our beer data set to two features: `alcohol_content` and `bitterness`.\n",
"\n",
"The following plot shows how these reduced feature vectors can be interpreted as point clouds. For every feature vector we color the points in green or red to indicate the according classes:"
"image/png": 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\n",
"<matplotlib.figure.Figure at 0x7ffb463d2a90>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"\n",
"# read some data\n",
"beer_data = pd.read_csv(\"beers.csv\")\n",
"\n",
"xv = beer_data[\"alcohol_content\"]\n",
"yv = beer_data[\"bitterness\"]\n",
"\n",
"colors = [\"rg\"[i] for i in beer_data[\"is_yummy\"]]\n",
"\n",
"plt.scatter(xv, yv, color=colors, marker='.');\n",
"plt.xlabel(\"alcohol_content\")\n",
"plt.ylabel(\"bitterness\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This plot tells us that:\n",
"1. The two features lack information for a 100% separation of the classes. \n",
"2. We could draw a line to separate most points of both clouds.\n",
"3. Later we could use this line to make a guess for classifying a new feature vector.\n",
"\n",
"Eventually **classification is about finding a procedure to separate two or more point clouds.**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we can see how additional features can support (improve?) classification. We add the `darkness` feature as the third dimension.\n"
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"<matplotlib.figure.Figure at 0x7ffb051510b8>"
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]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from mpl_toolkits.mplot3d import Axes3D\n",
"\n",
"fig = plt.figure(figsize=(20, 7))\n",
"\n",
"xv = beer_data[\"alcohol_content\"]\n",
"yv = beer_data[\"darkness\"]\n",
"zv = beer_data[\"bitterness\"]\n",
"\n",
"colors = [\"rg\"[i] for i in beer_data[\"is_yummy\"]]\n",
"\n",
"def plot(ax):\n",
" ax.scatter(xv, yv, zv, c=colors, marker='.') \n",
"\n",
" ax.set_xlabel('alcohol_content')\n",
" ax.set_ylabel('darkness')\n",
" ax.set_zlabel('bitterness');\n",
"\n",
"ax = fig.add_subplot(121, projection='3d')\n",
"\n",
"plot(ax)\n",
"ax.view_init(5, 275)\n",
"\n",
"ax = fig.add_subplot(122, projection='3d')\n",
"plot(ax)\n",
"ax.view_init(5, 5);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The first view is very similar to the scatter plot before and we don't see the effects of the third feature.\n",
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"\n",
"The second view shows the same cube rotated by 90˚ to the left. We see that the new dimenission adds extra information which could improve separation."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If we look at the beer example, we can assume that the person who rated beers has preferences like, \"I don't like high alcohol content\", \"I like fruity beer\", etc."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This means we could construct a score where high numbers relate to \"favorable beer\". One simple way to implement such a score is to use a weighted sum like\n",
"\n",
"\n",
" score = -0.1 * alcohol_content + 4 * bitterness + 0.8 * darkness + 1.8 * fruitiness \n",
"\n",
"Positive weights contribute to a heigher score and negative weights to a lower.\n",
"\n",
"The actual weights here are guessed and serve as an example.\n",
"\n",
"The size of the numbers also reflects the numerical ranges of the features: alcohol content is in the range 3 to 5.9, where as bitterness is between 0 and 1.08:"
]
},
{
"cell_type": "code",
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"metadata": {},
"outputs": [
{
"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>alcohol_content</th>\n",
" <th>bitterness</th>\n",
" <th>darkness</th>\n",
" <th>fruitiness</th>\n",
" <th>is_yummy</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>count</th>\n",
" <td>225.000000</td>\n",
" <td>225.000000</td>\n",
" <td>225.000000</td>\n",
" <td>225.000000</td>\n",
" <td>225.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>mean</th>\n",
" <td>4.711873</td>\n",
" <td>0.463945</td>\n",
" <td>2.574963</td>\n",
" <td>0.223111</td>\n",
" <td>0.528889</td>\n",
" </tr>\n",
" <tr>\n",
" <th>std</th>\n",
" <td>0.437040</td>\n",
" <td>0.227366</td>\n",
" <td>1.725916</td>\n",
" <td>0.117272</td>\n",
" <td>0.500278</td>\n",
" </tr>\n",
" <tr>\n",
" <th>min</th>\n",
" <td>3.073993</td>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>25%</th>\n",
" <td>4.429183</td>\n",
" <td>0.281291</td>\n",
" <td>1.197640</td>\n",
" <td>0.135783</td>\n",
" <td>0.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>50%</th>\n",
" <td>4.740846</td>\n",
" <td>0.488249</td>\n",
" <td>2.026548</td>\n",
" <td>0.242396</td>\n",
" <td>1.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>75%</th>\n",
" <td>5.005170</td>\n",
" <td>0.631056</td>\n",
