example_support_vector_machine.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "56f0b47e",
   "metadata": {},
   "source": [
    "# Example: Support-Vector-Machine Implementation on Dynex"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0670f510",
   "metadata": {},
   "source": [
    "Quantum computing algorithms for machine learning harness the power of quantum mechanics to enhance various aspects of machine learning tasks. Here is a summary of some prominent quantum computing algorithms for machine learning:\n",
    " \n",
    "1. **Quantum Support Vector Machine (QSVM):** QSVM is a quantum-inspired algorithm that aims to classify data using a quantum kernel function. It leverages the concept of quantum superposition and quantum feature mapping to potentially provide computational advantages over classical SVM algorithms in certain scenarios.\n",
    " \n",
    " \n",
    "2. **Quantum Principal Component Analysis (QPCA):** QPCA is a quantum version of the classical Principal Component Analysis (PCA) algorithm. It utilizes quantum linear algebra techniques to extract the principal components from high-dimensional data, potentially enabling more efficient dimensionality reduction in quantum machine learning.\n",
    " \n",
    " \n",
    "3. **Quantum Neural Networks (QNN):** QNNs are quantum counterparts of classical neural networks. They leverage quantum principles, such as quantum superposition and entanglement, to process and manipulate data. QNNs hold the potential to learn complex patterns and perform tasks like classification and regression, benefiting from quantum parallelism.\n",
    " \n",
    " \n",
    "4. **Quantum K-Means Clustering:** Quantum K-means is a quantum-inspired variant of the classical K-means clustering algorithm. It uses quantum algorithms to accelerate the clustering process by exploring multiple solutions simultaneously. Quantum K-means has the potential to speed up clustering tasks for large-scale datasets.\n",
    " \n",
    " \n",
    "5. **Quantum Boltzmann Machines (QBMs):** QBMs are quantum analogues of classical Boltzmann Machines, which are generative models used for unsupervised learning. QBMs employ quantum annealing to sample from a probability distribution and learn patterns and structures in the data.\n",
    " \n",
    " \n",
    "6. **Quantum Support Vector Regression (QSVR):** QSVR extends the concept of QSVM to regression tasks. It uses quantum computing techniques to perform regression analysis, potentially offering advantages in terms of efficiency and accuracy over classical regression algorithms.\n",
    " \n",
    "As both, Quantum computing and Neuromorphic computing are sharing similar efficiency, all the algorithms above can be computed efficiently on the Dynex platform, but without the limitations of number of available qubits, error correction or availability."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26a40798",
   "metadata": {},
   "source": [
    "In this example a classical classiﬁcation model, Kernel-Support Vector machine, is implemented as a Quadratic Unconstrained Binary Optimisation problem. Here, data points are classiﬁed by a separating hyperplane while maximizing the function margin. The problem is solved for a public Banknote Authentication dataset and the well-\n",
    "known Iris Dataset using the **Dynex Neuromorphic Computing Platform**."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2249cbe",
   "metadata": {},
   "source": [
    "## Problem Description "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33823bda",
   "metadata": {},
   "source": [
    "Support Vector Machines are supervised learning models that are used for classiﬁcation and regression analysis. The training set is given as {x1 ,x2 , ... xn } that are d-dimensional vectors in a some space χ ∈ Rd , where d is the dimension of each vector, i.e., the number of attributes of the training data. We are also given their labels {y1 , y2 , ..., yn }, where yi ∈ {1, −1}. SVMs use hyperplanes that separate the training data by a maximal margin. In general, SVMs allow one to project the training data in the space χ to a higher dimensional feature space F by z = Φ(x), where z ∈ F. To ﬁnd the optimal separating hyperplane having the maximum margin, the algorithm minimizes the following equation:"
