{ "cells": [ { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# HIDDEN\n", "import matplotlib\n", "#matplotlib.use('Agg')\n", "from datascience import *\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "import numpy as np\n", "import math\n", "import scipy.stats as stats\n", "plt.style.use('fivethirtyeight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Implementing the Classifier ###\n", "We are now ready to impelment a $k$-nearest neighbor classifier based on multiple attributes. We have used only two attributes so far, for ease of visualization. But usually predictions will be based on many attributes. Here is an example that shows how multiple attributes can be better than pairs." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Banknote authentication\n", "\n", "This time we'll look at predicting whether a banknote (e.g., a \\$20 bill) is counterfeit or legitimate. Researchers have put together a data set for us, based on photographs of many individual banknotes: some counterfeit, some legitimate. They computed a few numbers from each image, using techniques that we won't worry about for this course. So, for each banknote, we know a few numbers that were computed from a photograph of it as well as its class (whether it is counterfeit or not). Let's load it into a table and take a look." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
WaveletVar WaveletSkew WaveletCurt Entropy Class
3.6216 8.6661 -2.8073 -0.44699 0
4.5459 8.1674 -2.4586 -1.4621 0
3.866 -2.6383 1.9242 0.10645 0
3.4566 9.5228 -4.0112 -3.5944 0
0.32924 -4.4552 4.5718 -0.9888 0
4.3684 9.6718 -3.9606 -3.1625 0
3.5912 3.0129 0.72888 0.56421 0
2.0922 -6.81 8.4636 -0.60216 0
3.2032 5.7588 -0.75345 -0.61251 0
1.5356 9.1772 -2.2718 -0.73535 0
\n", "

... (1362 rows omitted)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "banknotes.scatter('WaveletVar', 'WaveletCurt', colors='Color')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pretty interesting! Those two measurements do seem helpful for predicting whether the banknote is counterfeit or not. However, in this example you can now see that there is some overlap between the blue cluster and the gold cluster. This indicates that there will be some images where it's hard to tell whether the banknote is legitimate based on just these two numbers. Still, you could use a $k$-nearest neighbor classifier to predict the legitimacy of a banknote.\n", "\n", "Take a minute and think it through: Suppose we used $k=11$ (say). What parts of the plot would the classifier get right, and what parts would it make errors on? What would the decision boundary look like?\n", "\n", "The patterns that show up in the data can get pretty wild. For instance, here's what we'd get if used a different pair of measurements from the images:" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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AUGLm5F285MReFs6vRAlnvuC+pXNwPUmo4mhs3v3uBZw4/yEShWtw3D/wta9v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Y3B4CYAA1NmyItlSaTCGNKfzv/q+GWAh3TXIr3loG0iiTsQOg1CEMo96ScYrZFqPYhom9SJjeGt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\nCklREEK4NFVV8fEx4vhfw1JFq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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "banknotes.scatter('WaveletSkew', 'Entropy', colors='Color')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There does seem to be a pattern, but it's a pretty complex one. Nonetheless, the $k$-nearest neighbors classifier can still be used and will effectively \"discover\" patterns out of this. This illustrates how powerful machine learning can be: it can effectively take advantage of even patterns that we would not have anticipated, or that we would have thought to \"program into\" the computer." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Multiple attributes\n", "\n", "So far I've been assuming that we have exactly 2 attributes that we can use to help us make our prediction. What if we have more than 2? For instance, what if we have 3 attributes?\n", "\n", "Here's the cool part: you can use the same ideas for this case, too. All you have to do is make a 3-dimensional scatterplot, instead of a 2-dimensional plot. You can still use the $k$-nearest neighbors classifier, but now computing distances in 3 dimensions instead of just 2. It just works. Very cool!\n", "\n", "In fact, there's nothing special about 2 or 3. If you have 4 attributes, you can use the $k$-nearest neighbors classifier in 4 dimensions. 