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+ "cell_type": "heading",
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+ "metadata": {},
+ "source": [
+ "Data Mining I: Nearest Neighbours"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In this notebook, you will use the nearest neighbour libraries in python to carry out the experiments which you carried out by hand in the module notes.\n",
+ "\n",
+ "We will see how to represent the data using pandas DataFrames, and how to use these dataframes to call the appropriate classifier functions."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import pandas as pd\n",
+ "\n",
+ "import matplotlib.pyplot as plt"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stderr",
+ "text": [
+ "/Users/agw96/virtualenv_environments/tm351/lib/python3.3/site-packages/pandas/io/excel.py:626: UserWarning: Installed openpyxl is not supported at this time. Use >=1.6.1 and <2.0.0.\n",
+ " .format(openpyxl_compat.start_ver, openpyxl_compat.stop_ver))\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "The `KNeighborsClassifier` classifier"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The `SKLearn` library in python provides a set of functions for carrying out k-nearest neighbour analyses. The library is imported with the `import` command:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from sklearn.neighbors import KNeighborsClassifier"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The first thing to do is to define a training set. The `KNeighborsClassifier` function takes two arguments. The first is a list of training cases, and the second is a list of the classes into which the training data is split.\n",
+ "\n",
+ "For example, suppose we were to use the data in figure 24.4. The datasets are:\n",
+ "\n",
+ "**Group A**\n",
+ "\n",
+ "|Patient Id|Exercise time (hours) | Sleep time (hours)|\n",
+ "|:---:|:----:|:----:|\n",
+ "|A1|0.7|5.2|\n",
+ "|A2|0.6|5.6|\n",
+ "|A3|1.0|5.0|\n",
+ "|A4|1.8|5.5|\n",
+ "|A5|3.0|6.6|\n",
+ "|A6|2.5|6.7|\n",
+ "|A7|1.3|6.6|\n",
+ "|A8|0.8|7.6|\n",
+ "|A9|1.2|6.4|\n",
+ "|A10|1.7|7.2|\n",
+ "\n",
+ "**Group B**\n",
+ "\n",
+ "|Patient Id|Exercise time (hours) | Sleep time (hours)|\n",
+ "|:---:|:----:|:----:|\n",
+ "|B1|2.7|6.2|\n",
+ "|B2|4.2|6.5|\n",
+ "|B3|4.3|7.1|\n",
+ "|B4|3.2|7.0|\n",
+ "|B5|3.5|6.0|\n",
+ "|B6|4.0|5.2|\n",
+ "|B7|2.7|7.2|\n",
+ "|B8|2.5|7.8|\n",
+ "|B9|3.8|6.4|\n",
+ "|B10|3.5|7.0|\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can represent this data in pandas using dataframes:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "classA=pd.DataFrame({'Exercise time': [0.7, 0.6, 1.0, 1.8, 3.0, 2.5, 1.3, 0.8, 1.2, 1.7],\n",
+ " 'Sleep time': [5.2, 5.6, 5.0, 5.5, 6.6, 6.7, 6.6, 7.6, 6.4, 7.2]},\n",
+ " index=['A1', 'A2', 'A3', 'A4', 'A5', 'A6', 'A7', 'A8', 'A9', 'A10'])\n",
+ "\n",
+ "classB=pd.DataFrame({'Exercise time': [2.7, 4.2, 4.3, 3.2, 3.5, 4.0, 2.7, 2.5, 3.8, 3.5],\n",
+ " 'Sleep time': [6.2, 6.5, 7.1, 7.0, 6.0, 5.2, 7.2, 7.8, 6.4, 7.0]},\n",
+ " index=['B1', 'B2', 'B3', 'B4', 'B5', 'B6', 'B7', 'B8', 'B9', 'B10'])\n"
+ ],
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+ " <th></th>\n",
+ " <th>Exercise time</th>\n",
+ " <th>Sleep time</th>\n",
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+ " <td> 5.2</td>\n",
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+ " <th>A5</th>\n",
+ " <td> 3.0</td>\n",
+ " <td> 6.6</td>\n",
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+ " <tr>\n",
+ " <th>A6</th>\n",
+ " <td> 2.5</td>\n",
+ " <td> 6.7</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>A7</th>\n",
+ " <td> 1.3</td>\n",
+ " <td> 6.6</td>\n",
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+ " <th>A8</th>\n",
+ " <td> 0.8</td>\n",
