diff --git a/machine_learning/Max-cut_2+_divisive_clustering.ipynb b/machine_learning/Max-cut_2+_divisive_clustering.ipynb new file mode 100644 index 0000000..600e1d6 --- /dev/null +++ b/machine_learning/Max-cut_2+_divisive_clustering.ipynb @@ -0,0 +1,702 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Unsupervised Quantum Learning with Max-cut: 2+ Clusters\n", + "\n", + "This notebook is an example of unsupervised machine learning on a quantum computer. The data used are from the iris dataset.\n", + "\n", + "In the [previous notebook](https://github.com/ajrazander/Unsupervised-QML/blob/master/Max-cut.ipynb), the max-cut problem was solved using QAOA which theoretically gives a quantum speed up to unsupervised learning. Solving the max-cut problem is a binary classifier though. So, if the data are more naturally separated into three or more groups, we're sunk! ... or are we?\n", + "\n", + "## Quantum Divisive Hierarchical Clustering\n", + "\n", + "One solution is to apply a divisive (\"top-down\") [hierarchial clustering](https://en.wikipedia.org/wiki/Hierarchical_clustering) scheme. This scheme starts with the whole dataset (the top). Using a binary classifier (like QAOA solving max-cut), the data is split into two child clusters. We then use the binary classifier to break each child cluster in two--resulting in four clusters. We continue this recursive application of the binary classifier on each child cluster until all data points sit in their own cluster (the bottom). For QAOA solving max-cut, a divisive hierarchical clustering algorithm would execute as follows: (0) solve the max-cut problem on the entire dataset resulting in two child clusters, (1) solve the max-cut problem on each child cluster, (2) repeat (1) until nearly every data point is in an individual cluster.\n", + "\n", + "You may be wondering, how would having every data point in its own cluster be useful? Answer: it isn't. But! Stopping before that point is very useful. Let's say our intuition tells us the data of interest has a few clusters. We can cleverly pick a stopping point **before** the every-data-point-is-its-own-cluster level. Ideally, the algorithm will stop at just a few clusters. We'd need some stop criteria that tells us the data is separated enough. Including the stop criteria modifies the divisive hierarchical clustering algorithm to: (0) solve the max-cut problem on the entire dataset resulting in two child clusters, (1) solve the max-cut problem on each child cluster, (2) repeat (1) until nearly every data point is in an individual cluster, (3) post-process the resulting tree of clusters according to the stop criteria.\n", + "\n", + "Let's get to it!" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "from numba import jit\n", + "from sklearn.datasets import load_iris\n", + "\n", + "import seaborn as sns\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "# Packages needs to access an IBM quantum computer. Not necessary for simulator.\n", + "# from qiskit import IBMQ\n", + "# IBMQ.load_account() # Load account from disk\n", + "\n", + "# Quantum Computing packages\n", + "from qiskit import BasicAer\n", + "from qiskit.aqua import QuantumInstance\n", + "from qiskit.aqua.algorithms import QAOA\n", + "from qiskit.aqua.translators.ising import max_cut\n", + "from qiskit.aqua.components.optimizers import COBYLA" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "number of data points: 150\n" + ] + } + ], + "source": [ + "# Import Iris dataset\n", + "iris_data = load_iris()\n", + "df = pd.DataFrame(iris_data.data, columns=iris_data.feature_names)\n", + "df['species'] = pd.Categorical.from_codes(iris_data.target, iris_data.target_names).astype(str)\n", + "print('number of data points:', len(df))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The iris dataset contains 150 data points. As in the previous notebook, we'll need to chop this down to ~12 points for a reasonable execution time. Different from the previous notebook, we'll keep all three species! " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Generate subset of data with fewer data points\n", + "df_sub = df.iloc[::13,:].reset_index(drop=True)\n", + "\n", + "# View data\n", + "sns.pairplot(data=df_sub, hue=\"species\", palette=\"husl\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# Remove species labels (otherwise it's not unsupervised learning!)\n", + "df_sub_wo_labels = df_sub.loc[:,['sepal length (cm)','sepal width (cm)','petal length (cm)','petal width (cm)']]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now that the data is all squared away, let's solve the max-cut problem with QAOA just as we did in the [previous notebook](https://github.com/ajrazander/Unsupervised-QML/blob/master/Max-cut.ipynb). This time, we want to solve the max-cut problem on each resulting child cluster as well. To do this, we will track how the data is cut each iteration and solve the max-cut problem on each resulting child cluster.\n", + "\n", + "Each division of the dataset into child clusters can be thought of as generating new leaf nodes on a binary tree. The root node is the whole dataset. The root node's two child nodes each contain roughly half of the dataset (assuming balanced data). Their child nodes contain roughly one quarter of the dataset and so on. Since the end case in the divisive hierarchical scheme has all $n$ data points in their own clusters, there must be $n$ leaf nodes. For a well balanced binary tree, that leaves (no pun intended) the height $h=\\log_2{\\left(n+1\\right)}$. For our situation this means at least $h$ iterations need to be completed.\n", + "\n", + "Let's put these pieces together. First we'll need to define a function that computes the $l^2\\text{-norm}$ as done in the previous notebook." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# Helper function for iterative QAOA solving\n", + "\n", + "# Computes pairwise L2-norms (@jit gives ~x10 speed up on my laptop)\n", + "@jit(nopython=True)\n", + "def calc_w(data_array):\n", + " n_instances = data_array.shape[0]\n", + " w = np.zeros((n_instances, n_instances))\n", + " for i in range(0, n_instances):\n", + " for j in range(0, n_instances):\n", + " w[i, j] = np.linalg.norm(data_array[i] - data_array[j])\n", + " return w" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we do the heavy lifting. The max-cut problem is solved recursively over the child clusters a total of $h$ times. Much of the code will be familiar to you from the previous notebook. The for loops and if statements are the only new machinery. They track the recursive component of the hierarchical scheme." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Iteration 1 of 3 completed\n", + "Iteration 2 of 3 completed\n", + "Iteration 3 of 3 completed\n" + ] + } + ], + "source": [ + "# THIS MAY TAKE SEVERAL MINUTES\n", + "\n", + "# Compute minimum number of iterations (i.e. height of a balanced binary tree)\n", + "h = int(np.log2(len(df_sub_wo_labels) + 1))\n", + "\n", + "# Copy df_sub_wo_labels so future manipulations don't affect df_sub_wo_labels\n", + "data = df_sub_wo_labels.copy()\n", + "\n", + "# QAOA hyperparameters and backend initialization\n", + "p = 1 # Number of adiabatic steps must be > 0\n", + "optimizer = COBYLA() # Classical optimizer\n", + "backend = BasicAer.get_backend('statevector_simulator') # Simulate on local machine\n", + "\n", + "# provider = IBMQ.get_provider(group='open') # Load provider to access IBM's cloud services\n", + "# backend = provider.get_backend('ibmq_essex') # Compute on one of IBM's quantum computer\n", + "\n", + "quantum_instance = QuantumInstance(backend, shots=1, skip_qobj_validation=False)\n", + "\n", + "# Iterate over height of dataset tree\n", + "for i in range(0, h):\n", + "\n", + " # Initialize label and cut weight columns to later store QAOA output\n", + " data.loc[:, 'clusters_iter_' + str(i)] = np.nan\n", + " data.loc[:, 'cuts_iter_' + str(i)] = np.nan\n", + " \n", + " # Select data from the previous child clusters\n", + " dfs = []\n", + " if i > 0:\n", + " cluster_range = data.loc[:, 'clusters_iter_' + str(i - 1)].unique()\n", + " for j in cluster_range:\n", + " df_cluster = data.loc[data['clusters_iter_' + str(i - 1)] == j, data.columns[:4]]\n", + " # if df_cluster length is 1 then it can't be further cut, so only consider lengths > 1\n", + " if len(df_cluster.index) > 1:\n", + " dfs.append(df_cluster)\n", + " else:\n", + " dfs.append(data[data.columns[:4]])\n", + "\n", + " # Solve max-cut with QAOA on each child cluster\n", + " for j, df_part in enumerate(dfs):\n", + " \n", + " # Calculate pairwise distances between points\n", + " w = calc_w(df_part.values)\n", + " \n", + " # Initialize QAOA and execute\n", + " qubit_ops, offset = max_cut.get_max_cut_qubitops(w)\n", + " qaoa = QAOA(qubit_ops, optimizer, p)\n", + " result = qaoa.run(quantum_instance)\n", + "\n", + " # Extract results\n", + " x = max_cut.sample_most_likely(result['eigvecs'][0])\n", + "\n", + " # Store cluster results (label and weight). Labels must be unqiue each iteration hence + 2*j\n", + " df_part.loc[:, 'clusters_iter_' + str(i)] = max_cut.get_graph_solution(x) + 2 * j\n", + " df_part.loc[:, 'cuts_iter_' + str(i)] = max_cut.max_cut_value(x, w)\n", + " \n", + " # Update data with new results\n", + " data.update(df_part)\n", + "\n", + " print('Iteration', i+1, 'of', h, 'completed') # Show execute status" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once the results are in, let's take a look at how the clustering compares to the known species labeling." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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sepal length (cm)sepal width (cm)petal length (cm)petal width (cm)speciesclusters_iter_0cuts_iter_0clusters_iter_1cuts_iter_1clusters_iter_2cuts_iter_2
05.13.51.40.2setosa0.0150.4608270.02.9748610.00.561177
14.33.01.10.1setosa0.0150.4608271.02.974861NaNNaN
25.03.41.60.4setosa0.0150.4608270.02.9748611.00.561177
35.13.41.50.2setosa0.0150.4608270.02.9748610.00.561177
46.93.14.91.5versicolor1.0150.4608273.030.8576433.03.252945
56.73.14.41.4versicolor1.0150.4608273.030.8576433.03.252945
66.02.94.51.5versicolor1.0150.4608273.030.8576432.03.252945
76.13.04.61.4versicolor1.0150.4608273.030.8576432.03.252945
86.53.05.82.2virginica1.0150.4608272.030.8576435.04.912491
97.73.86.72.2virginica1.0150.4608272.030.8576434.04.912491
107.42.86.11.9virginica1.0150.4608272.030.8576434.04.912491
116.83.25.92.3virginica1.0150.4608272.030.8576435.04.912491
\n", + "
" + ], + "text/plain": [ + " sepal length (cm) sepal width (cm) petal length (cm) petal width (cm) \\\n", + "0 5.1 3.5 1.4 0.2 \n", + "1 4.3 3.0 1.1 0.1 \n", + "2 5.0 3.4 1.6 0.4 \n", + "3 5.1 3.4 1.5 0.2 \n", + "4 6.9 3.1 4.9 1.5 \n", + "5 6.7 3.1 4.4 1.4 \n", + "6 6.0 2.9 4.5 1.5 \n", + "7 6.1 3.0 4.6 1.4 \n", + "8 6.5 3.0 5.8 2.2 \n", + "9 7.7 3.8 6.7 2.2 \n", + "10 7.4 2.8 6.1 1.9 \n", + "11 6.8 3.2 5.9 2.3 \n", + "\n", + " species clusters_iter_0 cuts_iter_0 clusters_iter_1 cuts_iter_1 \\\n", + "0 setosa 0.0 150.460827 0.0 2.974861 \n", + "1 setosa 0.0 150.460827 1.0 2.974861 \n", + "2 setosa 0.0 150.460827 0.0 2.974861 \n", + "3 setosa 0.0 150.460827 0.0 2.974861 \n", + "4 versicolor 1.0 150.460827 3.0 30.857643 \n", + "5 versicolor 1.0 150.460827 3.0 30.857643 \n", + "6 versicolor 1.0 150.460827 3.0 30.857643 \n", + "7 versicolor 1.0 150.460827 3.0 30.857643 \n", + "8 virginica 1.0 150.460827 2.0 30.857643 \n", + "9 virginica 1.0 150.460827 2.0 30.857643 \n", + "10 virginica 1.0 150.460827 2.0 30.857643 \n", + "11 virginica 1.0 150.460827 2.0 30.857643 \n", + "\n", + " clusters_iter_2 cuts_iter_2 \n", + "0 0.0 0.561177 \n", + "1 NaN NaN \n", + "2 1.0 0.561177 \n", + "3 0.0 0.561177 \n", + "4 3.0 3.252945 \n", + "5 3.0 3.252945 \n", + "6 2.0 3.252945 \n", + "7 2.0 3.252945 \n", + "8 5.0 4.912491 \n", + "9 4.0 4.912491 \n", + "10 4.0 4.912491 \n", + "11 5.0 4.912491 " + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Include results from QAOA in df_sub dataframe for comparison to species label\n", + "for i in range(0, h):\n", + " df_sub.loc[:, 'clusters_iter_' + str(i)] = data.loc[:, 'clusters_iter_' + str(i)]\n", + " df_sub.loc[:, 'cuts_iter_' + str(i)] = data.loc[:, 'cuts_iter_' + str(i)]\n", + "df_sub" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Under the \"cluster_2\" column, we see the clustering is not at all similar to the species labeling. This is because each data point is nearly in its own cluster. Let's assume we don't already know how the data should cluster, but we do have an educated guess that there is some \"best\" number of clusters less than the number of data points. As discussed in the introduction, we need to introduce some stop criteria. Let's first take a lesson from k-means.