" <td>4.043995</td>\n",
" <td>0.311874</td>\n",
" <td>1.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>max</th>\n",
" <td>5.955272</td>\n",
" <td>1.080170</td>\n",
" <td>7.221285</td>\n",
" <td>0.535315</td>\n",
" <td>1.000000</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" alcohol_content bitterness darkness fruitiness is_yummy\n",
"count 225.000000 225.000000 225.000000 225.000000 225.000000\n",
"mean 4.711873 0.463945 2.574963 0.223111 0.528889\n",
"std 0.437040 0.227366 1.725916 0.117272 0.500278\n",
"min 3.073993 0.000000 0.000000 0.000000 0.000000\n",
"25% 4.429183 0.281291 1.197640 0.135783 0.000000\n",
"50% 4.740846 0.488249 2.026548 0.242396 1.000000\n",
"75% 5.005170 0.631056 4.043995 0.311874 1.000000\n",
"max 5.955272 1.080170 7.221285 0.535315 1.000000"
]
},
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"beer_data.describe()"
]
},
{
"cell_type": "code",
"metadata": {},
"outputs": [],
"source": [
"scores =( -0.1 * beer_data[\"alcohol_content\"] + 3 * beer_data[\"bitterness\"] \n",
" + 0.8 * beer_data[\"darkness\"] + 1.8 * beer_data[\"fruitiness\"])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we can plot the histogram of the scores by classes:"
]
},
{
"cell_type": "code",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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C\n",
"<matplotlib.figure.Figure at 0x7ffb0504af98>"
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]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"scores_good = scores[beer_data[\"is_yummy\"] == 1]\n",
"scores_bad = scores[beer_data[\"is_yummy\"] == 0]\n",
"\n",
"plt.hist(scores_good, bins=25, color=\"green\", alpha=.5) \n",
"plt.hist(scores_bad, bins=25, color=\"red\", alpha=.5);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Consequence: A simple classifier could use these scores and use a threshold around 3.5 to assign a class label."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**This is how so called linear classifiers work. The magic is in computing the weights and the final threshold to guarantee good results.**\n",
"\n",
"*Comment*: although this seems to be a simple concept, linear classifiers can work very well, especially for higher resp. very high dimensions."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Geometrical interpretation of feature vectors\n",
"\n",
"If you take the values of a input-feature vector you can imagine this as a point in a d-dimensional space.\n",
"\n",
"\n",
"E.g. if a data set consists of feature vectors of length 2, you can interpret the first feature value as a x-coordinate and the second value as a y-coordinate.\n",
"\n",
"Labeled features then group such points to different point clouds.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example\n",
"\n",
"For sake of simplicity we restrict our beer data set to two features: `alcohol_content` and `bitterness`.\n",
"\n",
"The following plot shows how these reduced feature vectors can be interpreted as point clouds. For every feature vector we color points in green or red to indicate the according classes:"
]
},
{
"cell_type": "code",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"<matplotlib.figure.Figure at 0x7ffb40030e80>"
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]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"\n",
"# read some data\n",
"beer_data = pd.read_csv(\"beers.csv\")\n",
"\n",
"xv = beer_data[\"alcohol_content\"]\n",
"yv = beer_data[\"bitterness\"]\n",
"\n",
"colors = [\"rg\"[i] for i in beer_data[\"is_yummy\"]]\n",
"\n",
"plt.scatter(xv, yv, color=colors, marker='.');\n",
"plt.xlabel(\"alcohol_content\")\n",
"plt.ylabel(\"bitterness\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"What do we see here ?\n",
"\n",
"1. Both point clouds overlap, this tells us that the two features lack information for a 100% separation of classes. \n",
"2. We could draw a line to separate most points of both clouds.\n",
"3. Later we could use this line to make a guess for classifying a new feature vector.\n",
"\n",
"Eventually **classification is about finding a procedure to separate point clouds in an n-dimesional space.**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next we illustrate how more features can support classification. We add the `darkness` feature as third dimension.\n"
]
},
{
"cell_type": "code",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"<matplotlib.figure.Figure at 0x7ffb0505c128>"
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]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from mpl_toolkits.mplot3d import Axes3D\n",
"\n",
"fig = plt.figure(figsize=(20, 7))\n",
"\n",
"xv = beer_data[\"alcohol_content\"]\n",
"yv = beer_data[\"darkness\"]\n",
"zv = beer_data[\"bitterness\"]\n",
"\n",
"colors = [\"rg\"[i] for i in beer_data[\"is_yummy\"]]\n",