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+ " </tr>\n",
+ " <tr>\n",
+ " <th>A9</th>\n",
+ " <td> 1.2</td>\n",
+ " <td> 6.4</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>A10</th>\n",
+ " <td> 1.7</td>\n",
+ " <td> 7.2</td>\n",
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+ " </tbody>\n",
+ "</table>\n",
+ "</div>"
+ ],
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+ " Exercise time Sleep time\n",
+ "A1 0.7 5.2\n",
+ "A2 0.6 5.6\n",
+ "A3 1.0 5.0\n",
+ "A4 1.8 5.5\n",
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+ "A7 1.3 6.6\n",
+ "A8 0.8 7.6\n",
+ "A9 1.2 6.4\n",
+ "A10 1.7 7.2"
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+ " <th>Exercise time</th>\n",
+ " <th>Sleep time</th>\n",
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+ " <td> 2.7</td>\n",
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+ " <th>B2</th>\n",
+ " <td> 4.2</td>\n",
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+ " <th>B3</th>\n",
+ " <td> 4.3</td>\n",
+ " <td> 7.1</td>\n",
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+ " <tr>\n",
+ " <th>B4</th>\n",
+ " <td> 3.2</td>\n",
+ " <td> 7.0</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>B5</th>\n",
+ " <td> 3.5</td>\n",
+ " <td> 6.0</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>B6</th>\n",
+ " <td> 4.0</td>\n",
+ " <td> 5.2</td>\n",
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+ " <th>B7</th>\n",
+ " <td> 2.7</td>\n",
+ " <td> 7.2</td>\n",
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+ " <th>B8</th>\n",
+ " <td> 2.5</td>\n",
+ " <td> 7.8</td>\n",
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+ " <tr>\n",
+ " <th>B9</th>\n",
+ " <td> 3.8</td>\n",
+ " <td> 6.4</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>B10</th>\n",
+ " <td> 3.5</td>\n",
+ " <td> 7.0</td>\n",
+ " </tr>\n",
+ " </tbody>\n",
+ "</table>\n",
+ "</div>"
+ ],
+ "metadata": {},
+ "output_type": "pyout",
+ "prompt_number": 5,
+ "text": [
+ " Exercise time Sleep time\n",
+ "B1 2.7 6.2\n",
+ "B2 4.2 6.5\n",
+ "B3 4.3 7.1\n",
+ "B4 3.2 7.0\n",
+ "B5 3.5 6.0\n",
+ "B6 4.0 5.2\n",
+ "B7 2.7 7.2\n",
+ "B8 2.5 7.8\n",
+ "B9 3.8 6.4\n",
+ "B10 3.5 7.0"
+ ]
+ }
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+ "prompt_number": 5
+ },
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+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "\n",
+ "Now, to apply the classifier to this data, the `KNeighborsClassifier` takes two arguments, the first is a list of the training cases, and the second is a list containing a label for the classifier class in each case.\n",
+ "\n",
+ "The easiest way to implement this in python is to add a new column to each of the dataframes containing the training data, which contains the class of each instance.\n",
+ "\n",
+ "This is straightforward in pandas. (We will add the classifier column to a *copy* of each of `classA` and `classB`, so that the original data can be retrieved if necessary).\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Make a copy of the original data\n",
+ "trainingDataA = classA.copy()\n",
+ "\n",
+ "# Add a further column to add the classification data\n",
+ "trainingDataA['class']='A'\n",
+ "\n",
+ "trainingDataA"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "html": [
+ "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
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+ " <th>Exercise time</th>\n",
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+ " <th>A5</th>\n",
+ " <td> 3.0</td>\n",
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+ " <td> A</td>\n",
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+ " <tr>\n",
+ " <th>A6</th>\n",
+ " <td> 2.5</td>\n",
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+ " <td> A</td>\n",