\n", + "\n", + "## Stop Criteria Part 1: the elbow rule\n", + "\n", + "To find the best clustering, we first follow the elbow rule just like in k-means." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Plot max-cut weights vs number of clusters created\n", + "cluster_num = [] # initialize x-axis array\n", + "cuts = [] # initialize y-axis array\n", + "\n", + "# Extract max-cut weights and associated number of clusters from results in df_sub\n", + "for i in range(0, h):\n", + " # Collect max-cut weights\n", + " cuts += list(df_sub['cuts_iter_'+str(i)].unique())\n", + " # Number how many clusters have been made for this cut\n", + " cut_off = 2**i\n", + " for j in range(0, cut_off):\n", + " cluster_num.append(i+2)\n", + "\n", + "plt.scatter(cluster_num, cuts)\n", + "plt.xlabel('Number of clusters')\n", + "plt.ylabel('Max cut weight')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see from the plot, the elbow is at three clusters. However, which of the two possible 3 cluster configurations do we choose? Answer: the one with the higher cut weight. The higher cut weight indicates a more separated graph--exactly what we want.\n", + "\n", + "In summary, we followed the elbow rule and found we should stop at the max-cut with a weight of ~30. To get to this cut, we need to traverse the tree of max-cuts until we get to it. Let's dive in.\n", + "\n", + "## Stop Criteria Part 2: depth-first-search\n", + "\n", + "The task of finding the stopping point is best recast as a depth-first-search where the tree being searched is made from all the computed cut weights. Starting at the root node (150.5 when I ran it on my machine), we traverse down the tree to leaves with the **highest** cut weights. Along the way we \"keep\" those cuts we've encountered until there are as many clusters as the elbow rule advises.\n", + "\n", + "Let's visualize with a graph" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "from networkx.drawing.nx_agraph import graphviz_layout\n", + "\n", + "# Initialize graph\n", + "G = nx.DiGraph()\n", + "\n", + "# Set root node as weight of the very first cut; in this case 150.5\n", + "G.add_node(\"{:.1f}\".format(cuts[0]))\n", + "\n", + "# Add the remaining cut weights to the tree\n", + "for cut in cuts[1:]:\n", + " if np.isnan(cut): # ignore nan cut weights\n", + " continue\n", + " G.add_node(\"{:.1f}\".format(cut))\n", + "\n", + "# Add edges from parent to child clusters\n", + "for i in range(int(np.log2(len(cuts)+1))):\n", + " G.add_edge(\"{:.1f}\".format(cuts[i]), \"{:.1f}\".format(cuts[2*i+1]))\n", + " G.add_edge(\"{:.1f}\".format(cuts[i]), \"{:.1f}\".format(cuts[2*i+2]))\n", + "\n", + "# Plot graph\n", + "plt.title('Max-cut weights')\n", + "pos = graphviz_layout(G, prog='dot')\n", + "nx.draw(G, pos, with_labels=True, font_weight='bold', node_size=2000)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Following the stop criteria rules, we transverse the tree starting at the root node 150.5 when I ran this code. Since $30.9 > 3.0$, we move to 30.9 and keep that cut. At this point, the two cuts 150.5 and 30.9 generate 3 clusters labeled 0.0, 2.0, and 3.0. Since the elbow rule tells us to stop at 3 clusters, we stop here and we're done! Let's see how the stop criteria does by comparing these 3 clusters to the original species labeling." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# maximum number of clusters as given by the elbow rule\n", + "max_clusters = 3\n", + "\n", + "# Initialize final clustering column\n", + "df_sub.loc[:, 'final'] = np.nan\n", + "\n", + "# Extract clustering based on the stop criteria\n", + "for (cluster, cut_weight) in zip(df_sub[df_sub.columns[5::2]],df_sub[df_sub.columns[6::2]]):\n", + " # Find the maximum cut for this particular column of data\n", + " maxim = df_sub[cut_weight].max()\n", + " df_sub['final'].update(df_sub[cluster][df_sub[cut_weight] == maxim])\n", + " if len(df_sub['final'].unique()) >= max_clusters: # stop including clusters once the number of clusters reaches the elbow rule limit\n", + " break\n", + "\n", + "# Constrain data to final clustering assignments\n", + "df_sub_plot = df_sub[['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)', 'final']]\n", + "\n", + "# Visualize clustering\n", + "sns.pairplot(data=df_sub_plot, hue='final', palette=\"husl\", vars=df_sub.columns[:4])\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The plots look identical to the reduced dataset! Setosa is all in cluster 0; versicolor is all in cluster 2; and virginica is all in cluster 3. The divisive hierarchical quantum clustering did a great job!\n", + "\n", + "This technique uses the same quantum algorithm as the last notebook. The advantage presented here is simply in how we use the quantum algorithm. By post-processing the results in a divisive hierarchical way, we can build more complex unsupervised learning models while leveraging quantum speedup on [NISQ](https://arxiv.org/abs/1801.00862) devices.\n", + "\n", + "### Your turn\n", + "A great way to learn is to get your hands dirty. Mess around with this notebook and see what happens! Here are some questions to inspire your play:\n", + "* What happens if I create data for a **fourth species**?\n", + "* How could this scheme (or an adaptation) allow for larger datasets?\n", + "* How do these results change when I execute on a real quantum computer?\n", + "* What happens if I change the number of adiabatic steps (p) in the QAOA hyperparameters?\n", + "* What if I use VQE instead of QAOA to find the ground state of the cost Hamiltonian?" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.6.4" + }, + "notify_time": "30" + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/machine_learning/Max-cut_vs_k-means.ipynb b/machine_learning/Max-cut_vs_k-means.ipynb new file mode 100644 index 0000000..2f74aed --- /dev/null +++ b/machine_learning/Max-cut_vs_k-means.ipynb @@ -0,0 +1,399 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Unsupervised Quantum Learning with Max-cut\n", + "\n", + "This notebook is an example of unsupervised machine learning on a quantum computer. Both classical and quantum algorithms are used in classifying the iris dataset.\n", + "\n", + "First, we'll warm up on the classical k-means clustering algorithm. Hopefully, this quick review will refresh you on unsupervised learning. Next, we go quantum. The data are mapped to a graph; the [max-cut problem](https://en.wikipedia.org/wiki/Maximum_cut) is mapped to an Ising Hamiltonian; and QAOA solves for the ground state. If you want more details for each step check out this [kaggle tutorial](https://www.kaggle.com/efeergun96/unsupervised-learning-on-iris) on k-means, this [qiskit tutorial](https://github.com/qiskit-community/qiskit-qcgpu-provider/blob/master/examples/aqua/Max-Cut.ipynb) on max-cut, or the paper [*Unsupervised Machine Learning on a Hybrid Quantum Computer*](https://arxiv.org/abs/1712.05771) on going quantum. There are plenty of other resource out there, but these are the ones I've found useful.\n", + "\n", + "As usual, we import packages and take a peak at the data we'll be playing with." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "from sklearn.cluster import KMeans\n", + "from sklearn.datasets import load_iris\n", + "\n", + "import seaborn as sns\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Import Iris dataset\n", + "iris_data = load_iris()\n", + "df = pd.DataFrame(iris_data.data, columns=iris_data.feature_names)\n", + "df['species'] = pd.Categorical.from_codes(iris_data.target, iris_data.target_names).astype(str)\n", + "\n", + "# View data with known labels as a control to compare future clustering done by k-means and QAOA\n", + "sns.pairplot(data=df, hue=\"species\", palette=\"husl\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "At a glance, it looks like there are ~100+ data points grouped into three species with versicolor and virginica much closer to each other.