5 attributes? Work in 5-dimensional space. And no need to stop there! This all works for arbitrarily many attributes; you just work in a very high dimensional space. It gets wicked-impossible to visualize, but that's OK. The computer algorithm generalizes very nicely: all you need is the ability to compute the distance, and that's not hard. Mind-blowing stuff!\n", "\n", "For instance, let's see what happens if we try to predict whether a banknote is counterfeit or not using 3 of the measurements, instead of just 2. Here's what you get:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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TNDJNLwa8fhCqEUCYjm3bpFKpnEGC+SoJerVolnKNSinmzGmfcOyLLx7iBz94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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = plt.figure(figsize=(8,8)).add_subplot(111, projection='3d')\n", "ax.scatter(banknotes.column('WaveletSkew'), \n", " banknotes.column('WaveletVar'), \n", " banknotes.column('WaveletCurt'), \n", " c=banknotes.column('Color'));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Awesome! With just 2 attributes, there was some overlap between the two clusters (which means that the classifier was bound to make some mistakes for pointers in the overlap). But when we use these 3 attributes, the two clusters have almost no overlap. In other words, a classifier that uses these 3 attributes will be more accurate than one that only uses the 2 attributes.\n", "\n", "This is a general phenomenom in classification. Each attribute can potentially give you new information, so more attributes sometimes helps you build a better classifier. Of course, the cost is that now we have to gather more information to measure the value of each attribute, but this cost may be well worth it if it significantly improves the accuracy of our classifier.\n", "\n", "To sum up: you now know how to use $k$-nearest neighbor classification to predict the answer to a yes/no question, based on the values of some attributes, assuming you have a training set with examples where the correct prediction is known. The general roadmap is this:\n", "\n", "1. identify some attributes that you think might help you predict the answer to the question.\n", "2. Gather a training set of examples where you know the values of the attributes as well as the correct prediction.\n", "3. To make predictions in the future, measure the value of the attributes and then use $k$-nearest neighbor classification to predict the answer to the question." ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### Distance in Multiple Dimensions ###\n", "We know how to compute distance in 2-dimensional space. If we have a point at coordinates $(x_0,y_0)$ and another at $(x_1,y_1)$, the distance between them is\n", "\n", "$$D = \\sqrt{(x_0-x_1)^2 + (y_0-y_1)^2}.$$\n", "\n", "In 3-dimensional space, the points are $(x_0, y_0, z_0)$ and $(x_1, y_1, z_1)$, and the formula for the distance between them is\n", "\n", "$$\n", "D = \\sqrt{(x_0-x_1)^2 + (y_0-y_1)^2 + (z_0-z_1)^2}\n", "$$\n", "\n", "In $n$-dimensional space, things are a bit harder to visualize, but I think you can see how the formula generalized: we sum up the squares of the differences between each individual coordinate, and then take the square root of that. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the last section, we defined the function `distance` which returned the distance between two points. We used it in two-dimensions, but the great news is that the function doesn't care how many dimensions there are! It just subtracts the two arrays of coordinates (no matter how long the arrays are), squares the differences and adds up, and then takes the square root. To work in multiple dimensions, we don't have to change the code at all." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def distance(point1, point2):\n", " \"\"\"Returns the distance between point1 and point2\n", " where each argument is an array \n", " consisting of the coordinates of the point\"\"\"\n", " return np.sqrt(np.sum((point1 - point2)**2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's use this on a [new dataset](https://archive.ics.uci.edu/ml/datasets/Wine). The table `wine` contains the chemical composition of 178 different Italian wines. The classes are the grape species, called cultivars. There are three classes but let's just see whether we can tell Class 1 apart from the other two." ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": true }, "outputs": [], "source": [ "wine = Table.read_table('wine.csv')\n", "\n", "# For converting Class to binary\n", "\n", "def is_one(x):\n", " if x == 1:\n", " return 1\n", " else:\n", " return 0\n", " \n", "wine = wine.with_column('Class', wine.apply(is_one, 0))" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Class Alcohol Malic Acid Ash Alcalinity of Ash Magnesium Total Phenols Flavanoids Nonflavanoid phenols Proanthocyanins Color Intensity Hue OD280/OD315 of diulted wines Proline