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+ " <th>A7</th>\n",
+ " <td> 1.3</td>\n",
+ " <td> 6.6</td>\n",
+ " <td> A</td>\n",
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+ " <tr>\n",
+ " <th>A8</th>\n",
+ " <td> 0.8</td>\n",
+ " <td> 7.6</td>\n",
+ " <td> A</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>A9</th>\n",
+ " <td> 1.2</td>\n",
+ " <td> 6.4</td>\n",
+ " <td> A</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>A10</th>\n",
+ " <td> 1.7</td>\n",
+ " <td> 7.2</td>\n",
+ " <td> A</td>\n",
+ " </tr>\n",
+ " </tbody>\n",
+ "</table>\n",
+ "</div>"
+ ],
+ "metadata": {},
+ "output_type": "pyout",
+ "prompt_number": 6,
+ "text": [
+ " Exercise time Sleep time class\n",
+ "A1 0.7 5.2 A\n",
+ "A2 0.6 5.6 A\n",
+ "A3 1.0 5.0 A\n",
+ "A4 1.8 5.5 A\n",
+ "A5 3.0 6.6 A\n",
+ "A6 2.5 6.7 A\n",
+ "A7 1.3 6.6 A\n",
+ "A8 0.8 7.6 A\n",
+ "A9 1.2 6.4 A\n",
+ "A10 1.7 7.2 A"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Make a copy of the original data\n",
+ "trainingDataB = classB.copy()\n",
+ "\n",
+ "# Add a further column to add the classification data\n",
+ "trainingDataB['class']='B'\n",
+ "\n",
+ "trainingDataB"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "html": [
+ "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
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+ " <td> 6.0</td>\n",
+ " <td> B</td>\n",
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+ " <tr>\n",
+ " <th>B6</th>\n",
+ " <td> 4.0</td>\n",
+ " <td> 5.2</td>\n",
+ " <td> B</td>\n",
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+ " <tr>\n",
+ " <th>B7</th>\n",
+ " <td> 2.7</td>\n",
+ " <td> 7.2</td>\n",
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+ " <tr>\n",
+ " <th>B8</th>\n",
+ " <td> 2.5</td>\n",
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+ " <td> B</td>\n",
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+ " <tr>\n",
+ " <th>B9</th>\n",
+ " <td> 3.8</td>\n",
+ " <td> 6.4</td>\n",
+ " <td> B</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>B10</th>\n",
+ " <td> 3.5</td>\n",
+ " <td> 7.0</td>\n",
+ " <td> B</td>\n",
+ " </tr>\n",
+ " </tbody>\n",
+ "</table>\n",
+ "</div>"
+ ],
+ "metadata": {},
+ "output_type": "pyout",
+ "prompt_number": 7,
+ "text": [
+ " Exercise time Sleep time class\n",
+ "B1 2.7 6.2 B\n",
+ "B2 4.2 6.5 B\n",
+ "B3 4.3 7.1 B\n",
+ "B4 3.2 7.0 B\n",
+ "B5 3.5 6.0 B\n",
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+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can create the list `trainingData` by concatenating the lists `classA` and `classB`:\n",
+ "\n",
+ "<div style='color:red'>Do we need to draw attention to the reindexing? It's not particularly relevant to the point. Depends on how much they've seen on indexing in the earlier sections, I guess (Tony and Steven are still discussing this.</div>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "trainingData=trainingDataA.append(trainingDataB, ignore_index=True)\n",
+ "\n",
+ "trainingData"
+ ],
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+ "metadata": {},
+ "outputs": [
+ {
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+ " <tr>\n",
+ " <th>9 </th>\n",
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+ " <tr>\n",
+ " <th>10</th>\n",
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+ " <th>11</th>\n",
+ " <td> 4.2</td>\n",
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+ " </tr>\n",
+ " <tr>\n",
+ " <th>12</th>\n",
+ " <td> 4.3</td>\n",
+ " <td> 7.1</td>\n",
+ " <td> B</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>13</th>\n",
+ " <td> 3.2</td>\n",
+ " <td> 7.0</td>\n",
+ " <td> B</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>14</th>\n",
+ " <td> 3.5</td>\n",
+ " <td> 6.0</td>\n",
+ " <td> B</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>15</th>\n",
+ " <td> 4.0</td>\n",
+ " <td> 5.2</td>\n",
+ " <td> B</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>16</th>\n",
+ " <td> 2.7</td>\n",
+ " <td> 7.2</td>\n",
+ " <td> B</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>17</th>\n",
+ " <td> 2.5</td>\n",
+ " <td> 7.8</td>\n",
+ " <td> B</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>18</th>\n",
+ " <td> 3.8</td>\n",
+ " <td> 6.4</td>\n",
+ " <td> B</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>19</th>\n",
+ " <td> 3.5</td>\n",
+ " <td> 7.0</td>\n",
+ " <td> B</td>\n",
+ " </tr>\n",
+ " </tbody>\n",
+ "</table>\n",
+ "</div>"
+ ],
+ "metadata": {},
+ "output_type": "pyout",
+ "prompt_number": 8,
+ "text": [
+ " Exercise time Sleep time class\n",
+ "0 0.7 5.2 A\n",
+ "1 0.6 5.6 A\n",
+ "2 1.0 5.0 A\n",
+ "3 1.8 5.5 A\n",
+ "4 3.0 6.6 A\n",
+ "5 2.5 6.7 A\n",
+ "6 1.3 6.6 A\n",
+ "7 0.8 7.6 A\n",
+ "8 1.2 6.4 A\n",
+ "9 1.7 7.2 A\n",
+ "10 2.7 6.2 B\n",
+ "11 4.2 6.5 B\n",
+ "12 4.3 7.1 B\n",
+ "13 3.2 7.0 B\n",
+ "14 3.5 6.0 B\n",
+ "15 4.0 5.2 B\n",
+ "16 2.7 7.2 B\n",
+ "17 2.5 7.8 B\n",
+ "18 3.8 6.4 B\n",
+ "19 3.5 7.0 B"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The next step is to construct an appropriate classifier. Calling `KNeighborsClassifier` returns a classifier object which can be trained with the training data. The classifier is called with a suitable value of *k* with:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "k=3\n",
+ "classifier3 = KNeighborsClassifier(n_neighbors=k)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To train the classifier, the classifier is called with the training data as the first argument, and the classes of datapoints as the second argument:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "classifier3.fit(trainingData[['Exercise time', 'Sleep time']],\n",
+ " trainingData['class'])"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "pyout",
+ "prompt_number": 10,
+ "text": [
+ "KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',\n",
+ " n_neighbors=3, p=2, weights='uniform')"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Our k-NN classifier is now ready to be used. To use the classifier to classify a new instance, we use the command `predict` with the new instance.\n",
+ "\n",
+ "So in this case, if the new patient had an exercise time of 2.5 hours, and a sleep time of 6.5 hours, then to classify him/her, we call:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "print(classifier3.predict((2.5, 6.5)))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "['A']\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The classifier predicts that the patient should be placed in class A."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "\n",
+ "To implement a weighted voting scheme in Python, we can simply set the parameter weights to `'distance'` when we train the classifier as follows: \n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "k=3\n",
+ "classifier3 = KNeighborsClassifier(n_neighbors=k, weights='distance')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "classifier3.fit(trainingData[['Exercise time', 'Sleep time']],\n",
+ " trainingData['class'])"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "pyout",
+ "prompt_number": 13,
+ "text": [
+ "KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',\n",
+ " n_neighbors=3, p=2, weights='distance')"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "If the parameter weights is not specified, then by default it is set to `'uniform'`, to mean that each of the nearest neighbours is weighted equally."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "print(classifier3.predict((2.5, 6.5)))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "['A']\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Exercise 24.5a"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Redo Exercise 24.3 using Python."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We provide data for the two classes, *class A* and *class B* in the variables `classA` and `classB` respectively:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "classA=pd.DataFrame({'Attribute 1':[15.7, 15.6, 16.0, 16.8, 18.0, 17.5, 16.3, 15.8, 16.2, 16.7],\n",