   ]
  },
  {
   "attachments": {
    "eq1.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "8db9aff9",
   "metadata": {},
   "source": [
    "![eq1.png](attachment:eq1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38b12aa5",
   "metadata": {},
   "source": [
    "where w is the normal vector for the separating hyperplane given by the equation, w = i αi yi K(xi , x), which can be transferred into its dual form by maximising its primal Lagrangian. This is further formulated as a quadratic programming problem:"
   ]
  },
  {
   "attachments": {
    "eq2.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "9c2164c7",
   "metadata": {},
   "source": [
    "![eq2.png](attachment:eq2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a116aaa",
   "metadata": {},
   "source": [
    "where αi is the weight assigned to the training sample xi . If αi > 0, then xi is a support vector. C is a regularisation parameter that controls the trade-oﬀ between achieving a low training error and a low testing error such that a generalization can be obtained for unseen data. The function K(xi , xj ) = Φ(xi )T Φ(xj ) is Mercer’s kernel function which allows us to calculate the dot product in high-dimensional space without explicitly knowing the non-linear Mapping. There are diﬀerent forms of kernel functions, however, the SVM with a Gaussian Kernel (or RBF-kernel) has been popular because of its ability to handle cases with non-linear relation between classes and features and doing so while having less parameters. The Gaussian Kernel is deﬁned as"
   ]
  },
  {
   "attachments": {
    "eq3.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "56feeb4b",
   "metadata": {},
   "source": [
    "![eq3.png](attachment:eq3.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e0062c5",
   "metadata": {},
   "source": [
    "where γ > 0 is the hyperparameter. The coeﬃcients deﬁne a decision boundary that separates the vector space\n",
    "in two regions, corresponding to the predicted class labels. The decision function is fully speciﬁed by the support vectors and is used to predict samples around the optimal hyperplane. It is formulated as follows:"
   ]
  },
  {
   "attachments": {
    "eq4.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "0b5b80d5",
   "metadata": {},
   "source": [
    "![eq4.png](attachment:eq4.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d61fffba",
   "metadata": {},
   "source": [
    "## QUBO Formulation "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7c7f778",
   "metadata": {},
   "source": [
    "To translate the quadratic programming formulation to a QUBO formulation there are two main steps. First, the input has to be translated to binary input, using the encoding:"
   ]
  },
  {
   "attachments": {
    "eq5.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "2cbc5d23",
   "metadata": {},
   "source": [
    "![eq5.png](attachment:eq5.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cda79482",
   "metadata": {},
   "source": [
    "with aKn+k ∈ {0, 1} binary variables, K the number of binary variables to encode αn and B the base used for the encoding, usually B = 2. More details about the choice for K can be found in the references. The second step is to translate the constraints to the objective function, using a penalty factor ξ for a quadratic penalty. The value of ξ is determined before the training phase (if no particular value of ξ is known, a good strategy is to try exponentially growing sequences, ξ = {..., 10−4 , 10−3 , 10−2 , ...}) (We have optimized the value of ξ). \n",
    "\n",
    "The resulting objective function then becomes:"
   ]
  },
  {
   "attachments": {
    "eq6.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "66861891",
   "metadata": {},
   "source": [
    "![eq6.png](attachment:eq6.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5a9b4ad",