1 14.23 1.71 2.43 15.6 127 2.8 3.06 0.28 2.29 5.64 1.04 3.92 1065
1 13.2 1.78 2.14 11.2 100 2.65 2.76 0.26 1.28 4.38 1.05 3.4 1050
1 13.16 2.36 2.67 18.6 101 2.8 3.24 0.3 2.81 5.68 1.03 3.17 1185
1 14.37 1.95 2.5 16.8 113 3.85 3.49 0.24 2.18 7.8 0.86 3.45 1480
1 13.24 2.59 2.87 21 118 2.8 2.69 0.39 1.82 4.32 1.04 2.93 735
1 14.2 1.76 2.45 15.2 112 3.27 3.39 0.34 1.97 6.75 1.05 2.85 1450
1 14.39 1.87 2.45 14.6 96 2.5 2.52 0.3 1.98 5.25 1.02 3.58 1290
1 14.06 2.15 2.61 17.6 121 2.6 2.51 0.31 1.25 5.05 1.06 3.58 1295
1 14.83 1.64 2.17 14 97 2.8 2.98 0.29 1.98 5.2 1.08 2.85 1045
1 13.86 1.35 2.27 16 98 2.98 3.15 0.22 1.85 7.22 1.01 3.55 1045
\n", "

... (168 rows omitted)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "wine_with_colors.scatter('Flavanoids', 'Alcohol', colors='Color')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The blue points (Class 1) are almost entirely separate from the gold ones. That is one indication of why the distance between two Class 1 wines would be smaller than the distance between wines of two different classes. We can see a similar phenomenon with a different pair of attributes too:" ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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UhKpCqDhm6mPMRNN/94W/ZYdyyzbCa95sJu3A1qrTOf/whz/w2Wef8d577+20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\nc+bM4Y477nCv4y39AzW3p7H902aCXwghRN202TF+IYQQVZP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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "wine_with_colors.scatter('Alcalinity of Ash', 'Ash', colors='Color')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But for some pairs the picture is more murky." ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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bKxJBWAAttB0zwmRgL38OIYMgXAhMHJ4X8R4nGSxYsAm/38TlsiElvPTSVn71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\naE8ca7Mj4dTL8QSWVs4ZHEM49epGObcQBwNVUlJSV05kkQT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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "wine_with_colors.scatter('Magnesium', 'Total Phenols', colors='Color')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's see if we can implement a classifier based on all of the attributes. After that, we'll see how accurate it is." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A Plan for the Implementation ###\n", "It's time to write some code to implement the classifier. The input is a `point` that we want to classify. The classifier works by finding the $k$ nearest neighbors of `point` from the training set. So, our approach will go like this:\n", "\n", "1. Find the closest $k$ neighbors of `point`, i.e., the $k$ wines from the training set that are most similar to `point`.\n", "\n", "2. Look at the classes of those $k$ neighbors, and take the majority vote to find the most-common class of wine. Use that as our predicted class for `point`.\n", "\n", "So that will guide the structure of our Python code." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def closest(training, p, k):\n", " ...\n", "\n", "def majority(topkclasses):\n", " ...\n", "\n", "def classify(training, p, k):\n", " kclosest = closest(training, p, k)\n", " kclosest.classes = kclosest.select('Class')\n", " return majority(kclosest)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Implementation Step 1 ###\n", "To implement the first step for the kidney disease data, we had to compute the distance from each patient in the training set to `point`, sort them by distance, and take the $k$ closest patients in the training set. \n", "\n", "That's what we did in the previous section with the point corresponding to Alice. Let's generalize that code. We'll redefine `distance` here, just for convenience." ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def distance(point1, point2):\n", " \"\"\"Returns the distance between point1 and point2\n", " where each argument is an array \n", " consisting of the coordinates of the point\"\"\"\n", " return np.sqrt(np.sum((point1 - point2)**2))\n", "\n", "def all_distances(training, new_point):\n", " \"\"\"Returns an array of distances\n", " between each point in the training set\n", " and the new point (which is a row of attributes)\"\"\"\n", " attributes = training.drop('Class')\n", " def distance_from_point(row):\n", " return distance(np.array(new_point), np.array(row))\n", " return attributes.apply(distance_from_point)\n", "\n", "def table_with_distances(training, new_point):\n", " \"\"\"Augments the training table \n", " with a column of distances from new_point\"\"\"\n", " return training.with_column('Distance', all_distances(training, new_point))\n", "\n", "def closest(training, new_point, k):\n", " \"\"\"Returns a table of the k rows of the augmented table\n", " corresponding to the k smallest distances\"\"\"\n", " with_dists = table_with_distances(training, new_point)\n", " sorted_by_distance = with_dists.sort('Distance')\n", " topk = sorted_by_distance.take(np.arange(k))\n", " return topk" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's see how this works on our `wine` data. We'll just take the first wine and find its five nearest neighbors among all the wines. Remember that since this wine is part of the dataset, it is its own nearest neighbor. So we should expect to see it at the top of the list, followed by four others.\n", "\n", "First let's extract its attributes:" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": true }, "outputs": [], "source": [ "special_wine = wine.drop('Class').row(0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And now let's find its 5 nearest neighbors." ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Class Alcohol Malic Acid Ash Alcalinity of Ash Magnesium Total Phenols Flavanoids Nonflavanoid phenols Proanthocyanins Color Intensity Hue OD280/OD315 of diulted wines Proline Distance
1 14.23 1.71 2.43 15.6 127 2.8 3.06 0.28 2.29 5.64 1.04 3.92 1065 0
1 13.74 1.67 2.25 16.4 118 2.6 2.9 0.21 1.62 5.85 0.92 3.2 1060 10.3928
1 14.21 4.04 2.44 18.9 111 2.85 2.65 0.3 1.25 5.24 0.87 3.33 1080 22.3407
1 14.1 2.02 2.4 18.8 103 2.75 2.92 0.32 2.38 6.2 1.07 2.75 1060 24.7602
1 14.38 3.59 2.28 16 102 3.25 3.17 0.27 2.19 4.9 1.04 3.44 1065 25.0947
" ], "text/plain": [ "Class | Alcohol | Malic Acid | Ash | Alcalinity of Ash | Magnesium | Total Phenols | Flavanoids | Nonflavanoid phenols | Proanthocyanins | Color Intensity | Hue | OD280/OD315 of diulted wines | Proline | Distance\n", "1 | 14.23 | 1.71 | 2.43 | 15.6 | 127 | 2.8 | 3.06 | 0.28 | 2.29 | 5.64 | 1.04 | 3.92 | 1065 | 0\n", "1 | 13.74 | 1.67 | 2.25 | 16.4 | 118 | 2.6 | 2.9 | 0.21 | 1.62 | 5.85 | 0.92 | 3.2 | 1060 | 10.3928\n", "1 | 14.21 | 4.04 | 2.44 | 18.9 | 111 | 2.85 | 2.65 | 0.3 | 1.25 | 5.24 | 0.87 | 3.33 | 1080 | 22.3407\n", "1 | 14.1 | 2.02 | 2.4 | 18.8 | 103 | 2.75 | 2.92 | 0.32 | 2.38 | 6.2 | 1.07 | 2.75 | 1060 | 24.7602\n", "1 | 14.38 | 3.59 | 2.28 | 16 | 102 | 3.25 | 3.17 | 0.27 | 2.19 | 4.9 | 1.04 | 3.44 | 1065 | 25.0947" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "closest(wine, special_wine, 5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Bingo! The first row is the nearest neighbor, which is itself – there's a 0 in the `Distance` column as expected. All five nearest neighbors are of Class 1, which is consistent with our earlier observation that Class 1 wines appear to be clumped together in some dimensions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Implementation Steps 2 and 3 ###\n", "Next we need to take a \"majority vote\" of the nearest neighbors and assign our point the same class as the majority." ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def majority(topkclasses):\n", " ones = topkclasses.where('Class', are.equal_to(1)).num_rows\n", " zeros = topkclasses.where('Class', are.equal_to(0)).num_rows\n", " if ones > zeros:\n", " return 1\n", " else:\n", " return 0\n", "\n", "def classify(training, new_point, k):\n", " closestk = closest(training, new_point, k)\n", " topkclasses = closestk.select('Class')\n", " return majority(topkclasses)" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "classify(wine, special_wine, 5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we change `special_wine` to be the last one in the dataset, is our classifier able to tell that it's in Class 0?" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "special_wine = wine.drop('Class').row(177)\n", "classify(wine, special_wine, 5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Yes! The classifier gets this one right too.\n", "\n", "But we don't yet know how it does with all the other wines, and in any case we know that testing on wines that are already part of the training set might be over-optimistic. In the final section of this chapter, we will separate the wines into a training and test set and then measure the accuracy of our classifier on the test set. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [Root]", "language": "python", "name": "Python [Root]" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }