{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "dad48f92", "metadata": { "tags": [ "remove-input" ] }, "outputs": [ { "data": { "text/html": [ "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%html\n", "" ] }, { "cell_type": "markdown", "id": "802acf9e", "metadata": {}, "source": [ "# Unsupervised ML\n", "\n", "Unsupervised machine learning is useful when we have **unlabelled** data. This means we have *only input data* and *no output data*. Yet, while we are not predicting labels or values for outcome variables (because we have none!), we can still learn a lot about our data (and, hopefully, the world) by finding patterns in the input data we do have.\n", "\n", "The two broad kinds of unsupervised ML are cluserting algorithms and dimensionality reduction algorithms. We'll focus on clustering algorithms, where we aim to partition our observations into clusters based on similarities between them, measured in terms of their attributes. If you continue in data science, you'll also come across dimensionality reduction, which is a technique for reducing *high-dimensional data* (i.e., data with many, many attribute variables) into fewer dimensions that still capture the variation between our variables. This can be useful when our models perform worse on high-dimensional data, as we previewed briefly in the previous section.\n", "\n", "For now, we will focus on clustering algorithms. An example clustering tasks might be to group individual animals into different species based on various features, like height, weight, number of offspring, location, and so on. In this case, the researcher does not know what the species are, or even how many there are, but they want to explore the data to look for clusters that might be meaningful to distinguish between these animals based on the known attributes in the data. Note that generally the computer will be able to identify which observations belong to which cluster based on how similar or different they are in terms of their attributes, but it is up to the researcher to decide (a) how many clusters to look for, (b) if those clusters are *useful*, as well as (c) what those clusters might represent in real life.\n", "\n", "As another example: a company might use a clustering algorithm to group customers by purchasing behavior. Perhaps they have data on each customer's number of visits to the company website, visits to their various social media accounts, how many times they've opened emails from the company, and the frequency and quantity of purchases in the last year. The company could build a clustering algorithm to partition customers by their values on these attributes. Suppose they looked for and the computer identified three clusters -- someone from the company then might decide those customer groups reflect \"regular customers\", \"persuadable customers\", and \"one-time only\" customers -- or something. Again, the researcher ascribes *meaning* to the clusters -- the computer just finds out where they are based on how similar or different each observation is. All the computer is going to tell us is which observations belong to cluster 0, 1, or 2 -- and the computer of course is doing so based on the instructions we provide for finding the clusters.\n", "\n", "Let's make this more concrete by considering a common clustering algorithm, $k$-means.\n", "\n", "## Clustering algorithm: $k$-means\n", "\n", "The core idea in $k$-means is that observations of the same class will be clustered together in what we call the **feature space**, which simply refers to the spatial representation of our observations in terms of their values. A simple scatter plot of two attributes (say, height and weight of each animal) is an example of a 2D feature space. If we had three variables (say, we add number of offspring), we would have a three-dimensional scatterplot and thus a 3D feature space. As discussed in the previous section, it quickly becomes difficult to visualize 4, 5, and n-dimensional feature spaces, but luckily for us, computers are great at doing the calculations to find the distances between variables in multi-dimensional feature space.\n", "\n", "The core assumption, thus, is that differences in the features of our observations (e.g., the height, weight, and offspring numbers) are representative of different classes or categories of those observations (i.e., different species). Note that this is an *assumption* and is not guaranteed. I may have a principled, theoretical reason to expect that there are three species in my dataset, and that the values for the attributes for which I have data are different in ways that reflect these three species, but I do not know for sure whether that's true.