   "metadata": {},
   "source": [
    "## Implementation "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b55f169",
   "metadata": {},
   "source": [
    "First we load all the required libraries, including the Dynex SDK:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4c52a895",
   "metadata": {},
   "outputs": [],
   "source": [
    "import dynex\n",
    "import dimod"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0f9a8b92",
   "metadata": {},
   "outputs": [],
   "source": [
    "from itertools import product\n",
    "import json\n",
    "import random \n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import networkx as nx\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import time "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "824fb9dd",
   "metadata": {},
   "source": [
    "A function to load the training data is being created. In our implementation, we will use the Standard Banknote Authenthication dataset and the well known Iris Datataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f13fc0ff",
   "metadata": {},
   "outputs": [],
   "source": [
    "def load_data(data_file,N,validation_pts):\n",
    "    training_data = np.loadtxt('./datasets/{}.txt'.format(data_file), delimiter=',')\\\n",
    "\n",
    "    for i in range(N+validation_pts):\n",
    "        if(training_data[i][-1] == 0):\n",
    "            training_data[i][-1] = -1\n",
    "\n",
    "    data = training_data[:N+validation_pts, :2]\n",
    "    t = training_data[:N + validation_pts, -1]\n",
    "\n",
    "    x_min, x_max = 1000, 0\n",
    "    y_min, y_max = 1000, 0\n",
    "    # rescalling data\n",
    "    for i in range(N+validation_pts):\n",
    "        x_min = min(data[i][0], x_min)\n",
    "        x_max = max(data[i][0], x_max)\n",
    "        y_min = min(data[i][1], y_min)\n",
    "        y_max = max(data[i][1], y_max)\n",
    "\n",
    "    for i in range(N+validation_pts):\n",
    "        data[i][0] = (data[i][0] - x_min)/(x_max - x_min)\n",
    "        data[i][1] = (data[i][1] - y_min)/(y_max - y_min)\n",
    "\n",
    "    return data,t"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4cffce7",
   "metadata": {},
   "source": [
    "Next we build a Support-Vector-Machine class implementing the algorithm above. It supports five sampler types:\n",
    "\n",
    "- **DNX** The Dynex Neuromorphic sampler\n",
    "- **EXACT** A brute force exact solver which tries all combinations. Very limited problem size\n",
    "- **QPU** D-Wave Quantum Processor (QPU) based D-Wave sampler\n",
    "- **HQPU** D-Wave Advantage Hybrid Solver\n",
    "- **SA** Simulated Annealing using the SimulatedAnnealerSampler from the D-Wave Ocean SDK"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6a56e68c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def delta(i, j):\n",
    "    if i == j:\n",
    "        return 1\n",
    "    else:\n",
    "        return 0\n",
    "\n",
    "class SVM:\n",
    "    def __init__(self,B,K,C,gamma,xi,N,sampler_type) -> None:\n",
    "        self.gamma = gamma\n",
    "        self.B = B\n",
    "        self.K = K \n",
    "        self.C = C \n",
    "        self.xi = xi \n",
    "        self.N = N\n",
    "        self.sampler_type = sampler_type\n",
    "\n",
    "        if(sampler_type == 'HQPU'):\n",
    "            self.sampler = LeapHybridSampler()\n",
    "        if(sampler_type == 'SA'):\n",
    "            self.sampler = neal.SimulatedAnnealingSampler()\n",
    "        if(sampler_type == 'QPU'):\n",
    "            self.sampler = EmbeddingComposite(DWaveSampler())\n",
    "        if(sampler_type == 'DNX'):\n",
    "            self.sampler = '';\n",
    "        if(sampler_type == 'EXACT'):\n",
    "            self.sampler = dimod.ExactSolver();\n",
    "\n",
    "        pass\n",
    "\n",
    "    def kernel(self,x, y):\n",
    "        if self.gamma == -1:\n",
    "            k = np.dot(x, y)\n",
    "        elif self.gamma >= 0:\n",
    "            k = np.exp(-self.gamma*(np.linalg.norm(x-y, ord=2)))\n",
    "        \n",
    "        return k\n",
