{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# How HDBSCAN Works\n", "\n", "HDBSCAN is a clustering algorithm developed by [Campello, Moulavi, and Sander](http://link.springer.com/chapter/10.1007%2F978-3-642-37456-2_14). It extends DBSCAN by converting it into a hierarchical clustering algorithm, and then using a technique to extract a flat clustering based in the stability of clusters. The goal of this notebook is to give you an overview of how the algorithm works and the motivations behind it. In contrast to the HDBSCAN paper I'm going to describe it without reference to DBSCAN. Instead I'm going to explain how I like to think about the algorithm, which aligns more closely with [Robust Single Linkage](http://cseweb.ucsd.edu/~dasgupta/papers/tree.pdf) with [flat cluster extraction](http://link.springer.com/article/10.1007%2Fs10618-013-0311-4) on top of it.\n", "\n", "Before we get started we'll load up most of the libraries we'll need in the background, and set up our plotting (because I believe the best way to understand what is going on is to actually see it working in pictures)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ ":0: FutureWarning: IPython widgets are experimental and may change in the future.\n" ] } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "import sklearn.datasets as data\n", "%matplotlib inline\n", "sns.set_context('poster')\n", "sns.set_style('white')\n", "sns.set_color_codes()\n", "plot_kwds = {'alpha' : 0.5, 's' : 80, 'linewidths':0}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The next thing we'll need is some data. To make for an illustrative example we'll need the data size to be fairly small so we can see what is going on. It will also be useful to have several clusters, preferably of different kinds. Fortunately sklearn has facilities for generating sample clustering data so I'll make use of that and make a dataset of one hundred data points." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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/L1y4UDt27FBra6vWr1+vnTt36qtf/ap+9rOfJatLAAAAAOJkC4fD4XR3IlFn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\nCKCnp6fgqcvssTZqc9bTZVM4HA7rnfB6+fnzJ4a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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "moons, _ = data.make_moons(n_samples=50, noise=0.05)\n", "blobs, _ = data.make_blobs(n_samples=50, centers=[(-0.75,2.25), (1.0, 2.0)], cluster_std=0.25)\n", "test_data = np.vstack([moons, blobs])\n", "plt.scatter(test_data.T[0], test_data.T[1], color='b', **plot_kwds)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, the best way to explain HDBSCAN is actually just use it and then go through the steps that occurred along the way teasing out what is happening at each step. So let's load up the [hdbscan library](https://github.com/lmcinnes/hdbscan) and get to work." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import hdbscan" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "HDBSCAN(algorithm='best', alpha=1.0, approx_min_span_tree=True,\n", " gen_min_span_tree=True, leaf_size=40, memory=Memory(cachedir=None),\n", " metric='euclidean', min_cluster_size=5, min_samples=None, p=None)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "clusterer = hdbscan.HDBSCAN(min_cluster_size=5, gen_min_span_tree=True)\n", "clusterer.fit(test_data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So now that we have clustered the data -- what actually happened? We can break it out into a series of steps\n", "\n", "1. Transform the space according to the density/sparsity.\n", "2. Build the minimum spanning tree of the distance weighted graph.\n", "3. Construct a cluster hierarchy of connected components.\n", "4. Condense the cluster hierarchy based on minimum cluster size.\n", "5. Extract the stable clusters from the condensed tree." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Transform the space\n", "\n", "To find clusters we want to find the islands of higher density amid a sea of sparser noise -- and the assumption of noise is important: real data is messy and has outliers, corrupt data, and noise. The core of the clustering algorithm is single linkage clustering, and it can be quite sensitive to noise: a single noise data point in the wrong place can act as a bridge between islands, gluing them together. Obviously we want our algorithm to be robust against noise so we need to find a way to help 'lower the sea level' before running a single linkage algorithm.\n", "\n", "How can we characterize 'sea' and 'land' without doing a clustering? As long as we can get an estimate of density we can consider lower density points as the 'sea'. The goal here is not to perfectly distinguish 'sea' from 'land' -- this is an initial step in clustering, not the ouput -- just to make our clustering core a little more robust to noise. So given an identification of 'sea' we want to lower the sea level. For practical purposes that means making 'sea' points more distant from each other and from the 'land'.\n", "\n", "That's just the intuition however. How does it work in practice? We need a very inexpensive estimate of density, and the simplest is the distance to the *k*th nearest neighbor. If we have the distance matrix for our data (which we will need imminently anyway) we can simply read that off; alternatively if our metric is supported (and dimension is low) this is the sort of query that [kd-trees](http://scikit-learn.org/stable/modules/neighbors.html#k-d-tree) are good for. Let's formalise this and (following the DBSCAN, LOF, and HDBSCAN literature) call it the **core distance** defined for parameter *k* for a point *x* and denote as $\\mathrm{core}_k(x)$. Now we need a way to spread apart points with low density (correspondingly high core distance). The simple way to do this is to define a new distance metric between points which we will call (again following the literature) the **mutual reachability distance**. We define mutual reachability distance as follows:\n", "\n", "
$d_{\\mathrm{mreach-}k}(a,b) = \\max \\{\\mathrm{core}_k(a), \\mathrm{core}_k(b), d(a,b) \\}$
\n", "\n", "where $d(a,b)$ is the original metric distance between *a* and *b*. Under this metric dense points (with low core distance) remain the same distance from each other but sparser points are pushed away to be at least their core distance away from any other point. This effectively 'lowers the sea level' spreading sparse 'sea' points out, while leaving 'land' untouched. The caveat here is that obviously this is dependent upon the choice of *k*; larger *k* values interpret more points as being in the 'sea'. All of this is a little easier to understand with a picture, so let's use a *k* value of five. Then for a given point we can draw a circle for the core distance as the circle that touches the fifth nearest neighbor, like so:\n", "\n", "\"Diagram\n", "\n", "Pick another point and we can do the same thing, this time with a different set of neighbors (one of them even being the first point we picked out).\n", "\n", "\"Diagram\n", "\n", "And we can do that a third time for good measure, with another set of five nearest neighbors and another circle with slightly different radius again.\n", "\n", "\"Diagram\n", "\n", "Now if we want to know the mutual reachabiility distance between the blue and green points we can start by draing in and arrow giving the distance between green and blue:\n", "\n", "\"Diagram\n", "\n", "This passes through the blue circle, but not the green circle -- the core distance for green is larger than the distance between blue and green. Thus we need to mark the mutual reachability distance between blue and green as larger -- equal to the radius of the green circle (easiest to picture if we base one end at the green point).\n", "\n", "\"Diagram\n", "\n", "On the other hand the mutual reachablity distance from red to green is simply distance from red to green since that distance is greater than either core distance (i.e. the distance arrow passes through both circles).\n", "\n", "\"Diagram\n", "\n", "In general there is [underlying theory](http://arxiv.org/pdf/1506.06422v2.pdf) to demonstrate that mutual reachability distance as a transform works well in allowing single linkage clustering to more closely approximate the hierarchy of level sets of whatever true density distribution our points were sampled from." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Build the minimum spanning tree\n", "\n", "Now that we have a new mutual reachability metric on the data we want start finding the islands on dense data. Of course dense areas are relative, and different islands may have different densities. Conceptually what we will do is the following: consider the data as a weighted graph with the data points as vertices and an edge between any two points with weight equal to the mutual reachability distance of those points.\n", "\n", "Now consider a threshold value, starting high, and steadily being lowered. Drop any edges with weight above that threshold. As we drop edges we will start to disconnect the graph into connected components. Eventually we will have a hierarchy of connected components (from completely connected to completely disconnected) at varying threshold levels.\n", "\n", "In practice this is very expensive: there are $n^2$ edges and we don't want to have to run a connected components algorithm that many times. The right thing to do is to find a minimal set of edges such that dropping any edge from the set causes a disconnection of components. But we need more, we need this set to be such that there is no lower weight edge that could connect the components. Fortunately graph theory furnishes us with just such a thing: the minimum spanning tree of the graph.\n", "\n", "We can build the minimum spanning tree very efficiently via [Prim's algorithm](https://en.wikipedia.org/wiki/Prim%27s_algorithm) -- we build the tree one edge at a time, always adding the lowest weight edge that connects the current tree to a vertex not yet in the tree. You can see the tree HDBSCAN constructed below; note that this is the minimum spanning tree for *mutual reachability distance* which is different from the pure distance in the graph. In this case we had a *k* value of 5.\n", "\n", "In the case that the data lives in a metric space we can use even faster methods, such as Dual Tree Boruvka to build the minimal spanning tree." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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c6SMZBbCJj0QxfG5sFEoDl89G09M8/0+vYSVsFiyrIBAIUF1dPeXPsG2beCxJ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\nWE/a61UMP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LerNrC7dQ92s51lxbcM9rTEAJGa49558MEHT3pfXV0dS5cuxWw293lcCY4H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\nxdiwYQMbNmygvr6e9evXZ3qIf/azn/Hss8/S0NBAI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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clusterer.minimum_spanning_tree_.plot(edge_cmap='viridis', \n", " edge_alpha=0.6, \n", " node_size=80, \n", " edge_linewidth=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Build the cluster hierarchy\n", "\n", "Given the minimal spanning tree, the next step is to convert that into the hierarchy of connected components. This is most easily done in the reverse order: sort the edges of the tree by distance (in increasing order) and then iterate through, creating a new merged cluster for each edge. The only difficult part here is to identify the two clusters each edge will join together, but this is easy enough via a [union-find](https://en.wikipedia.org/wiki/Disjoint-set_data_structure) data structure. We can view the result as a dendrogram as we see below:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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v9o+kTFCxBwAAQJVlsVh06tQp1apVS88884zuvPNOJScn65VXXtFvv/2mCRMmFDknIyND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\neyNeZoiPj1dBQYFOnDjhGPvwww9VXl6u3r17m7OIGri8Yr9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4WY+9t+RRl1bsDx06pKNH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\nrkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clusterer.single_linkage_tree_.plot(cmap='viridis', colorbar=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This brings us to the point where robust single linkage stops. We want more though; a cluster hierarchy is good, but we really want a set of flat clusters. We could do that by drawing a a horizontal line through the above diagram and selecting the clusters that it cuts through. This is in practice what [DBSCAN](http://scikit-learn.org/stable/modules/clustering.html#dbscan) effectively does (declaring any singleton clusters at the cut level as noise). The question is, how do we know where to draw that line? DBSCAN simply leaves that as a (very unintuitive) parameter. Worse, we really want to deal with variable density clusters and any choice of cut line is a choice of mutual reachability distance to cut at, and hence a single fixed density level. Ideally we want to be able to cut the tree at different places to select our clusters. This is where the next steps of HDBSCAN begin and create the difference from robust single linkage." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Condense the cluster tree\n", "\n", "The first step in cluster extraction is condensing down the large and complicated cluster hierarchy into a smaller tree with a little more data attached to each node. As you can see in the hierarchy above it is often the case that a cluster split is one or two points splitting off from a cluster; and that is the key point -- rather than seeing it as a cluster splitting into two new clusters we want to view it as a single persistent cluster that is 'losing points'. To make this concrete we need a notion of **minimum cluster size** which we take as a parameter to HDBSCAN. Once we have a value for minimum cluster size we can now walk through the hierarchy and at each split ask if one of the new clusters created by the split has fewer points than the minimum cluster size. If it is the case that we have fewer points than the minimum cluster size we declare it to be 'points falling out of a cluster' and have the larger cluster retain the cluster identity of the parent, marking down which points 'fell out of the cluster' and at what distance value that happened. If on the other hand the split is into two clusters each at least as large as the minimum cluster size then we consider that a true cluster split and let that split persist in the tree. After walking through the whole hierarchy and doing this we end up with a much smaller tree with a small number of nodes, each of which has data about how the size of the cluster at that node descreases over varying distance. We can visualize this as a dendrogram similar to the one above -- again we can have the width of the line represent the number of points in the cluster. This time, however, that width varies over the length of the line as points fall our of the cluster. For our data using a minimum cluster size of 5 the result looks like this:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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jxuiOO+4o0fdyOop2AAAABMXKHVFlGgFPat+/f782btyo7Oxsn/Pp6emSpE8/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\nqFGWP8PWkY8AAAAAzo9OOwAAAILDmvZ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clusterer.condensed_tree_.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is much easier to look at and deal with, particularly in as simple a clustering problem as our current test dataset. However we still need to pick out clusters to use as a flat clustering. Looking at the plot above should give you some ideas about how one might go about doing this." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Extract the clusters\n", "\n", "Intuitively we want the choose clusters that persist and have a longer lifetime; short lived clusters are ultimately probably merely artifcacts of the single linkage approach. Looking at the previous plot we could say that we want to choose those clusters that have the greatest area of ink in the plot. To make a flat clustering we will need to add a further requirement that, if you select a cluster, then you cannot select any cluster that is a descendant of it. And in fact that intuitive notion of what should be done is exactly what HDBSCAN does. Of course we need to formalise things to make it a concrete algorithm.\n", "\n", "First we need a different measure than distance to consider the persistence of clusters; instead we will use $\\lambda = \\frac{1}{\\mathrm{distance}}$. For a given cluster we can then define values $\\lambda_{\\mathrm{birth}}$ and $\\lambda_{\\mathrm{death}}$ to be the lambda value when the cluster split off and became it's own cluster, and the lambda value (if any) when the cluster split into smaller clusters respectively. In turn, for a given cluster, for each point *p* in that cluster we can define the value $\\lambda_p$ as the lambda value at which that point 'fell out of the cluster' which is a value somewhere between $\\lambda_{\\mathrm{birth}}$ and $\\lambda_{\\mathrm{death}}$ since the point either falls out of the cluster at some point in the cluster's lifetime, or leaves the cluster when the cluster splits into two smaller clusters. Now, for each cluster compute the **stability** to as\n", "\n", "$\\sum_{p \\in \\mathrm{cluster}} (\\lambda_p - \\lambda_{\\mathrm{birth}})$.\n", "\n", "Declare all leaf nodes to be selected clusters. Now work up through the tree (the reverse topological sort order). If the sum of the stabilities of the child clusters is greater than the stability of the cluster then we set the cluster stability to be the sum of the child stabilities. If, on the other hand, the cluster's stability is greater than the su of it's children then we declare the cluster to be a selected cluster, and unselect all its descendants. Once we reach the root node we call the current set of selected clusters our flat clsutering and return that.\n", "\n", "Okay, that was wordy and complicated, but it really is simply performing our 'select the clusters in the plot with the largest total ink area' subject to descendant constraints that we explained earlier. We can select the clusters in the condensed tree dendrogram via this algorithm, and you get what you expect:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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rsd6n8nz2n7si1ffx3+GSY3B73SF5o0DNJ3u9ODh/AYq+2gDBYkHG2N+gzeib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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clusterer.condensed_tree_.plot(select_clusters=True, selection_palette=sns.color_palette())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have the clusters it is a simple enough matter to turn that into cluster labelling as per the sklearn API. Any point not in a selected cluster is simply a noise point (and assigned the label -1). We can do a little more though: for each cluster we have the $\\lambda_p$ for each point *p* in that cluster; If we simply normalize those values (so they range from zero to one) then we have a measure of the strength of cluster membership for each point in the cluster. The hdbscan library returns this as a `probabilities_` attribute of the clusterer object. Thus, with labels and membership strengths in hand we can make the standard plot, choosing a color for points based on cluster label, and desaturating that color according the strength of membership (and make unclustered points pure gray)." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Qvab8EzKDVq/qZxJR4xOl0n+CBXntbS2bjscxffIUUGByZyYew9TJU9UvioiW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\nOtTar54hty7fXLVixhSQqkgcAAARBYIhdfZPyuMNKifbpqqSnITeeB0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "palette = sns.color_palette()\n", "cluster_colors = [sns.desaturate(palette[col], sat) \n", " if col >= 0 else (0.5, 0.5, 0.5) for col, sat in \n", " zip(clusterer.labels_, clusterer.probabilities_)]\n", "plt.scatter(test_data.T[0], test_data.T[1], c=cluster_colors, **plot_kwds)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And that is how HDBSCAN works. It may seem somewhat complicated -- there are a fair number of moving parts to the algorithm -- but ultimately each part is actually very straightforward and can be optimized well. Hopefully with a better understanding both of the intuitions and some of the implementation details of HDBSCAN you will feel motivated to [try it out](https://github.com/lmcinnes/hdbscan). The library continues to develop, and will provide a base for new ideas including a near parameterless Persistent Density Clustering algorithm, and a new semi-supervised clustering algorithm." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.11" } }, "nbformat": 4, "nbformat_minor": 0 }