\n", "\n", "### Steps in the algorithm\n", "\n", "The $k$-means clustering algorithm proceeds according to the following high-level steps, which are also depicted in the visualization below. Suppose we have an unlabelled dataset in which we hope to discover some underlying structure. Then:\n", "\n", "1. We (humans) choose the number of clusters to look for, $k$\n", "2. The algorithm selects $k$ random points and assigns them as centroids.\n", "3. Assign each data point to the closest centroid (often calculated by Euclidean distance, just as we saw with $k$-NN)\n", "4. Compute the centroid of the newly-formed cluster\n", "5. Repeat steps 3-4 until the centroid location is stable." ] }, { "cell_type": "markdown", "id": "7bc7b2ac", "metadata": {}, "source": [ ":::{figure-md} k_means\n", "\"k_means\"\n", "\n", "Visualization of the five steps in $k$-means\n", ":::" ] }, { "cell_type": "markdown", "id": "4c74f2ea", "metadata": {}, "source": [ "Unsupervised techniques don't generally use a training and test set because we don't have any labels against which to test our predictions. Evaluation of $k$-means thus generally is done based first by theory: Do these clusters make sense given my knowledge and expectations of the underlying data? Second, because $k$-means is based on the random placement of our initial $k$ centroids, running the same model over and over (with different random states!) and ending up with the same, or at least roughly the same, clusters over and over and also help increase our confidence that these clusters are at least robust, or informative of *something* in the data. Again, the actual meaning, or even label we might assign to the clusters, is up to us.\n", "\n", "Aside: $k$-means (and other clustering techniques) can feel unsatisfying to newcomers to unsupervised learning, as it can feel like we are just squinting our eyes at a scatterplot and trying to derive meaning, tea-leaves style. To some extent there is some interpretation -- we ultimately decide if these clusters are *useful* to us as we attempt to understand our world, but there's a little more behind the clusters themselves than tea leaves, as the clusters are based on actual distances in the feature space. That said, \"unsupervised machine learning clustering algorithm\" sounds *extremely* high-tech, when really what we are doing, in the wise words of a former DS4E professor, Sarah Shugars, boils down to \"fancy counting.\"" ] }, { "cell_type": "markdown", "id": "3713d54d", "metadata": {}, "source": [ "## Example" ] }, { "cell_type": "markdown", "id": "bab6a94f", "metadata": {}, "source": [ "To keep things simple, we'll yet again turn to our trusty horses dataset to build some further intuition for how $k$-means works, as well as implement it in python. Unlike with supervised ML, we're going to cut right to the \"canned\" version from our friends at `sklearn`. Thus, first, we'll need a few new packages." ] }, { "cell_type": "code", "execution_count": 2, "id": "1cb58b92", "metadata": { "tags": [ "full-width" ] }, "outputs": [ { "data": { "text/html": [ "
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namepricesexheightcolorlocationmarkingsweightfoaldateregistrationsdisciplinestemperament
0Captain5000.0Gelding14.212DunNantucket, MassachusettsNaNNaN4-MayNorwegian Fjord Horse Registry (04-6018-G)Beginner/Family Cowboy Mounted Shooting Trai...1.005
1Eternal Goodness8500.0Gelding16.205ChestnutBrooklyn, ConnecticutNaNNaN3-MayJC - Jockey Club ()Jumper (Competed or Shown) Hunter (Competed or...1.010
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" ], "text/plain": [ " name price sex height color \\\n", "0 Captain 5000.0 Gelding 14.212 Dun \n", "1 Eternal Goodness 8500.0 Gelding 16.205 Chestnut \n", "\n", " location markings weight foaldate \\\n", "0 Nantucket, Massachusetts NaN NaN 4-May \n", "1 Brooklyn, Connecticut NaN NaN 3-May \n", "\n", " registrations \\\n", "0 Norwegian Fjord Horse Registry (04-6018-G) \n", "1 JC - Jockey Club () \n", "\n", " disciplines temperament \n", "0 Beginner/Family Cowboy Mounted Shooting Trai... 1.005 \n", "1 Jumper (Competed or Shown) Hunter (Competed or... 1.010 " ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "## new packages for k-means ##\n", "from sklearn.preprocessing import StandardScaler # for feature scaling\n", "from sklearn.cluster import KMeans # our kmeans algorithm\n", "from sklearn import metrics # for evaluation metrics\n", "\n", "horses = pd.read_csv('data/horses.csv')\n", "horses.head(2)" ] }, { "cell_type": "markdown", "id": "2547c017", "metadata": {}, "source": [ "Recall that three of our variables are numeric: `price`, `height`, and `temperament`. We'll use all three for our $k$-means clustering algorithm, meaning python will look for clusters in the 3D feature space. \n", "\n", "But first, let's plot height vs. temperament to get a feel for things. Notice this is not the most beautiful data in the world (though I think we can all agree it is the most fascinating!), but it will do for our illustrative purposes." ] }, { "cell_type": "code", "execution_count": 3, "id": "1a5c0662", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.scatter(horses['height'], horses['temperament'])\n", "plt.xlabel('height')\n", "plt.ylabel('temperament')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "21d8b440", "metadata": {}, "source": [ "Eventually, we are going to project our clusters (calculated from three dimensions) onto this particular 2D scatterplot. To get there, we set up for $k$-means much like we did for $k$-NN." ] }, { "cell_type": "code", "execution_count": 4, "id": "549ff4e4", "metadata": {}, "outputs": [], "source": [ "X = horses[['temperament', 'height', 'price']].values # indicate our three features for analysis\n", "\n", "scaler = StandardScaler() # standardize our features (Z-scores FTW!)\n", "scaled_features = scaler.fit_transform(X)" ] }, { "cell_type": "code", "execution_count": 5, "id": "26b18a3b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "KMeans(init='random', n_clusters=3, random_state=44)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# initialize k-means, set k=3, set random state for replicability\n", "\n", "kmeans = KMeans(init='random', n_clusters=3, n_init=10, max_iter=300, random_state=44)\n", "\n", "# run k-means!\n", "\n", "kmeans.fit(scaled_features) " ] }, { "cell_type": "markdown", "id": "cb458c08", "metadata": {}, "source": [ "And ... we did it! We assigned every observation to one of three clusters. But ... how can we see what those clusters are? One way is to add the newly assigned labels as a new variable to our dataframe:" ] }, { "cell_type": "code", "execution_count": 6, "id": "277d1016", "metadata": { "tags": [ "full-width" ] }, "outputs": [ { "data": { "text/html": [ "
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namepricesexheightcolorlocationmarkingsweightfoaldateregistrationsdisciplinestemperamentcluster
0Captain5000.0Gelding14.212DunNantucket, MassachusettsNaNNaN4-MayNorwegian Fjord Horse Registry (04-6018-G)Beginner/Family Cowboy Mounted Shooting Trai...1.0052
1Eternal Goodness8500.0Gelding16.205ChestnutBrooklyn, ConnecticutNaNNaN3-MayJC - Jockey Club ()Jumper (Competed or Shown) Hunter (Competed or...1.0102
2Dustys Fly Boy15000.0Gelding15.192GrullaDallas, TexasNaN1200 pounds6-AprAQHA - American Quarter Horse Association (484...Beginner/Family (Champion) Youth/4-H Horse (Ch...1.0122
3A FEDERAL HOLIDAY8500.0Mare14.999GreyHOLSTEIN, Iowastar, strip, & snip. 3 white socks.NaN5-AprAQHA - American Quarter Horse Association ()Western Pleasure (Show) (Competed or Shown) Yo...1.0132
4WIMPYS TRADITIONSTEP15000.0Gelding14.999PalominoHOWELL, MichiganNaN1000 pounds9-AprAQHA - American Quarter Horse Association (526...Youth/4-H Horse (Trained) Ranch Horse (Trained...1.0132
\n", "
" ], "text/plain": [ " name price sex height color \\\n", "0 Captain 5000.0 Gelding 14.212 Dun \n", "1 Eternal Goodness 8500.0 Gelding 16.205 Chestnut \n", "2 Dustys Fly Boy 15000.0 Gelding 15.192 Grulla \n", "3 A FEDERAL HOLIDAY 8500.0 Mare 14.999 Grey \n", "4 WIMPYS TRADITIONSTEP 15000.0 Gelding 14.999 Palomino \n", "\n", " location markings weight \\\n", "0 Nantucket, Massachusetts NaN NaN \n", "1 Brooklyn, Connecticut NaN NaN \n", "2 Dallas, Texas NaN 1200 pounds \n", "3 HOLSTEIN, Iowa star, strip, & snip. 3 white socks. NaN \n", "4 HOWELL, Michigan NaN 1000 pounds \n", "\n", " foaldate registrations \\\n", "0 4-May Norwegian Fjord Horse Registry (04-6018-G) \n", "1 3-May JC - Jockey Club () \n", "2 6-Apr AQHA - American Quarter Horse Association (484... \n", "3 5-Apr AQHA - American Quarter Horse Association () \n", "4 9-Apr AQHA - American Quarter Horse Association (526... \n", "\n", " disciplines temperament cluster \n", "0 Beginner/Family Cowboy Mounted Shooting Trai... 1.005 2 \n", "1 Jumper (Competed or Shown) Hunter (Competed or... 1.010 2 \n", "2 Beginner/Family (Champion) Youth/4-H Horse (Ch... 1.012 2 \n", "3 Western Pleasure (Show) (Competed or Shown) Yo... 1.013 2 \n", "4 Youth/4-H Horse (Trained) Ranch Horse (Trained... 1.013 2 " ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "horses['cluster'] = kmeans.labels_ # add a variable called \"cluster\" that contains the k-means labels\n", "horses.head()" ] }, { "cell_type": "markdown", "id": "d6b92191", "metadata": {}, "source": [ "If you look to the last variable, you'll see we now have cluster numbers assigned to each variable. To see which observation ended up in which cluster, we go back to our original 2D scatterplot (which, again, will project the clusters calculated based on three dimensions)." ] }, { "cell_type": "code", "execution_count": 7, "id": "bcbb9110", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = plt.figure(figsize=(6,4)).add_subplot(111)\n", "ax.scatter(horses['height'], \n", " horses['temperament'], \n", " c = horses['cluster'], s=50);\n", "ax.set_xlabel(\"height\")\n", "ax.set_ylabel(\"temperament\");" ] }, { "cell_type": "markdown", "id": "a6c8e05a", "metadata": {}, "source": [ "Ta da! We did it! We have partitioned our observations into three clusters. You can also run this many times and see for yourself that the clusters are relatively stable over time. \n", "\n", "So, have we learned anything about some underlying structure or pattern in the data? Well, it's hard to say. We can observe the following about the clusters so far:\n", "\n", "- **yellow**: these horses are taller and calmer (lower temperament score = more calm)\n", "- **purple**: these horses are about the same height as the horses in the yellow cluster, but they are less calm, or more \"hot\"\n", "- **green**: the horses in this cluster are all shorter than the other two clusters, and they have a range of temperaments\n", "\n", "It's up to us, the researchers, to decide if those clusters \"mean\" anything in the real world. This is one big area where substantive expertise matters -- if you're reading this book and you know a lot about horses, you may be shouting some particular names or descriptors that might map well to these clusters (feel free to let us know what they are!).\n", "\n", "Recall also we are plotting clusters based on three dimensions (height, temperament, price) on a 2D scatterplot. Thus, the cluster assignments may be picking up price differences in the horses as well.\n", "\n", "Let's project our clusters onto a *different* 2D scatter to see if any other helpful patterns arise in terms of what these clusters might represent in real life." ] }, { "cell_type": "code", "execution_count": 8, "id": "f81fd5a8", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = plt.figure(figsize=(6,4)).add_subplot(111)\n", "ax.scatter(horses['height'], \n", " horses['price'], \n", " c = horses['cluster'], s=50);\n", "ax.set_xlabel(\"height\")\n", "ax.set_ylabel(\"price\");" ] }, { "cell_type": "markdown", "id": "7819dfc1", "metadata": {}, "source": [ "Here see the same information in a slightly different format: height does not seem to be a big factor in distinguishing yellow from purple horses, and neither does price. The distinction in this cluster really does seem to be driven by temperament.\n", "\n", "Finally, we can also inspect all three dimensions in a 3D scatterplot as we did with *k*-NN." ] }, { "cell_type": "code", "execution_count": 9, "id": "63e45750", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = plt.figure(figsize=(8,8)).add_subplot(111, projection='3d')\n", "ax.scatter(horses['height'], \n", " horses['price'], \n", " horses['temperament'], \n", " c = horses['cluster'], s=50);\n", "ax.set_xlabel(\"height\")\n", "ax.set_ylabel(\"price\")\n", "ax.set_zlabel(\"temperament\");" ] }, { "cell_type": "markdown", "id": "adad8763", "metadata": {}, "source": [ "In the above plot, we can see that:\n", "\n", "- **yellow** horses are tall and calm, but not as expensive as purple ones\n", "- **purple** horses are slightly less tall than yellow ones, but more expensive and less calm\n", "- **green** horses are, indeed, shorter and mostly (though not entirely) less expensive than the other two clusters, and appear to have something of a range of temperaments\n", "\n", "A (perhaps) reasonable \"interpretation\" of these clusters, then, might be that given their price and temperament, **purple** horses might be racehorses, **yellow** horses might be horses used in other types of competitions, and **green** horses might be more recreational or kid-friendly horses.\n", "\n", "Again, this application of \"meaning\" comes from us, the researchers. What do you think the clusters represent?\n", "\n", "Because we are working with three features, we can visualize the full picture. If we had four, five, or many more features, we would not be able to visualize the full picture at once; rather, we'd have to continue to inspect partial views on 2D and 3D plots.\n", "\n", "In addition, notice that we've only explored $k=3$. We encourage you to try other values for $k$. Which one do you think best captures the variation in the data?" ] }, { "cell_type": "code", "execution_count": null, "id": "6a9d5310", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Tags", "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.7" } }, "nbformat": 4, "nbformat_minor": 5 }