    "\n",
    "    def predict_class(self,x_test, alpha, b):\n",
    "        N = len(alpha)\n",
    "        f = sum([alpha[n]*self.t[n]*self.kernel(self.data[n], x_test)\n",
    "                    for n in range(N)]) + b\n",
    "        return f\n",
    "\n",
    "    def train_SVM(self,data,t):\n",
    "        self.data = data \n",
    "        self.t = t \n",
    "        Q_tilde = np.zeros((self.K*self.N, self.K*self.N))\n",
    "        for n in range(self.N):\n",
    "            for m in range(self.N):\n",
    "                for k in range(self.K):\n",
    "                    for j in range(self.K):\n",
    "                        Q_tilde[(self.K*n+k, self.K*m+j)] = 0.5*(self.B**(k+j))*t[n]*t[m] * \\\n",
    "                            (self.kernel(data[n], data[m])+self.xi) - \\\n",
    "                            (delta(n, m)*delta(k, j)*(self.B**k))\n",
    "\n",
    "        Q = np.zeros((self.K*self.N, self.K*self.N))\n",
    "        for j in range(self.K*self.N):\n",
    "            Q[(j, j)] = Q_tilde[(j, j)]\n",
    "            for i in range(self.K*self.N):\n",
    "                if i < j:\n",
    "                    Q[(i, j)] = Q_tilde[(i, j)] + Q_tilde[(j, i)]\n",
    "\n",
    "        size_of_q = Q.shape[0]\n",
    "        qubo = {(i, j): Q[i, j]\n",
    "                for i, j in product(range(size_of_q), range(size_of_q))}\n",
    "\n",
    "        now = time.perf_counter();\n",
    "        \n",
    "        if(self.sampler_type == 'HQPU'):\n",
    "            response = self.sampler.sample_qubo(qubo)\n",
    "        if(self.sampler_type == 'SA'):\n",
    "            response = self.sampler.sample_qubo(qubo, num_reads=100)\n",
    "        if(self.sampler_type == 'QPU'):\n",
    "            response = self.sampler.sample_qubo(qubo, num_reads=100)\n",
    "        if(self.sampler_type == 'EXACT'):\n",
    "            response = self.sampler.sample_qubo(qubo)\n",
    "        if(self.sampler_type == 'DNX'):\n",
    "            bqm = dimod.BinaryQuadraticModel.from_qubo(qubo);\n",
    "            model = dynex.BQM(bqm);\n",
    "            sampler = dynex.DynexSampler(model, mainnet=True, description='QSVM');\n",
    "            response = sampler.sample(num_reads=100000, annealing_time = 500);\n",
    "            \n",
    "        #print(f'Solver Time: {time.perf_counter() - now}') \n",
    "\n",
    "        a = response.first.sample\n",
    "\n",
    "        alpha = {}\n",
    "        for n in range(self.N):\n",
    "            alpha[n] = sum([(self.B**k)*a[self.K*n+k] for k in range(self.K)])\n",
    "\n",
    "        b = sum([alpha[n]*(self.C-alpha[n])*(t[n]-(sum([alpha[m]*t[m]*self.kernel(data[m], data[n])\n",
    "                                                    for m in range(self.N)]))) for n in range(self.N)])/sum([alpha[n]*(self.C-alpha[n]) for n in range(self.N)])\n",
    "\n",
    "        return alpha, b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1acee8d",
   "metadata": {},
   "source": [
    "The probability or the certainty with which a class is predicted by the model, is deﬁned as the conﬁdence of the classiﬁer. The higher the absolute value of the decision function, for a given data point, the more probable\n",
    "it is that the data point belongs to a particular class. We create a function to create contour plots of the decision function, with the horizontal and vertical axis representing the data points and the decision function for the corresponding points being represented by the colour gradient:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b5bf7642",
   "metadata": {},
   "outputs": [],
   "source": [
    "def  plot_figure(SVM,alpha,data,t,b,N,sampler_type):\n",
    "    plt.figure()\n",
    "    cm = plt.cm.RdBu\n",
    "\n",
    "    xx, yy = np.meshgrid(np.linspace(0.0, 1.0, 80),\n",
    "                            np.linspace(0.0, 1.0, 80))\n",
    "    Z = []\n",
    "    for row in range(len(xx)):\n",
    "        Z_row = []\n",
    "        for col in range(len(xx[row])):\n",