+ " 'Attribute 2':[20.2, 20.6, 20.0, 20.5, 21.6, 21.7, 21.6, 22.6, 21.4, 22.2],\n",
+ " 'Attribute 3':[1.3, 2.2, 3.4, 4.2, 5.5, 6.7, 7.6, 8.2, 9.0, 9.7]})\n",
+ "\n",
+ "classB=pd.DataFrame({'Attribute 1':[14.05, 16.3, 16.45, 14.8, 15.25, 16.0, 14.05, 13.75, 15.7, 15.25],\n",
+ " 'Attribute 2':[19.3, 19.75, 20.65, 20.5, 19.0, 17.8, 20.8, 21.7, 19.6, 20.5],\n",
+ " 'Attribute 3':[6.6, 7.2, 8.0, 9.1, 9.9, 11.0, 12.2, 13.2, 14.5, 14.5]})\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "classA"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "html": [
+ "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
+ "<table border=\"1\" class=\"dataframe\">\n",
+ " <thead>\n",
+ " <tr style=\"text-align: right;\">\n",
+ " <th></th>\n",
+ " <th>Attribute 1</th>\n",
+ " <th>Attribute 2</th>\n",
+ " <th>Attribute 3</th>\n",
+ " </tr>\n",
+ " </thead>\n",
+ " <tbody>\n",
+ " <tr>\n",
+ " <th>0</th>\n",
+ " <td> 15.7</td>\n",
+ " <td> 20.2</td>\n",
+ " <td> 1.3</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1</th>\n",
+ " <td> 15.6</td>\n",
+ " <td> 20.6</td>\n",
+ " <td> 2.2</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2</th>\n",
+ " <td> 16.0</td>\n",
+ " <td> 20.0</td>\n",
+ " <td> 3.4</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3</th>\n",
+ " <td> 16.8</td>\n",
+ " <td> 20.5</td>\n",
+ " <td> 4.2</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>4</th>\n",
+ " <td> 18.0</td>\n",
+ " <td> 21.6</td>\n",
+ " <td> 5.5</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>5</th>\n",
+ " <td> 17.5</td>\n",
+ " <td> 21.7</td>\n",
+ " <td> 6.7</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>6</th>\n",
+ " <td> 16.3</td>\n",
+ " <td> 21.6</td>\n",
+ " <td> 7.6</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>7</th>\n",
+ " <td> 15.8</td>\n",
+ " <td> 22.6</td>\n",
+ " <td> 8.2</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>8</th>\n",
+ " <td> 16.2</td>\n",
+ " <td> 21.4</td>\n",
+ " <td> 9.0</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>9</th>\n",
+ " <td> 16.7</td>\n",
+ " <td> 22.2</td>\n",
+ " <td> 9.7</td>\n",
+ " </tr>\n",
+ " </tbody>\n",
+ "</table>\n",
+ "</div>"
+ ],
+ "metadata": {},
+ "output_type": "pyout",
+ "prompt_number": 16,
+ "text": [
+ " Attribute 1 Attribute 2 Attribute 3\n",
+ "0 15.7 20.2 1.3\n",
+ "1 15.6 20.6 2.2\n",
+ "2 16.0 20.0 3.4\n",
+ "3 16.8 20.5 4.2\n",
+ "4 18.0 21.6 5.5\n",
+ "5 17.5 21.7 6.7\n",
+ "6 16.3 21.6 7.6\n",
+ "7 15.8 22.6 8.2\n",
+ "8 16.2 21.4 9.0\n",
+ "9 16.7 22.2 9.7"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "classB"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "html": [
+ "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
+ "<table border=\"1\" class=\"dataframe\">\n",
+ " <thead>\n",
+ " <tr style=\"text-align: right;\">\n",
+ " <th></th>\n",
+ " <th>Attribute 1</th>\n",
+ " <th>Attribute 2</th>\n",
+ " <th>Attribute 3</th>\n",
+ " </tr>\n",
+ " </thead>\n",
+ " <tbody>\n",
+ " <tr>\n",
+ " <th>0</th>\n",
+ " <td> 14.05</td>\n",
+ " <td> 19.30</td>\n",
+ " <td> 6.6</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1</th>\n",
+ " <td> 16.30</td>\n",
+ " <td> 19.75</td>\n",
+ " <td> 7.2</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2</th>\n",
+ " <td> 16.45</td>\n",
+ " <td> 20.65</td>\n",
+ " <td> 8.0</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3</th>\n",