\n", + "\n", + "Since the quantum computer will be simulated on laptops and not supercomputers, **let's reduce the dataset** to ~12 for a reasonable run time. Though the details haven't been explained yet, max-cut can only split data into two clusters. (More on that later.) For now, we'll need remove one of the species. To be nice to the quantum computer, let's remove virginica. If it can't cluster setosa and versicolor, we know quantum computers are really in trouble. If it can... well, maybe they really do have a shot at unsupervised learning." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Generate subset of data with fewer data points\n", + "df_sub = df.iloc[::9,:].reset_index(drop=True)\n", + "\n", + "# Constrain data to 2 species\n", + "df_sub = df_sub.loc[(df_sub['species'] == 'setosa') | (df_sub['species'] == 'versicolor')]\n", + "\n", + "# View data with known labels as a control to compare future clustering done by k-means and QAOA\n", + "sns.pairplot(data=df_sub, hue=\"species\", palette=\"husl\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Some dimensions of the feature space show the setosa and versicolor distributions quite close (e.g. sepal width vs. sepal length), while others have them separated (e.g. petal length vs. petal width). Those close features will make it harder to cluster, but with the more separated features, there's definitely room for accurate clustering. Let's see how k-means handles this.\n", + "\n", + "## A Classical Approach\n", + "K-means groups data into k clusters by minimizing each cluster's sum-of-squares also known as inertia\n", + "\n", + "$$\n", + "\\sum_{i=0}^{n} \\min_{\\mu_j \\in C}(\\lvert\\lvert x_i - \\mu_j\\rvert\\rvert^2)\n", + "$$\n", + "\n", + "where $\\mu_j$ is the mean of the jth cluster within the set $C$ of clusters.\n", + "(See scikit-learn's [clustering user guide](https://scikit-learn.org/stable/modules/clustering.html#k-means) for more details.) The optimal number of clusters $k$ is known for this data ($k=2$) since the reduced dataset only contains two species. However, let's pretend that's unknown as that would be the case for a real unsupervised learning application. We can use the [elbow rule](https://en.wikipedia.org/wiki/Elbow_method_(clustering)) to find our \"unknown\" optimal $k$." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Remove species labels (otherwise it's not unsupervised learning!)\n", + "df_sub_wo_labels = df_sub.loc[:,['sepal length (cm)','sepal width (cm)','petal length (cm)','petal width (cm)']]\n", + "\n", + "# Elbow rule: compute inertia for difference k's\n", + "inertia = []\n", + "K = range(1, len(df_sub_wo_labels))\n", + "for k in K:\n", + " kmeans = KMeans(n_clusters=k, random_state=0).fit(df_sub_wo_labels)\n", + " inertia.append(kmeans.inertia_)\n", + "\n", + "# Visualize elbow rule\n", + "plt.plot(K, inertia)\n", + "plt.xlabel('Number of clusters')\n", + "plt.ylabel('Sum of squares distances about centroids')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Two is obviously the most \"elbowy\" and thus the optimal $k$. Let's fit and visualize the k-means algorithm with the optimal $k = 2$." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Use optimal k for final k-means model\n", + "optimal_k = 2\n", + "kmeans = KMeans(n_clusters=optimal_k, random_state=0).fit(df_sub_wo_labels)\n", + "\n", + "# Add k-means labeling to dataframe for later comparison\n", + "df_sub['label'] = kmeans.labels_\n", + "\n", + "# Visualize clustering done by k-means algorithm\n", + "sns.pairplot(data=df_sub, hue='label', palette=\"husl\", vars=df_sub.columns[:-2])\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The plots looks identical to the reduced dataset plot! Yay! With $k = 2$, the k-means algorithm clustering did a fantastic job on the iris dataset! The elbow rule really pulled through. Let's see how the quantum computer fares.\n", + "\n", + "## A Quantum Approach\n", + "\n", + "One approach to unsupervised quantum machine learning is to map the problem to a graph optimization problem (specifically max-cut in this notebook). The graph optimization problem can then be mapped to a cost Hamiltonian which can be efficiently solved by a quantum computer. (Cost Hamiltonians are the quantum computer version of cost functions.)\n", + "\n", + "### Make a Graph\n", + "\n", + "The first step is to map the data to a graph by calculating the pairwise \"distances\" between each data point. These distances will weight the edges of the graph. Let's use the $l^2\\text{-norm}$ (i.e. vector magnitude). Remember, we're using a subset of the iris dataset to facilitate faster computation. " + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "ExecuteTime": { + "end_time": "2018-11-19T20:10:21.407379Z", + "start_time": "2018-11-19T20:10:21.393951Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Weight matrix size: (12, 12)\n" + ] + } + ], + "source": [ + "# Get number of data entries\n", + "n_instances = len(df_sub_wo_labels)\n", + "\n", + "# Convert dataframe into array\n", + "data_array = df_sub_wo_labels.values\n", + "\n", + "# Calculate pairwise L2-norms (better performance for larger datasets can be acheived by using numba)\n", + "w = np.zeros((n_instances, n_instances))\n", + "for i in range(0, n_instances):\n", + " for j in range(0, n_instances):\n", + " w[i, j] = np.linalg.norm(data_array[i] - data_array[j])\n", + "\n", + "print('Weight matrix size:', w.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Cast Max-cut as a Cost Hamiltonian\n", + "\n", + "To separate the graph into clusters, the graph is cut with a [max-cut](https://en.wikipedia.org/wiki/Maximum_cut): meaning the graph is separated in two while maximizing the total weight of the 'cut' edges. This is an NP-hard problem. However, it maps to an Ising model, which can be solved efficiently on a quantum computer! By efficiently, I mean it can solve the max-cut problem **FASTER** than a classical computer (theoretically speaking). **That is why this method is so interesting and important.** Though, it's been [proposed](https://www.nature.com/articles/s41598-019-43176-9) this won't actually be the case until there are quantum computers with hundreds of qubits.\n", + "\n", + "Let's max-cut!\n", + "\n", + "The cost of one cut between nodes $i$ and $j$ is the edge's weight $w_{ij}$ that lies between them. In separating the graph into two sets of nodes ($S_1$ for cluster 1 and $S_2$ for cluster 2), the total weight of a cut $\\delta(S)$ is\n", + "\n", + "$$\n", + "w(\\delta(S)) = \\sum_{i\\in S_1, j\\in S_2} w_{ij}.\n", + "$$\n", + "\n", + "Assuming a fully connected graph and accounting for the symmetry of $w_{ij}$ (i.e. $w_{ij} = w_{ji}$), the sum can be expanded to\n", + "$$\n", + "\\begin{align}\n", + "w(\\delta(S)) & = \\frac{1}{2}\\sum_{(ij) \\in \\delta(S_1)} w_{ij} \\\\\n", + "& = \\frac{1}{4}\\sum_{ij} w_{ij} - \\frac{1}{4} \\sum_{ij} w_{ij} \\hat{\\sigma}_i^z \\hat{\\sigma}_j^z \\\\\n", + "& = \\frac{1}{4}\\sum_{ij} w_{ij} (1- \\hat{\\sigma}_i^z \\hat{\\sigma}_j^z).\n", + "\\end{align}\n", + "$$ \n", + "\n", + "We can explicitly see it's connection to the Ising Hamiltonian (external field $h = 0$ and irrelevant constant $C$)\n", + "\n", + "$$\n", + "H_{ising} = -\\sum_{ij}J_{ij}\\hat{\\sigma}_i^z\\hat{\\sigma}_j^z + C\n", + "$$\n", + "\n", + "where $J_{ij} = \\frac{w_{ij}}{4}$. We interpret the output of the Ising model as follows. The spin variables $\\hat{\\sigma}_i^z \\in \\{-1, +1\\}$ take on the value $\\hat{\\sigma}_i^z = +1$ for data in cluster 0, and $\\hat{\\sigma}_i^z = -1$ for data in cluster 1. To solve the optimization problem, the quantum computer finds the ground state of $H_{ising}$ and we're done! There are a variety of algorithms that can find the ground state of a cost Hamiltonian. In this notebook, we will use QAOA.\n", + "\n", + "Side note: The Ising model is conventionally written as a sum over all **nearest neighbor** pairs $\\sum_{}$. Since the graph is fully connected (or can be made fully connected by adding edges of weight zero), $\\sum_{}$ is identical to the double sum $\\sum_{ij}$.