    "            target = np.array([xx[row][col], yy[row][col]])\n",
    "            Z_row.append(SVM.predict_class(target, alpha, b))\n",
    "        Z.append(Z_row)\n",
    "\n",
    "    cnt = plt.contourf(xx, yy, Z, levels=np.arange(-1, 1.1,\n",
    "                                                    0.1), cmap=cm, alpha=0.8, extend=\"both\")\n",
    "\n",
    "    plt.contour(xx, yy, Z, levels=[0.0], colors=(\n",
    "        \"black\",), linestyles=(\"--\",), linewidths=(0.8,))\n",
    "    plt.colorbar(cnt, ticks=[-1, 0, 1])\n",
    "\n",
    "    red_sv = []\n",
    "    blue_sv = []\n",
    "    red_pts = []\n",
    "    blue_pts = []\n",
    "\n",
    "    for i in range(N):\n",
    "        if(alpha[i]):\n",
    "            if(t[i] == 1):\n",
    "                blue_sv.append(data[i, :2])\n",
    "            else:\n",
    "                red_sv.append(data[i, :2])\n",
    "\n",
    "        else:\n",
    "            if(t[i] == 1):\n",
    "                blue_pts.append(data[i, :2])\n",
    "            else:\n",
    "                red_pts.append(data[i, :2])\n",
    "\n",
    "    plt.scatter([el[0] for el in blue_sv],\n",
    "                [el[1] for el in blue_sv], color='b', marker='^', edgecolors='k', label=\"Type 1 SV\")\n",
    "\n",
    "    plt.scatter([el[0] for el in red_sv],\n",
    "                [el[1] for el in red_sv], color='r', marker='^', edgecolors='k', label=\"Type -1 SV\")\n",
    "\n",
    "    plt.scatter([el[0] for el in blue_pts],\n",
    "                [el[1] for el in blue_pts], color='b', marker='o', edgecolors='k', label=\"Type 1 Train\")\n",
    "\n",
    "    plt.scatter([el[0] for el in red_pts],\n",
    "                [el[1] for el in red_pts], color='r', marker='o', edgecolors='k', label=\"Type -1 Train\")\n",
    "\n",
    "    \n",
    "    plt.legend(loc='lower right', fontsize='x-small')\n",
    "    plt.savefig(f'{sampler_type}.jpg')\n",
    "\n",
    "def compute_metrics(SVM,alpha,data,t,b,N,validation_pts):\n",
    "    tp, fp, tn, fn = 0, 0, 0, 0\n",
    "    for i in range(N, N+validation_pts):\n",
    "        predicted_cls = SVM.predict_class(data[i], alpha, b)\n",
    "        y_i = t[i]\n",
    "        if(y_i == 1):\n",
    "            if(predicted_cls > 0):\n",
    "                tp += 1\n",
    "            else:\n",
    "                fp += 1\n",
    "        else:\n",
    "            if(predicted_cls < 0):\n",
    "                tn += 1\n",
    "            else:\n",
    "                fn += 1\n",
    "\n",
    "    precision = tp / (tp + fp)\n",
    "    recall = tp / (tp + fn)\n",
    "    f_score = tp/(tp + 1/2*(fp+fn))\n",
    "    accuracy = (tp + tn)/(tp+tn+fp+fn)\n",
    "\n",
    "    return precision,recall,f_score,accuracy\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70ccd8d4",
   "metadata": {},
   "source": [
    "## Computation (Main-Net)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c0c3b28",
   "metadata": {},
   "source": [
    "The simulations were run using the following parameter values: K = 2, B = 2, C = 3, ξ = 0.001, γ = 16. We do not intend to optimize C, γ as our aim is to study the behaviour for same hyper parameters. However ξ has been optimized by the authors in the references:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "89184093",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training set: 120 validation set: 30 total: 150\n"
     ]
    }
   ],
   "source": [
    "B = 2;\n",
    "K = 2;\n",
    "C = 3;\n",
    "gamma = 16;\n",
    "xi = 0.001;\n",
    "dataPoints = 150; # size of data points\n",
    "spl = \"DNX\";     # sampler\n",
    "trainingPoints = int(dataPoints * 0.80)\n",
    "validationPoints = dataPoints - trainingPoints; \n",
    "print('Training set:', trainingPoints,'validation set:',validationPoints, 'total:',dataPoints)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b558759",
   "metadata": {},
   "source": [
    "First we load the dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "389dca93",
   "metadata": {},
   "outputs": [],
   "source": [