+ " <td> 14.80</td>\n",
+ " <td> 20.50</td>\n",
+ " <td> 9.1</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>4</th>\n",
+ " <td> 15.25</td>\n",
+ " <td> 19.00</td>\n",
+ " <td> 9.9</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>5</th>\n",
+ " <td> 16.00</td>\n",
+ " <td> 17.80</td>\n",
+ " <td> 11.0</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>6</th>\n",
+ " <td> 14.05</td>\n",
+ " <td> 20.80</td>\n",
+ " <td> 12.2</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>7</th>\n",
+ " <td> 13.75</td>\n",
+ " <td> 21.70</td>\n",
+ " <td> 13.2</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>8</th>\n",
+ " <td> 15.70</td>\n",
+ " <td> 19.60</td>\n",
+ " <td> 14.5</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>9</th>\n",
+ " <td> 15.25</td>\n",
+ " <td> 20.50</td>\n",
+ " <td> 14.5</td>\n",
+ " </tr>\n",
+ " </tbody>\n",
+ "</table>\n",
+ "</div>"
+ ],
+ "metadata": {},
+ "output_type": "pyout",
+ "prompt_number": 17,
+ "text": [
+ " Attribute 1 Attribute 2 Attribute 3\n",
+ "0 14.05 19.30 6.6\n",
+ "1 16.30 19.75 7.2\n",
+ "2 16.45 20.65 8.0\n",
+ "3 14.80 20.50 9.1\n",
+ "4 15.25 19.00 9.9\n",
+ "5 16.00 17.80 11.0\n",
+ "6 14.05 20.80 12.2\n",
+ "7 13.75 21.70 13.2\n",
+ "8 15.70 19.60 14.5\n",
+ "9 15.25 20.50 14.5"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 4,
+ "metadata": {},
+ "source": [
+ "Solution 24.5(a)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To redo Exercise 24.3, we will follow the same pattern that we have just seen in the notebook.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "First, take training copies of the two classes, and add a new column to each to represent the class that each data point belongs to."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "trainingDataA=classA.copy()\n",
+ "trainingDataA['class']='A'\n",
+ "\n",
+ "trainingDataB=classB.copy()\n",
+ "trainingDataB['class']='B'\n",
+ "\n",
+ "trainingData=trainingDataA.append(trainingDataB, ignore_index=True)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "trainingData"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "html": [
+ "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
+ "<table border=\"1\" class=\"dataframe\">\n",
+ " <thead>\n",
+ " <tr style=\"text-align: right;\">\n",
+ " <th></th>\n",
+ " <th>Attribute 1</th>\n",
+ " <th>Attribute 2</th>\n",
+ " <th>Attribute 3</th>\n",
+ " <th>class</th>\n",
+ " </tr>\n",
+ " </thead>\n",
+ " <tbody>\n",
+ " <tr>\n",
+ " <th>0 </th>\n",
+ " <td> 15.70</td>\n",
+ " <td> 20.20</td>\n",
+ " <td> 1.3</td>\n",
+ " <td> A</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1 </th>\n",
+ " <td> 15.60</td>\n",
+ " <td> 20.60</td>\n",
+ " <td> 2.2</td>\n",
+ " <td> A</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2 </th>\n",
+ " <td> 16.00</td>\n",
+ " <td> 20.00</td>\n",
+ " <td> 3.4</td>\n",
+ " <td> A</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3 </th>\n",
+ " <td> 16.80</td>\n",
+ " <td> 20.50</td>\n",
+ " <td> 4.2</td>\n",
+ " <td> A</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>4 </th>\n",
+ " <td> 18.00</td>\n",
+ " <td> 21.60</td>\n",
+ " <td> 5.5</td>\n",
+ " <td> A</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>5 </th>\n",
+ " <td> 17.50</td>\n",
+ " <td> 21.70</td>\n",
+ " <td> 6.7</td>\n",
+ " <td> A</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>6 </th>\n",
+ " <td> 16.30</td>\n",
+ " <td> 21.60</td>\n",
+ " <td> 7.6</td>\n",
+ " <td> A</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>7 </th>\n",
+ " <td> 15.80</td>\n",
+ " <td> 22.60</td>\n",
+ " <td> 8.2</td>\n",
+ " <td> A</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>8 </th>\n",
+ " <td> 16.20</td>\n",
+ " <td> 21.40</td>\n",
+ " <td> 9.0</td>\n",