\n", + "\n", + "The ideas and derivation presented here are directly found in the paper [*Unsupervised Machine Learning on a Hybrid Quantum Computer*](https://arxiv.org/abs/1712.05771).\n", + "\n", + "### Solve the Max-cut Problem with QAOA\n", + "\n", + "[QAOA](https://arxiv.org/abs/1411.4028) is a quantum optimizer that will adiabatically find the ground state of a cost Hamiltonian--exactly what we need! Thankfully, [qiskit](https://qiskit.org) has a QAOA function all ready for us to use! Let's import the packages, initialize the QAOA algorithm with the weights $w$ we previously calculated and run it!!" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# Packages needs to access an IBM quantum computer. Not necessary for simulator.\n", + "# from qiskit import IBMQ\n", + "# IBMQ.load_account() # Load account from disk\n", + "\n", + "# Quantum Computing packages\n", + "from qiskit import BasicAer\n", + "from qiskit.aqua import QuantumInstance\n", + "from qiskit.aqua.algorithms import QAOA\n", + "from qiskit.aqua.translators.ising import max_cut\n", + "from qiskit.aqua.components.optimizers import COBYLA" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "# QAOA hyperparameters and initialization\n", + "p = 1 # Number of adiabatic steps must be > 0\n", + "optimizer = COBYLA() # Classical optimizer\n", + "qubit_ops, offset = max_cut.get_max_cut_qubitops(w) # Compute qubit operations for QAOA algo\n", + "qaoa = QAOA(qubit_ops, optimizer, p) # initialize QAOA algorithm\n", + "\n", + "# Initialize quantum simulator\n", + "backend = BasicAer.get_backend('statevector_simulator') # Simulate on local machine\n", + "\n", + "# Initialize quantum computer\n", + "# provider = IBMQ.get_provider(group='open') # Load provider to access IBM's cloud services\n", + "# backend = provider.get_backend('ibmq_essex') # Compute on one of IBM's quantum computer\n", + "\n", + "quantum_instance = QuantumInstance(backend, shots=1)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Execute QAOA on quantum simulator (or real device)\n", + "result = qaoa.run(quantum_instance)\n", + "\n", + "# Extract results\n", + "x = max_cut.sample_most_likely(result['eigvecs'][0])\n", + "\n", + "# Extract cluster labels and include them in df_sub\n", + "labels = pd.DataFrame(max_cut.get_graph_solution(x), columns=['label'])\n", + "df_sub['label'] = labels\n", + "\n", + "# Show data by cluster\n", + "sns.pairplot(data=df_sub,hue='label', palette=\"husl\", vars=df_sub.columns[:-2])\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The plots look identical to the reduced dataset! All of setosa is in cluster 0, and all of versicolor is in cluster 1. For this simple example of solving max-cut with QAOA, the results look spectacular!\n", + "\n", + "### Your turn\n", + "A great way to learn is to get your hands dirty. Mess around with this notebook and see what happens! Here are some questions to inspire your play:\n", + "* How do these results change when I execute on a real quantum computer?\n", + "* What happens if I filter out fewer data points?\n", + "* What happens if I include some data from the third species?\n", + "* What happens if I change the number of adiabatic steps (p) in the QAOA hyperparameters?\n", + "* What if I use VQE instead of QAOA to find the ground state of the cost Hamiltonian?\n", + "\n", + "### Next time\n", + "**What about the third species?** We ignored it here because max-cut only classifies data into two clusters. Is there a way to use max-cut to give a 3 cluster classification? Or for that matter, any number of cluster classifications? That would make for a much more useful unsupervised learning algorithm. Hint: the answer is YES. Let's discuss it in the [next notebook](https://github.com/ajrazander/Unsupervised-QML/blob/master/Max-cut_2%2B_divisive_clustering.ipynb)." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.6.4" + }, + "notify_time": "10" + }, + "nbformat": 4, + "nbformat_minor": 2 +}