    "data,t = load_data('banknote_1',trainingPoints,validationPoints)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2eabb15",
   "metadata": {},
   "source": [
    "We create the Support-Vector-Machine class given the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "1811815f",
   "metadata": {},
   "outputs": [],
   "source": [
    "_SVM = SVM(B,K,C,gamma,xi,trainingPoints,spl)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7019ade6",
   "metadata": {},
   "source": [
    "And finally train the SVM:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "bc2057e2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "╭────────────┬───────────┬───────────┬─────────┬────────┬─────────┬───────┬──────┬──────────┬────────────╮\n",
      "│   DYNEXJOB │   ELAPSED │   WORKERS │   CHIPS │      ✔ │   STEPS │   LOC │    ✔ │   ENERGY │          ✔ │\n",
      "├────────────┼───────────┼───────────┼─────────┼────────┼─────────┼───────┼──────┼──────────┼────────────┤\n",
      "│       5029 │      0.35 │         4 │ 1554222 │ 114176 │     500 │  4621 │ 4621 │  7272542 │ 7276642.00 │\n",
      "╰────────────┴───────────┴───────────┴─────────┴────────┴─────────┴───────┴──────┴──────────┴────────────╯\n",
      "╭───────────┬───────────────┬─────────┬───────┬────────────┬────────────┬───────────────┬──────────╮\n",
      "│    WORKER │       VERSION │   CHIPS │   LOC │     ENERGY │    RUNTIME │   LAST UPDATE │   STATUS │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963327 │ 2.3.0.SRB.234 │  100000 │ 14294 │ 7272542.00 │   0.75 min │     1.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963288 │ 2.3.0.SRB.235 │   60736 │ 14296 │ 7297489.00 │   0.30 min │    35.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963349 │ 2.3.0.SRB.235 │  100000 │ 14299 │ 7299370.00 │   0.55 min │     7.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963331 │ 2.3.0.SRB.234 │  100000 │ 14293 │ 7301848.00 │   0.73 min │     1.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963271 │ 2.3.0.OZM.123 │  100000 │ 14313 │ 7306919.00 │   0.07 min │    51.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963304 │ 2.3.0.OZM.123 │   22912 │ 14315 │ 7308767.00 │   0.05 min │    47.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963256 │ 2.3.0.SRB.235 │   88398 │ 14294 │ 7313710.00 │   0.42 min │    32.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963286 │ 2.3.0.OZM.123 │   56160 │ 14325 │ 7319512.00 │   0.05 min │    50.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133826593 │ 2.3.0.OZM.122 │   89920 │ 14313 │ 7319965.00 │ 596.32 min │    33.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963303 │ 2.3.0.OZM.123 │   74016 │ 14317 │ 7321688.00 │   0.05 min │    47.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963326 │ 2.3.0.OZM.123 │   22912 │ 14316 │ 7322120.00 │   0.12 min │    39.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963261 │ 2.3.0.OZM.123 │  100000 │ 14315 │ 7324521.00 │   0.07 min │    52.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963258 │ 2.3.0.OZM.123 │   90336 │ 14324 │ 7325032.00 │   0.05 min │    53.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963263 │ 2.3.0.OZM.124 │   66592 │  4837 │ 7326707.00 │   0.05 min │    52.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963319 │ 2.3.0.OZM.122 │   22144 │ 14324 │ 7330683.00 │   0.05 min │    44.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963250 │ 2.3.0.OZM.123 │   67008 │ 14326 │ 7331708.00 │   0.07 min │    54.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963282 │ 2.3.0.OZM.123 │   66560 │ 14318 │ 7335465.00 │   0.12 min │    46.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963328 │ 2.3.0.OZM.124 │   67840 │  5070 │ 7336164.00 │   0.07 min │    41.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963284 │ 2.3.0.OZM.122 │    1920 │ 14320 │ 7337412.00 │   0.05 min │    50.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963275 │ 2.3.0.OZM.124 │   66432 │  4621 │ 7341014.00 │   0.05 min │    51.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963313 │ 2.3.0.OZM.123 │   13760 │ 14333 │ 7344341.00 │   0.05 min │    46.