"\n",
"def plot(ax):\n",
" ax.scatter(xv, yv, zv, c=colors, marker='.') \n",
"\n",
" ax.set_xlabel('alcohol_content')\n",
" ax.set_ylabel('darkness')\n",
" ax.set_zlabel('bitterness');\n",
"\n",
"ax = fig.add_subplot(121, projection='3d')\n",
"\n",
"plot(ax)\n",
"ax.view_init(3, 273)\n",
"\n",
"ax = fig.add_subplot(122, projection='3d')\n",
"plot(ax)\n",
"ax.view_init(3, 3);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The first view is very similar to the scatter plot before as we don't see the effects of the third feature. \n",
"\n",
"The second view shows the same cube rotated by 90˚ to the left. We see that the new dimenission adds extra information which could improve separation. So tiling the plane which separates in the first view could improve separation.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Decision surfaces\n",
"\n",
"For a weighted sum of two features `x` and `y` the equation\n",
"\n",
"\n",
" weight_x * x + weight_y * y = threshold\n",
" \n",
"\n",
"defines a line in 2d space. Points fulfilling\n",
"\n",
" weight_x * x + weight_y * y < threshold\n",
" \n",
" \n",
"vs\n",
"\n",
" weight_x * x + weight_y * y > threshold\n",
" \n",
"\n",
"are located on opposite sides of this line. Such a classifier thus determines a line which separates the feature space in two parts according to the two classes."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets visualize this! \n",
"\n",
"We \n",
"\n",
"- create random points in 2D,\n",
"- compute scores for given weights\n",
"- split points according to their score compared to the threshold \n",
"- plot them in different colors.\n",
"\n",
"Additionally we did some math and computed the decision line:"
]
},
{
"cell_type": "code",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"<matplotlib.figure.Figure at 0x7ffb050610f0>"
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},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"\n",
"wx = -.5\n",
"wy = 1.2\n",
"threshold = 0.2\n",
"\n",
"weights = np.array((wx, wy))\n",
"points_2d = np.random.random((200, 2))\n",
"scores = points_2d @ weights # matrix - vector product\n",
"\n",
"above_points = points_2d[scores > threshold]\n",
"below_points = points_2d[scores < threshold]\n",
"\n",
"plt.scatter(above_points[:, 0], above_points[:, 1], c=\"g\", marker=\".\", label=\"above\")\n",
"plt.scatter(below_points[:, 0], below_points[:, 1], c=\"r\", marker=\".\", label=\"below\")\n",
"\n",
"# plot decision line\n",
"x = np.linspace(-.01, 1.01, 2)\n",
"y = threshold / weights[1] - weights[0] / weights[1] * x\n",
"plt.plot(x, y, 'k:')\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Higher dimensions**: For 3D features a linear classifiers separates classes by a plane, and for higher dimensions `n` we get `n-1` dimensional planes."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example\n",
"\n",
"In the beer example, features fulfilling\n",
"\n",
" -0.1 * alcohol_content + 4 * bitterness + 0.8 * darkness + 1.9 * fruitiness == threshold\n",
" \n",
"are located on a 3D-plane in 4D. \n",
"\n",
"Points in the \"not yummy\" class fulfilling\n",
"\n",
" -0.1 * alcohol_content + 4 * bitterness + 0.8 * darkness + 1.9 * fruitiness < threshold\n",
" \n",
"and points in the \"yummy class\"\n",
"\n",
" -0.1 * alcohol_content + 4 * bitterness + 0.8 * darkness + 1.9 * fruitiness > threshold\n",
" \n",
"are located on different sides of this plane.\n",
"\n",
"Again: **Here the classifier separates the 4d space into two parts, the separation boundary is a plane in this space.**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To illustrate this, we use ignore `fruitiness` such that we have 3 features:\n",
"\n",
"**REPEAT!!**\n"
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"<matplotlib.figure.Figure at 0x7ffb04e6ab38>"
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},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from mpl_toolkits.mplot3d import Axes3D\n",
"\n",
"fig = plt.figure(figsize=(20, 7))\n",
"\n",
"xv = beer_data[\"alcohol_content\"]\n",
"yv = beer_data[\"darkness\"]\n",
"zv = beer_data[\"bitterness\"]\n",
"\n",
"colors = [\"rg\"[i] for i in beer_data[\"is_yummy\"]]\n",
"\n",
"def plot(ax):\n",
" ax.scatter(xv, yv, zv, c=colors, marker='.') \n",
"\n",
" ax.set_xlabel('alcohol_content')\n",
" ax.set_ylabel('darkness')\n",
" ax.set_zlabel('bitterness');\n",
"\n",
"ax = fig.add_subplot(121, projection='3d')\n",
"\n",
"plot(ax)\n",
"ax.view_init(5, 275)\n",
"\n",
"ax = fig.add_subplot(122, projection='3d')\n",
"plot(ax)\n",
"ax.view_init(5, 5);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The first view is very similar to the scatter plot we have already seen before as we barely can see the effects of the third feature.\n",
"\n",
"The second view shows the same cube rotated by 90˚ to the left. We see that the new dimenission adds extra information which could improve separation."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### About 2D examples\n",
"\n",
"For the sake of simplicity and visualisation we continue with 2 dimensional examples.\n",
"\n",
"It is clear that such examples only represent very small subset of realistic ML scenarios. But most concepts can be illustrated in 2- or 3D without loss of generality.\n",
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"\n",
"The examples also might look artificial, but general classifiers should work on all kind of problems."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## More complex decision surfaces"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The next example data set can not bew classified by a line, the decision line is curved:\n"
]
},
{
"cell_type": "code",
"execution_count": 165,
"metadata": {},
"outputs": [
{
"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>a</th>\n",
" <th>b</th>\n",
" <th>label</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>-3.591782</td>\n",
" <td>3.612599</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>6.580586</td>\n",
" <td>-2.105557</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>-0.670938</td>\n",
" <td>-5.905074</td>\n",
" <td>1</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" a b label\n",
"0 -3.591782 3.612599 1\n",
"1 6.580586 -2.105557 1\n",
"2 -0.670938 -5.905074 1"
]
},
"execution_count": 165,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df = pd.read_csv(\"2d_points.csv\")\n",
"df.head(3)"
]
},
{
"cell_type": "code",
"execution_count": 285,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"xv = df[\"a\"]\n",
"yv = df[\"b\"]\n",
"\n",
"colors = [\"rg\"[i] for i in df[\"label\"]]\n",
"plt.figure(figsize=(5, 5))\n",
"plt.xlim([-8, 8])\n",
"plt.ylim([-8, 8])\n",
"plt.scatter(xv, yv, color=colors, marker=\".\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this case the decision line is curved and is looks like a circle. A hand-crafted classifier could classify new points based on their distance to the center.\n",
"\n",
"\n",
"It should be clear that a linear classifier is not suitable for this problem !\n",
"\n",
"### Example for feature engineering\n",
"\n",
"To improve ML performance we can try to enhance / transform a given feature-set by transformations. This process is called **feature engineering**.\n",
"\n",
"In the previous example we see that the distance of the origin of a point could be used to implement a classifier.\n",
"\n",
"Computing the distance of a point to the origin (0, 0) using the euclidian formula includes terms $x^2$ and $y^2$. \n",
"\n",
"Let us create a scatter plot for this transformation:"
]
},
{
"cell_type": "code",
"execution_count": 286,
"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": [
"plt.scatter(xv ** 2, yv ** 2, color=colors, marker='.');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you can see both sets can be separated by a line now !"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Another example for feature engineering\n",
"\n",
"**COMMENT UWE: is this section too much ?**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The so called \"xor-problem\" is a typical benchmark problem for machine learning. The following example illustrates this problem:"
]
},
{
"cell_type": "code",
"execution_count": 370,
"metadata": {},
"outputs": [
{
"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>x</th>\n",
" <th>y</th>\n",
" <th>label</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>-1.539782</td>\n",
" <td>0.950822</td>\n",
" <td>False</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.436266</td>\n",
" <td>-1.768324</td>\n",
" <td>False</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>-1.466436</td>\n",
" <td>1.391890</td>\n",
" <td>False</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>-1.037642</td>\n",
" <td>-0.953587</td>\n",
" <td>True</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>-0.691444</td>\n",
" <td>-0.219826</td>\n",
" <td>True</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" x y label\n",
"0 -1.539782 0.950822 False\n",
"1 0.436266 -1.768324 False\n",
"2 -1.466436 1.391890 False\n",
"3 -1.037642 -0.953587 True\n",
"4 -0.691444 -0.219826 True"
]
},
"execution_count": 370,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"xor = pd.read_csv(\"xor.csv\")\n",
"xor.head()"
]
},
{
"cell_type": "code",
"execution_count": 349,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"xv = xor[\"x\"]\n",
"yv = xor[\"y\"]\n",
"\n",
"colors = [\"rg\"[i] for i in xor[\"label\"]]\n",
"plt.figure(figsize=(5, 5))\n",
"plt.xlim([-2, 2])\n",
"plt.ylim([-2, 2])\n",
"plt.title(\"green points have label True\")\n",
"plt.scatter(xv, yv, color=colors, marker=\".\");"
]