+ " <td> A</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>9 </th>\n",
+ " <td> 16.70</td>\n",
+ " <td> 22.20</td>\n",
+ " <td> 9.7</td>\n",
+ " <td> A</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>10</th>\n",
+ " <td> 14.05</td>\n",
+ " <td> 19.30</td>\n",
+ " <td> 6.6</td>\n",
+ " <td> B</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>11</th>\n",
+ " <td> 16.30</td>\n",
+ " <td> 19.75</td>\n",
+ " <td> 7.2</td>\n",
+ " <td> B</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>12</th>\n",
+ " <td> 16.45</td>\n",
+ " <td> 20.65</td>\n",
+ " <td> 8.0</td>\n",
+ " <td> B</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>13</th>\n",
+ " <td> 14.80</td>\n",
+ " <td> 20.50</td>\n",
+ " <td> 9.1</td>\n",
+ " <td> B</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>14</th>\n",
+ " <td> 15.25</td>\n",
+ " <td> 19.00</td>\n",
+ " <td> 9.9</td>\n",
+ " <td> B</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>15</th>\n",
+ " <td> 16.00</td>\n",
+ " <td> 17.80</td>\n",
+ " <td> 11.0</td>\n",
+ " <td> B</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>16</th>\n",
+ " <td> 14.05</td>\n",
+ " <td> 20.80</td>\n",
+ " <td> 12.2</td>\n",
+ " <td> B</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>17</th>\n",
+ " <td> 13.75</td>\n",
+ " <td> 21.70</td>\n",
+ " <td> 13.2</td>\n",
+ " <td> B</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>18</th>\n",
+ " <td> 15.70</td>\n",
+ " <td> 19.60</td>\n",
+ " <td> 14.5</td>\n",
+ " <td> B</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>19</th>\n",
+ " <td> 15.25</td>\n",
+ " <td> 20.50</td>\n",
+ " <td> 14.5</td>\n",
+ " <td> B</td>\n",
+ " </tr>\n",
+ " </tbody>\n",
+ "</table>\n",
+ "</div>"
+ ],
+ "metadata": {},
+ "output_type": "pyout",
+ "prompt_number": 19,
+ "text": [
+ " Attribute 1 Attribute 2 Attribute 3 class\n",
+ "0 15.70 20.20 1.3 A\n",
+ "1 15.60 20.60 2.2 A\n",
+ "2 16.00 20.00 3.4 A\n",
+ "3 16.80 20.50 4.2 A\n",
+ "4 18.00 21.60 5.5 A\n",
+ "5 17.50 21.70 6.7 A\n",
+ "6 16.30 21.60 7.6 A\n",
+ "7 15.80 22.60 8.2 A\n",
+ "8 16.20 21.40 9.0 A\n",
+ "9 16.70 22.20 9.7 A\n",
+ "10 14.05 19.30 6.6 B\n",
+ "11 16.30 19.75 7.2 B\n",
+ "12 16.45 20.65 8.0 B\n",
+ "13 14.80 20.50 9.1 B\n",
+ "14 15.25 19.00 9.9 B\n",
+ "15 16.00 17.80 11.0 B\n",
+ "16 14.05 20.80 12.2 B\n",
+ "17 13.75 21.70 13.2 B\n",
+ "18 15.70 19.60 14.5 B\n",
+ "19 15.25 20.50 14.5 B"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In this case, we want to use a classifier with *k=5*, so initialise the classifier appropriately:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "# Training k-NN classifier with our training set\n",
+ "k = 5\n",
+ "classifier5 = KNeighborsClassifier(n_neighbors=k)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "...and train the classifier again using the data in the dataframes:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "classifier5.fit(trainingData[['Attribute 1', 'Attribute 2', 'Attribute 3']],\n",
+ " trainingData['class']) \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "pyout",
+ "prompt_number": 21,
+ "text": [
+ "KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',\n",
+ " n_neighbors=5, p=2, weights='uniform')"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can then predict the class of the new data point by calling the `predict` method on the classifier:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Classifying a new data point, and show the result of\n",
+ "# entering it into the classifier:\n",
+ "print(classifier5.predict((15.8, 20.1, 7.0)))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "['B']\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Has the new datapoint been correctly classified?"
+ ]
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file
projects / tm351-notebooks.git / blobdiff