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963242 │ 2.3.0.OZM.124 │   10080 │  5349 │ 7350389.00 │   0.05 min │    56.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963253 │ 2.3.0.OZM.124 │   10112 │  5204 │ 7356731.00 │   0.05 min │    54.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963252 │ 2.3.0.OZM.124 │   15968 │  4939 │ 7359542.00 │   0.07 min │    53.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963381 │ 2.3.0.OZM.121 │   74016 │ 14347 │ 7395535.00 │   0.42 min │     7.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "├───────────┼───────────────┼─────────┼───────┼────────────┼────────────┼───────────────┼──────────┤\n",
      "│ 133963308 │ 2.3.0.OZM.124 │   66400 │  5007 │ 8420093.00 │   0.07 min │    46.00s ago │  \u001b[1;31mSTOPPED\u001b[0m │\n",
      "╰───────────┴───────────────┴─────────┴───────┴────────────┴────────────┴───────────────┴──────────╯\n",
      "[DYNEX] FINISHED READ AFTER 0.35 SECONDS\n",
      "[DYNEX] COMPUTING FILE 7b571423084b1b730d156570b9c650a4.bin REMOVED\n",
      "[DYNEX] SAMPLESET LOADED\n"
     ]
    }
   ],
   "source": [
    "alpha, b = _SVM.train_SVM(data, t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f07e69f",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "Using the functions for plotting the graphs and printing metrics, we analyse the result:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "49879914",
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_figure(_SVM,alpha,data,t,b,trainingPoints,spl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "110e5956",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "precision=1.0 recall=0.8823529411764706 f_score=0.9375 accuracy=0.9333333333333333\n"
     ]
    }
   ],
   "source": [
    "precision,recall,f_score,accuracy = compute_metrics(_SVM,alpha,data,t,b,trainingPoints,validationPoints)\n",
    "print(f'{precision=} {recall=} {f_score=} {accuracy=}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e89a711",
   "metadata": {},
   "source": [
    "The following chart shows the results of the experiments conducted on the D-Wave system using the various samplers as described above. Note that the authors observed that the QPU is not able to ﬁnd embeddings for instances larger that 90:"
   ]
  },
  {
   "attachments": {
    "fig1.png": {
     "image/png": 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    }
   },
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   "source": [
    "![fig1.png](attachment:fig1.png)"
   ]
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   "source": [
    "## References "
   ]
  },
  {
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   "id": "8bd0cefb",
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   "source": [
    "[1] Harshil Singh Bhatia and Frank Phillipson: Performance Analysis of Support Vector Machine Implementations on the D-Wave Quantum Annealer, International Conference on Computational Science, p.84-97, 2021, Springer\n",
    "\n",
    "[2] Booth, M., Reinhardt, S.P., Roy, A.: Partitioning Optimization Problems for Hybrid Classical/Quantum Execution. Technical report, D-Wave Systems (2017)\n",
    "\n",
    "[3] Chang, C.C., Lin, C.J.: LIBSVM: a library for support vector machines. ACM Trans. Intell. Syst. Technol. 2, 27:1–27:27.\n",
    "\n",
    "[4] Chatterjee, R., Yu, T.: Generalized coherent states, reproducing kernels, and quantum support vector machines. Quantum Inf. Comput. 17(15–16), 1292–1306 (2017)\n",
    "\n",
    "[5] Choi, V.: Minor-embedding in adiabatic quantum computation: I. the parameter setting problem. Quantum Inf. Process. 7(5), 193–209 (2008)\n",
    "\n",
    "[6] Coﬀrin, C.J.: Challenges with chains: testing the limits of a d-wave quantum annealer for discrete optimization. Technical report, Los Alamos National Lab. (LANL), Los Alamos, NM (United States) (2019)\n",
    "\n",
    "[7] Willsch, D., Willsch, M., De Raedt, H., Michielsen, K.: Support vector machines on the d-wave quantum annealer. Comput. Phys. Commun. 248, 107006 (2020)"
   ]
  }
 ],
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