Support Vector Machine-1-Linearly Separable Data.ipynb

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    "# Support Vector Machine (SVM) Classification: Linearly Separable Data\n",
    "\n",
    "SVM is a discriminative learning algorithm that makes an **assumption on the form of the discriminant (decision boundary)** between the classes.\n",
    "\n",
    "In a binary classification problem, the form of the SVM discriminant function is modeled by the **widest possible boundary** between the classes. That's why SVM is known as **large margin classifier**. \n",
    "\n",
    "The goal of the large margin SVM classifier is to maximize the margin between two classes. However it has to respect a **constraint**: \n",
    "    \n",
    "    -- The margin should be maximized while making sure that data are correctly classified (i.e., data belonging to two classes are off the margin).\n",
    "\n",
    "Hence the SVM classification can be modeled as a constrained maximization problem.\n",
    "\n",
    "Depending on the nature of the data, the SVM constrained maximization algorithm varies.\n",
    "\n",
    "To understand different SVM algorithms and approaches, we will consider several cases in this notebook series on SVM.\n",
    "\n",
    "- Linearly Separable Data\n",
    "        -- No Outlier\n",
    "        -- Outlier\n",
    "- Linearly Non-Separable Data\n",
    "        -- Feature Augmentation\n",
    "        -- Kernelized SVM: Polynomial Kernel\n",
    "        -- Kernelized SVM: Gaussian Radial Basis Function (RBF) Kernel\n",
    "\n",
    "\n",
    "\n",
    "## Index for the Notebook Series on SVM \n",
    "\n",
    "There are 7 notebooks on SVM based classifiers.\n",
    "\n",
    "1. Support Vector Machine-0-Bird's-eye View\n",
    "        \n",
    "        -- A bird's-eye view representation of the main algorithms of the Support Vector Machine (SVM) model for solving binary classification problems. \n",
    "\n",
    "2. Support Vector Machine-1-Linearly Separable Data\n",
    "        \n",
    "        -- Hard margin & soft margin classifier using the LinearSVC model\n",
    "        \n",
    "3. Support Vector Machine-2-Nonlinear Data\n",
    "        \n",
    "        -- Polynomial models with LinearSVC and Kernelized SVM (Polynomial & Gaussian RBF kernel)\n",
    "4. Support Vector Machine-3-Gaussian RBF Kernel\n",
    "        \n",
    "        -- In depth investigation of Gaussian RBF Kernel (how to fine tune the hyperparameters)\n",
    "        \n",
    "5. Support Vector Machine-4-Multiclass Classification\n",
    "    \n",
    "        -- Multiclass classification using the SVC class that implements the One-versus-One (OvO) technique\n",
    "        \n",
    "        \n",
    "6. Support Vector Machine-5-Stochastic Gradient Descent-Linear Data\n",
    "\n",
    "        -- The SGD algorithm for the SVM model to solve a binary classification problem on a linearly separable dataset.\n",
    "\n",
    "\n",
    "7. Support Vector Machine-6-Stochastic Gradient Descent-Nonlinear Data\n",
    "\n",
    "        -- The SGD algorithm for the SVM model to solve a binary classification problem on a linearly non-separable dataset.\n",
    "\n",
    "\n",
    "\n",
    "Finally, we will apply SVM on **two application scenarios**. We will see that these two applications require two very different SVM algorithms (linear and complex models). We will conduct in dept investigations on these two models in the context of these two applications.\n",
    "6. Application 1 - Image Classification (Gaussian RBF model performs well & why)\n",
    "7. Application 2 - Text Classification (LinearSVC performs well & why)\n",
    "\n",
    "\n",
    "In this notebook we will investigate the Support Vector Machine (SVM) algorithm in the context of **linearly separable** data. Our goal is to develop a mathematical understanding of the SVM algorithm.\n",
    "\n",
    "\n",
    "## Mathematical Foundation of SVM\n",
    "\n",
    "There are at least two very different ways to find the maximum margin decision boundary.\n",
    "\n",
    "- Modeling the max margin problem as a constrained optimization problem and solove it using Quadratic Programming (QP) solver\n",
    "- Modeling the max margin problem as an unconstrained optimization problem and solve it using Gradient Descent/coordinate descent \n",
    "\n",
    "\n",
    "### Constrained Optimization Problem\n",
    "\n",
    "We can model the max margin problem as a constrained optimization problem in two ways.\n",
    "- Primal Problem (computationally expensive for large feature dimension)\n",
    "- Dual Problem\n",
    "\n",
    "\n",
    "### Primal Problem\n",
    "\n",
    "The SVM finds the max margin decision boundary by solving the following constrained optimization problem.\n",
    "\n",
    "$min_{\\vec{w}, b} \\frac{1}{2}\\vec{w}^T.\\vec{w} + C\\sum_{i=1}^{N} \\xi_i$\n",
    "\n",
    "Subject to the following constraints:\n",
    "\n",
    "$y_i(\\vec{w}^T.\\vec{x}_i + b) \\geq 1 - \\xi_i$   $\\forall i$\n",
    "\n",
    "$\\xi_i \\geq 0$\n",
    "\n",
    "\n",
    "\n",
    "Here:\n",
    "- $\\xi$: slack variable that controls margin violation. \\#($\\xi > 0$) = the number of non-separable points (measure of error/misclassification).\n",
    "\n",
    "- C: regularization/penalty. Controls the trade-off between margin maximization and error minimization.\n",
    "\n",
    "This convex optimization problem is known as the **primal problem** and its complexity depends on feature dimension.\n",
    "\n",
    "We can use a Quadratic Programming (QP) solver to find optimal $\\vec{w}$ and b for the primal problem:\n",
    "https://cvxopt.org/\n",
    "\n",
    "\n",
    "\n",
    "<img src=\"https://engineering.unl.edu/images/uploads/SVM-Max-MarginClassifier-2.png\" width=400 height=200>\n",
    "     \n",
    "### Dual Problem \n",
    "\n",
    "Due to the computational complexity of the primal optimization (minimization) problem, we transform it into a form such that its complexity no more depends on the feature dimension, instead depends on the size of the data. This new form is known as the dual form and we solve the **dual optimization (maximization) problem**.\n",
    "\n",
    "$max_{\\alpha_1, ..\\alpha_N} \\sum_{i=1}^{N}\\alpha_i - \\frac{1}{2}\\sum_{i=1}^{N}\\sum_{j=1}^{N} \\alpha_i \\alpha_j y_i y_j \\vec{x_i}^T.\\vec{x_j} $\n",
    "\n",
    "Subject to the constraints:\n",
    "\n",
    "$\\sum_{i=1}^{N}\\alpha_i y_i = 0$\n",
    "\n",
    "$\\alpha_i \\geq 0 $\n",
    "\n",
    "Here $\\alpha$ is the Lagrange multiplier.\n",
    "\n",
    "The complexity of the dual problem depends on the size of the training data (N), not on the feature dimension. Thus, for high-dimensional data, solving the dual problem is much more efficient than solving the primal problem.\n",
    "\n",
    "\n",
    "\n",
    "##### Since we are using linearly separable data in this notebook, we will not have to solve the dual version of the problem. This knowledge will be useful for setting the \"dual\" hyperparameter.\n",
    "\n",
    "\n",
    "\n",
    "## Unconstrained Optimization Problem for Gradient Descent\n",
    "\n",
    "We can implement the gradient descent (GD) or stochastic gradient descent (SGD) or coordinate descent (CD) based approach to find optimal $\\vec{w}$ and $b$ for the SVM classsifier. The SGD aproach is useful for **online learning**.\n",
    "\n",
    "To apply these iterative optimazation approaches for the SVM, we define the cost function as follows.\n",
    "\n",
    "\n",
    "$min_{\\vec{w},b}\\frac{1}{2}\\vec{w}^T.\\vec{w} + C\\sum_{i=1}^{N}h(y_i(\\vec{w}^T.\\vec{x}_i + b)) $\n",
    "\n",
    "\n",
    "Here:\n",
    "- $h(z)$: the Hinge loss function: $h(z) = max(0, 1 - z)$\n",
    "- C: regularization/penalty. Controls the trade-off between margin maximization and error minimization.\n",
    "\n",
    "The Hinge loss function varies between 0 and $(1 - y_i(\\vec{w}^T.\\vec{x}_i + b))$. It represents the error/loss due to misclassification.\n",
    "\n",
    "<img src=\"https://engineering.unl.edu/images/uploads/SVM1.png\" width=400 height=200>\n",
    "\n",
    "Observe that the Hinge loss or cost function of SVM is similar to the Linear Regression and Logistic Regression regularized cost function.\n",
    "\n",
    "In case of SVM:\n",
    "- The first term is the regularization/penalty term\n",
    "- The second term is the loss objective function\n",
    "\n",
    "Unlike Linear/Logistic regression, the regularization/penalty parameter (C) is with the loss function.\n",
    "\n",
    "\n",
    "It's a hyperparameter that controls the trade-off between margin maximization and error minimization.\n",
    "     - If C is too large, we have a high penalty for nonseparable points, and we may store many support vectors and overfit. \n",
    "     - If C is too small, we may find too simple solutions that underfit. \n",
    "     \n",
    "\n",
    "\n",
    "## SVM using Scikit-Learn\n",
    "\n",
    "\n",
    "Scikit-Learn provides four SVM models to perform classification:\n",
    "\n",
    "- SVC (Solves the dual optimization problem. Used to implement kernelized SVM, such as polynomial kernel, Gaussian Radial Basis Function or RBF kernel)\n",
    "- LinearSVC (Uses the Coordinate Descent approach. Similar to SVC with linear kernel)\n",
    "- NuSVC (Nu-Support Vector Classification. Similar to SVC but uses a parameter to control the number of support vectors)\n",
    "- SGDClassifier (Uses Stochastic Gradient Descent approach)\n",
    "\n",
    "We will investigate both SVC and LinearSVC in greater detail. Also for the image classsification application we will use the SGDClasssifier.\n",
    "\n",
    "\n",
    "## Scikit-Learn SVM Model Complexity\n",
    "\n",
    "\n",
    "- SVC: $O(N^2d)$ ~ $O(N^3d)$\n",
    "- LinearSVC: $O(Nd)$ \n",
    "\n",
    "N: No. of training data\n",
    "\n",
    "d: No. of features\n",
    "\n",
    "\n",
    "The LinearSVC class is based on the liblinear library, which implements an optimized algorithm for linear SVMs. It does not support the kernel trick, but it scales almost linearly with the number of training instances and the number of features ($O(Nd)$). Moreover, the LinearSVC class has more flexibility in the choice of penalties (l2 & l1) and loss functions. \n",
    "\n",
    "\n",
    "The SVC class is based on the libsvm library, which implements an algorithm that supports the kernel trick. Due to its complexity between $O(N^2d)$ ~ $O(N^3d)$, it gets dreadfully slow when N gets large (e.g., hundreds of thousands of instances). However, SVC is perfect for **complex but small or medium** training sets. It scales well with the number of features, especially with sparse features (i.e., when each instance has few nonzero features). \n",
    "\n",
    "\n",
    "## How do We Choose the Optimal Model (between SVC & LinearSVC)?\n",
    "\n",
    "Model selection is done by hyperparameter tuning. We can choose both the algorithm (LilearSVC, SVC with varying kernels) and the optimal hyperparameters via cross-validated grid search.\n",
    "\n",
    "However, brute-force grid search is time consuming. We should have a high-level understanding of the suitability of the algorithms based on the dataset. Then, we can fine tune the hyperparameters.\n",
    "\n",
    "So, before doing any Machine Learning with SVM, we should address these questions.\n",
    "\n",
    "- How do we choose the most suitable model between LinearSVC and SVC?\n",
    "- If SVC is suitable, then how do we choose the optimal kernel (usually between polynomial and RBF)?\n",
    "\n",
    "\n",
    "\n",
    "# Guideline (Rough) to Choose the Suitable Model Based on the Data\n",
    "\n",
    "- N is very large but d is small ($N > d$): LinearSVC\n",
    "- d is large relative to N ($d \\geq N$): LinearSVC\n",
    "- N is small to medium and d small ($N > d$): SVC with Gaussian RBF kernel\n",
    "\n",
    "\n",
    "In this notebook we will classify a linearly separable dataset. Both N and d are small in this dataset. Also, it is linearly separable.\n",
    "\n",
    "Thus, will use the **LinearSVC** model. \n",
    "\n",
    "\n",
    "\n",
    "## LinearSVC Class: Hyperparameter Setting:\n",
    "\n",
    "- The \"loss\" hyperparameter should be set to \"hinge\". \n",
    "\n",
    "- The hyperparameter \"C\" controls the penalty for the error (margin violation). It should be selected via grid search. We will investigate its effect shortly.\n",
    "\n",
    "- Finally, for better performance we should set the \"dual\" hyperparameter to False, unless there are more features than training instances.\n",
    "\n",
    "\n",
    "\n",
    "### Scaling\n",
    "\n",
    "The SVM classfication is influenced by the varying scale of the features. \n",
    "\n",
    "SVMs try to fit the largest possible “street” between the classes. So if the training set is not scaled, the SVM will tend to neglect small features. \n",
    "\n",
    "\n",
    "Thus, we should standardize the data before training.\n",
    "\n",
    "\n",
    "## Linearly Separable Data: Two Cases\n",
    "\n",
    "We will consider two cases.\n",
    "\n",
    "- Data doesn't have outlier\n",
    "- Data has outliers"
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn import datasets\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.svm import LinearSVC\n",
    "\n",
    "np.random.seed(43)"
   ]
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    "## No Outlier: Hard Margin Classification\n",
    "\n",
    "\n",
    "We will use a synthetic dataset that doesn't have any outlier. We will implement the SVM by imposing all instances be off the street and on the right side. \n",
    "\n",
    "This is called **hard margin classification**."
   ]
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   "source": [
    "## Synthetic Dataset for Hard Margin Classification"
   ]
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cO9gZ+rkqeZBz7lvm17+9UtJnrLNeqPzcxCdJeoVzrsicy1fIb5P/ZmY/Ld/reZ/8MXiRfM/9q5xz/cHrH8gHxH9tZh+T9KPy81v3Snp632v/SX4ZnqvM7H/Jb7PPOOey5grnuUI+UdLbzexc+YRi35a0Xn4+9fclFVnT9Zcl/aqZdZdsOiK/n54j6U+cc98boUwAUCoCTgAp+ZnOo98X5Nemm5hz7m/N7OnyPSMXyA+H+6Z84PJ7kv6587pl8wuuv0N+7c2T5But2+SH2pYScHZcLd8LdoNzbthww65vyQcoz5bPVPtY+SDzG/LZb9/dPyzVOXexmd0gv6bjb8ln0rxXfp7cb2V8xl/Ib/vfkg+g/lU+yOgPNC6QXz/yZ+W3z53y6zUekc8IXIhz7i4ze678epP/Rb737lPyDe8/kM8a2+9u+WRF75BfT/Mh+URMr+/NnjvgM0fdJnle0nkcle85u1t+P/yRcy5riPSvyWfI/UX5QP4r8vWgmyymt4wHzOxi+Syx75Ffs3OX/HDLt8vfaLhEPvi5V35e6Ad0LMFTFX5Pvif5sf2/cM5dZWZfk58r3R2Ofpuk85xzw3qdu+/xHTN7tnwgtk2+PpwsPzz845Le6ZzLmof9NvlkQ1vlE0/dLr9tNml1wPlH8muVvlh+3dgp+WC2cMDpnDvSOU9s73zmb3d+9VX5pYqGZpvuuLFTlufLb9PlTjleL1/3AaAx3TXTAACRMrNflA8SXuqc+6MAyjMn39j9befcGxstDAAAaBRzOAEgfq+SH8r5kaYLAgAA0IshtQAQoc4anz8l6SxJZ0v6rf71JAEAAJpGwAkAcTpDfv3Kb8nPT31ns8UBAABYjTmcAAAAAIBKMIcTAAAAAFCJyofUrlu3zs3NzVX9MQAAAACABuzZs+egc+6Hs35XecA5NzenpaWlqj8GAAAAANAAM9uf9zuG1AIAAAAAKkHACQAAAACoBAEnAAAAAKASjazDeeTIEd199936/ve/38THB+2EE07Q6aefrrVr1zZdFAAAAACYSCMB5913361HPOIRmpubk5k1UYQgOed06NAh3X333Xr84x/fdHEAAAAAYCKNDKn9/ve/r5mZGYLNPmammZkZen4BAAAAJKGxOZwEm9nYLgAAAABS0dqkQffee69e/OIX64lPfKLOOOMMbdmyRXfccYf27dunM888s5LPfPDBB/VLv/RLetKTnqRnPOMZ2rdvXyWfAwAAAAAhiCLgXFyU5uakqSn/c3Fxsvdzzum8887TOeeco7vuuku333673vzmN+vrX/96GcXN9f73v1+nnHKKvvjFL+pXf/VX9YY3vKHSzwMAAACAJgUfcC4uSpdeKu3fLznnf1566WRB5w033KC1a9fqsssue/i5DRs26Kyzzlrxun379umss87Sxo0btXHjRn3605+WJH3ta1/T2WefrQ0bNujMM8/UJz/5SS0vL+vCCy/UmWeeqac+9am6/PLLV33un//5n2vbtm2SpJ//+Z/X3/3d38k5N/4XAQAAAICANZKldhQ7dkiHD6987vBh//z8/HjvuXfvXm3atGno60477TRdf/31OuGEE3TnnXfqJS95iZaWlvTBD35Qz3nOc7Rjxw4tLy/r8OHDuvXWW3XPPfdo7969kqRvfetbq97vnnvu0Y/92I9Jko477jg96lGP0qFDh7Ru3brxvggAAAAABCz4gPPAgdGeL9ORI0f06le/WrfeeqvWrFmjO+64Q5L09Kc/XRdffLGOHDmiF77whdqwYYOe8IQn6Etf+pJe85rX6HnPe56e/exnr3q/rN5MkgQBAAAASFXwQ2rXrx/t+SKe8pSnaM+ePUNfd/nll+sxj3mMbrvtNi0tLemhhx6SJJ199tm66aab9LjHPU5bt27Vtddeq1NOOUW33XabzjnnHF155ZV62ctetur9Tj/9dH3lK1+RJP3gBz/Q/fffr1NPPXX8LwIAAAAAAQs+4Ny5U5qeXvnc9LR/flznnnuuHnzwQb3vfe97+Lmbb75Zn/jEJ1a87v7779djH/tYTU1Naffu3VpeXpYk7d+/X6eddppe/vKX65JLLtEtt9yigwcP6ujRozr//PP1pje9Sbfccsuqz33BC16gXbt2SZI+/OEP69xzz6WHEwAAAECygh9S252nuWOHH0a7fr0PNsedvyn5Yawf/ehH9brXvU5vfetbdcIJJ2hubk7vete7Vrxu+/btOv/88/Wnf/qnetaznqWTTjpJknTjjTfq7W9/u9auXauTTz5Z1157re655x5ddNFFOnr0qCTpLW95y6rPveSSS7R161Y96UlP0qmnnqo//uM/Hv9LAAAAAEDgrOosqZs3b3ZLS0srnvv85z+vJz/5yZV+bszYPgAAAEC1FhfL7dRqMzPb45zbnPW74IfUAgAAABhP2evZp6KKpReRjYATAAAASBBBVb5BSy+iXAScAAAAQIIIqvI1ufRi2xBwAgAAAAkiqMpXxdKLyEbACQAAACSIoCpfFUsvIhsBJwAAAJAggqp88/PS1VdLs7OSmf959dVkqa1CawPOe++9Vy9+8Yv1xCc+UWeccYa2bNmiO+64Q/v27dOZZ55ZyWfedNNN2rhxo4477jh9+MMfruQzAAAAUK9QM8ESVA02Py/t2ycdPep/sl2qEUfAWfJR7JzTeeedp3POOUd33XWXbr/9dr35zW/W17/+9VKKm2f9+vW65ppr9NKXvrTSzwEAAEA9Qs8ES1CFpoUfcFZwFN9www1au3atLrvssoef27Bhg84666wVr9u3b5/OOussbdy4URs3btSnP/1pSdLXvvY1nX322dqwYYPOPPNMffKTn9Ty8rIuvPBCnXnmmXrqU5+qyy+/fNXnzs3N6WlPe5qmpsLf7AAAABiOTLDAYOFHPhUcxXv37tWmTZuGvu60007T9ddfr1tuuUUf+tCH9Cu/8iuSpA9+8IN6znOeo1tvvVW33XabNmzYoFtvvVX33HOP9u7dq89+9rO66KKLxi4fAAAA4kAmWEwi1OHYZTqu6QIM1eBRfOTIEb361a/WrbfeqjVr1uiOO+6QJD396U/XxRdfrCNHjuiFL3yhNmzYoCc84Qn60pe+pNe85jV63vOep2c/+9mVlw8AAADNWr/eD8DLeh4YpDuQs9u31h3IKaU19Dn8Hs4K8jk/5SlP0Z49e4a+7vLLL9djHvMY3XbbbVpaWtJDDz0kSTr77LN100036XGPe5y2bt2qa6+9Vqeccopuu+02nXPOObryyiv1spe9bOzyAQAAIA5kgi1HrD19k5S7LcOxww84KziKzz33XD344IN63/ve9/BzN998sz7xiU+seN3999+vxz72sZqamtLu3bu1vLwsSdq/f79OO+00vfzlL9cll1yiW265RQcPHtTRo0d1/vnn601vepNuueWWscsHAACAOFSdCTbWQKyoxUVp3TrpggvCTbyUZ9JUM20Zjm3OuUo/YPPmzW5paWnFc5///Of15Cc/ufibLC76UP/AAd+zuXPnxEfxV7/6Vb3uda/Tnj17dMIJJ2hubk7vete7tHbtWj3/+c/X3r17deedd+r888/X9PS0nvWsZ+nd7363HnjgAe3atUtvf/vbtXbtWp188sm69tpr9e1vf1sXXXSRjh49Kkl6y1veouc+97krPvPmm2/Weeedp29+85s64YQT9CM/8iP63Oc+t6psI28fAAAAJKd/yKXk+11SWdok6/v1mp31mXVDNTeXPZy6aLkn/fuQmNke59zmzN9FEXC2DNsHAAAAKQUkWfK+X5eZX84lVFNTvmezX9Fyp3RDYVDAGf6QWgAAAKCFUh9yOex7hJ54adJUM1UPxw4FAScAAAAQoApyZwZl0PeIIfFSGalm5ud9b/XRo/5nasGmRMAJAAAQndQTycBLPQNu1veTpJmZOHr62tJDOanG1uF0zsnMmvr4YFU9pxYAAMStLWv34dj+LDl3ZjBS+H7z83GVtwmNJA368pe/rEc84hGamZkh6OzhnNOhQ4f0ne98R49//OObLg4AAAhQ6olkAMRnUNKgRno4Tz/9dN199936xje+0cTHB+2EE07Q6aef3nQxAABAoFJPJAMgLY0EnGvXrqUHDwAAYAzr12f3cIaQSKaCpdMBRI6kQQAAABEJNZFMd27p/v1+bcLu3FISGgHDpZwIjIATAAAgIk1lxhzWIN6xY+UC9pL//44d1ZYLiF3qN2saSRoEAAAwLoZt1q8/M67ke1V7A92pKd9Y7mfm1xgEkC2FRGCDkgbRwwkAAKKRek9AqIr0XubNIQ1hbmlqUh5+2UapJwIj4AQAANFg2GYzijSIQ51bmhpuuqQn9Zs1BJwAACAaqfcEhKpIg7ipuaXDpNYbyE2XavXXl+3bq68/qd+sIeAEAAATqbNBn3pPQKiKNojn5/2cs6NH/c8Qgs3UegO56VKdrPrynvdUX39CvVlTFgJOAAAwtrob9Kn3BEyiysA/1gZxir2B3HSpTlZ96VdV/QntZk2ZCDgBAMDYhjXoyw6Cmg58Qh2eWUfgH2ODOMXeQG66VKdovYi5/jSBZVEAAMDYBi2FsXv38KU0YlJkaZCmpLCsQhVS3S4sDVSNvPrSL/b6UwWWRQEAAKXq9vTl3bdevz694Ywhf5+iPXmh9tBWJdXewBh7m2OQVV/6pVB/6kbACQAARtI7fDNLt0GW2nDGkL9PkXl9KSbQGabpIdiIS1Z9eeUrqT+TYkgtAAAYyaBhZ7Ozx4b3pTacMeTvU2S4b8jlBxA3htQCAIDS5PXoma0c3pfacMaQv0+RnryQe2gBrJTS8HcCTgAAMJKiyzKkNpwx9O8zbF5fHctppNRIBpqS2vB3htQCAICRhJytFfmq3m/UC6AcMQ5/Z0gtAAAZ6I0ZT+g9fchW9X4LOYsvEJPUhr8TcAIAWim1IUt1a9uyDKncnKhyv6XWSEZxqRwfoahj+HudCDgBAK1EbwyK4uZEMak1klEMx0f5Qk5QNg4CTgBAK9Ebg6K4OVFMao1kFMPxUb7Upi0QcAIAWoneGBTFzYli6mwkt2kIZ+jfleOjGilNWyDgBAC00ji9MaE3/FANbk4UV0cjuU1DOGP4rhwf5UrxOkPACQBopVF7Y2Jo+KEaDBUNS94Qzm3b0jseYxiuyvFRnlSvMwScAIDWGqU3JoaGH6qR2nyq0Izao5M3VHN5Wbr4Yunkk/1+MpPWrYu7sR7DcNWyj48Ue/iKSvU6Q8AJAEABMTT8xtHmxt0oJh0qynbONk6PzqChmg89JH33u8f+f+iQdNFF8W7vWIarljWUukh9SPlYSvU6Q8AJAEABsTT8RtHU8K2UG4xZUh0mV4ZxenSyhnAOcuRIvD1Ekw5Xje1YG1YfUj+WUrzOSJI55yr9gM2bN7ulpaVKPwMAgKp1Gzq9jaHp6biHVs7N+QZbv9lZ30tRhRS34zBNbOdYTE35wKGfme8ty7O46OdsLi8X+5xh7xeyxUUfcB044AOPnTuLHSsxHmvD6kPqx1KM+6zLzPY45zZn/o6AEwCAYsZt+IVq3Mb+JFJvMGZpYjvHYpL6kNU4z5Ny/coT47E2rMxtOJZivc4MCjgZUgsAQEEprYsmNTN8K9U5SoOkOkyuDJMMGe1PVjMzI61Zs/p1a9e2M2NqjMfasPrQhmMpteuMRMAJAMhQ97yf2OYZpaKJ5Qza0GDsx7IR+SbNcNrbOD94UNq1yweeXTMz0gc+kEajfVQxHmvD6gPHUqScc5U+Nm3a5AAA8VhYcG562jk/cMk/pqf98yl8HlZaWHBudtY5M/+z6u3e1v1d93ZGGJrc76keaxxLYZK05HLiQeZwAgBWqHreT//8lAce8EsXVPV5CE+sc5SAUYSQAIZjDXUhaRAAoLAqkzKMkuQjpSQQANonxqQ9wLhIGgQAKKzKeT9Za6yNWg4A+ZgPHY4Yk/YAVSDgBACsUGVShqINLZJAAKPrjiDYv9+PUti/3/+foLMZMSbtAapAwAkAWGHSrJGD5DW0Zmaq+bxR0TuEmGWNIDh82D+P+pFRFfAIOAEAq1S1DlheA+yKK5pfd6zp3qFYgt1YytlGDOGs36Djocqbd0BMCDgBALUJuQHWZO9Q0+6B9kQAACAASURBVMHuoHL1Nqa3bw+znPAmGcLJjYTRFTluq7p5B8SELLUAEBjS2Dejyuy8w4SYzTIro7BZ9jYi62YYxl2GI4TlO2IU4nELNIUstQAwRCh390Pt6WqDJhN8hDgUMqvHN+8eNUM2w9A/gmBmRjrxRGnr1sHnNeZ+jmeS4zaUa84kUvgOqAcBJ4DWCynIo+HXnCYTfISYzXKUIJKsm+HoDuHcvVv63vekQ4eGn9dCvOERg3GP25CuOeNK4TugPgScAFovpCCPhl9zqppfWqQXIMRslnmNZrOV/2+6nMg2ynktxBseMRj3uA3pmjOuFL4D6kPACaD1QgryaPg1q+wEH0V7AUJMppTXmL7ssrDKiWyjnNdCvOERuu5c+8OHpTVr/HNFj4eQrjnjivk7MBS4fgScABoVwok/pCCPhl+Yxq2nr31t8V6A0LJZ5gXBV10VVjmRbZTzWog3PMpSxTWm90aSJC0vHztPF9lmIV1zxhXrdwhhKHAI7Z7aOecqfWzatMkBQJaFBeemp53zp33/mJ72z7exHL3lmZ11zsz/bKocTQtlO4xbPxYWVv5N78OsnrLHKJT9Hrsmz2uh7MOqtsHsbPZxPTvbbLnqFOt3mHTfTSrW7VaEpCWXEw8ScAJoTNMn/l6hNJDghXRRHree5v1dU3U8BiHt9xQ0cV4LaR9WdY0p40ZSCtecGL+DWbM3AUNq95RtUMDJOpwAGtPkuocIW0jr241bT/P+TpIWFsIZrhjSuq8h7XeMJ6R9WMU1ZnHRLzOT9b7U0/A1XT9TbvewDieAIMU6BwTVCykhxbj1NO/3MzNhBZtNz2fqFdJ+x3hC2odVXGN27MgPGMqYa9/K+X01ajpPQlvbPQScABrT9Ikf4QrpojxuPc37uyuuKLd8kwhtaYOQ9jvGE9I+rOIakxc4O1dfVmuMr+kEWW1t9xBwApjIJHdji574uePbPiFdlMdtoDTdsCkipN4oKaz9jvGEtA+rOAbzAufZ2fHfsyu0G0BFxHh9bjIjeAzXhUrkTe4s60HSICBddSSHCCkBBeoVekKK0MtXRIgJLFLYrm0X2z4cpbxVXpOaTmgzqpCuz6HXudDLVwaRpRZAFSZprBY9+YbYIAZCamhNIpXvAYxrnGOgquAhtutdKOUN/TwWevnKMijgJEstkLCqs0+Om22tO0+ld+jQ9HT2sJKUM7ohXk1nOixTSFlqgbqFdCyPcm0MQSjX55D2YZbQy1cWstQCLVRH8oFxk0OMMk8lpAQUSF/R+UihzX2cRJPzmYCmhXQsxza/L5Trc0j7MEvo5asDASeQqDqSD2QlhzCTtmwZ/HejnHxDSkCBtI1ykyaUhhaAyYR2LMd0AyiU63No+7Bf6OWrAwEnkKg67qjNz0vbtvkgs8s5adeuwT2po5x8Y7vji3iNcpMmlIYWgMlwLI8vlOtz6Psw9PLVgYATGCLGlN9SfXfUrrtu9RyOYT2po558Y7rji3iNcpMmlIYW0CvW61WTso7lbdv8NYztOFwI1+fQz8ehl68WedmEynqQpRYxizmzWNGyT5ptb9w07m1IEY64hJJxEfWo8xxUx2fFfL0KCdsRGI/IUguMJ/bMYsOyT5aRES/2bQR0xZYhsheZZkdT576u67M4F5eD7QiMZ1CWWgJOYIA6Un432VAs48IacyMdcajzGIkxcOMYHF2dQUVdnxXKEhWxYzsC42FZFGBMVc+DrGPpkkHKSCzE3ARUqe5jJIT5SKOqIyN1aupcpqCuzyITZjnYjui1uCitW+fbN2b+38zpHR0BJzBA1ZnFmm4olnVhjbGRjjg0fYzEgDXeRldnUFHXZ5EJsxxsR3QtLkoXXywdOnTsuUOHpIsumjzobFuCLwJOYICqe++abihyYU1Pahexpo+RGNAjM7o6z31lftag45vRJuVgO4ar7uvbjh3SQw+tfv7IkcluejY9uq0RedmEynqQpTYOZAxtRghZMdn3kwtlG6aYXTGEY6QrlP3cL8X9XofYstSyn9FmTdT/vCz8RTLxDxLSda1MGpClloATXMQaxLaPX0j7MMWLWCjbN5Ry5Ak1GEZ5Ujy+J9VEvedYa0YT9T/vMyf93HGXkwsdAScGGuUg5kRbPrZp3EJqBKZ6EQvhGAlpP4cmhP3TBqke3+Nq4iZQ6DeeUtZE/V9YcO7441d/5tq1k+3zVK8ngwJOlkVB4RTgpN4HVgsphT7rx1UnpP0cEq4L9ck7vteskXbtat/2buJ8xzm2OU1t+8VF6bWvPZY4aGZGuuKKyY63VM+bLIuCgYomnCBbJLBaSAlbSAJVnZD2c0hSvC6Emngr6/iWpOXlFiQcydBEQrGQkpiFWk+r0tT1bX5eOnjwWD/kwYOTB4VtTExFwFmzEE8QRQ/ikE60QCjH0rgXwSrK38aLWF0I5rOldl0IOXtk9/hes2b172IP8sfRxE2gUG48hVxPq5La9a11y8nljbUt68EczmNCHvtfZA5OqmPOEZ/QjqVR57CFVn54w/Zj1XMVm5wLOe5np3ZdiOH7MJfTa/MczhjqKdpHJA0KQ+wniFBOtEDsx1Ls5U9R0+e3Jj9/ks/OSqpx/PHxXhdiCOZiOn+keJMmhCRZMdRTtM+ggJMhtTWKfehRasMZqhDKMM/UxX4sxV7+FDU9F7HJz5/0s50b/P+YVD1ksoxrRCzDu+sY9tnEsMQQhkKGMrQXKIqAs0YpnCDKPNGmFpy1cU5FU2I/lmIvf4qavgnQ5OdP8tk7dkhHjqx87siReOcTVhnMlXWNiOXmb9M3cVIWy00HoIuAs4CyAiNOEMekGJxxca1P7MdS7OVPUdM3AZr8/Ek+u+lAvWxVBnNlXiNC6GUbJrW6EZJYbjoAD8sba1vWI/Y5nGXPq5lk7H8I8wbKEtMclKKYU1Gv2I+H2MufGuZwjvfZeefy7vmcen1M264RKV7nQ8X1BCEQSYPGF8oJs+nGUNlSvPCGUlcwOi7WcK75ehBjltqsa1Mq16myte0akVq7JVRsZ4SCgHMCoQRGqV2oUvs+zhU76TfdoE1Fmdsxhos19QYh69bPQT2diONcUzbOXdVLsT2FOBFwTiCUAzmUwLcsoVx4y74YDnq/UL5z7MrejqEc43moN4hFatepKhCAoWwcdwjFoIDT/O+rs3nzZre0tFTpZ1Spm9ymd6L/9HT9k7Pn5nxinX6zsz5hQIwWF32yhAMHfHKKnTvr3aZ179sU92ETyt6OU1P+8tzPzCfkaBr1BrGgrgL147hDKMxsj3Nuc9bvyFI7RCiZwFLMatl0lr26s8qSsa8cZW/HprOTDkO9QSiGZWxP8ToFjKuupd847hADAs4M/ScJqfn046EEvimpuyEfemATi7K3Y+gXa+oNQlBkKSuuU4BX59JvHHeIAQFnn5DXhyyzR7CuO28hq7shH3pgE4sqtuOJJx7798xMWBdr6g3qMui6UHRESNMjV4AQ5B0v27aN1u4q2lbjuEPoCDj71D3MsgkhB9V1qrshz13IcpS5HbvHwqFDx5773vfKK2sZqDeow7DrAkO7geLyjovl5eLtLtpqSAlJg/qEnkCkDEwwP6bpxEWo1rD9y7HQPt06sX+/tGaNbwDOznLsDzsWOFaA4vKOl36Djh+OOcRmUNIgAs4+bTjA2xBUA0WyEHMstEtWnehqIvt4SIYdC6FkbAdiMOhc02vQtYbrE2JDltoRpDxfqjsXIO8eA0lIELpR5h4XGR5PQp52yaoTXalNnRjVsGOBod1Acf3Hy5o12a8bdK3h+oSUEHD2SfWi2jsXIEsqQTXGF3oiqVHnsxSZc5byDaZhQt/fVRg237DN8xGLHAskJgGK6z1edu0a/VrT5usTEuScq/SxadMmh+bNzjrnm+mrH7Ozzi0sNF1CNGlhwbnp6ZX1Yno6rHqRV4dnZyd7/cKCf86sPcdCDPu7CoPOg4PqUlu08VgA6jLO8cUxiZhIWnI58SBzOFuCuQAYJIa5y6PWYeac5Ythf1eBOZwAAFSDOZxgLgAGimHJg1HrcKrD48sQw/6uQm+dkI7Nq6JuAABQHQLOlgh5LkAb55KFJoYbEuPU4TbPORt0XJW9v2M6hrt1wjnpBz/wP9tWN4AYxXSeAbASAWdLhNrbw8LGYQj5hkRXqHU4RMOOqzL3d1XHMI1LAF20FYDI5U3uLOtB0iAMMmoiGFRnWHICkhfEo8hxVdb+rOIYbmtSI2Tj3OO1eTvQVgDCJ5IGIVQkM4oDCXjiUudxVcVntTWpEVZr27lncdGvB3vggB/ivnOn/55t2w79aCsA4RuUNIiAE42iYRkH9lNc6txfVXwWjUt0tencMyio3LGjPdshS5vqARArstQiWDHMHUR7s5rGqs7jqorPiiGJVRHMQ51cm849O3asXrLn8GHpta9t13bIQlsBiBsBJxpFIpg4pBIAtEWdx1UVn5VC4zL2JCehBMttOvfkBY+HDkmnnpr9u6LbIZT9OS7aCkDcGFILYKi2zx9C/fLmssUi5iGAIR3vIZWlanl1RpJmZqTvfW+87dCmbQigOQypDUSMdxhjLPO42vRdR8XdZdQt9jVUYx4CmTe0c8eO+svSpnPPoB78++4bfzuEtD8BtBM9nDWJ8Q5jjGUeVbcXZf9+fxHvPRxS+64A6hNzDydJm5qzbp0fQtuPJFwAQkcPZwBivMMYY5lH0TvHSlp9QU7puwJt1sTohRDnoRbdDm2aNxmaK64gCReA9BBw1iTG4VVNl7nqRmJWQN0v5P2TIoY1o2xlJe8ZtW6GNhR0lO0QYrDcFiThApAihtTWJMbhVU2WuY7hvHnDjHqFvH9Sk7XPzaTLLpOuuqq5ciFuZZzHUpheMOp2iD1pE1ZifwKo2qAhtQScNYmxwdJkmesIdgdlBJTC3z+pydsfZtLu3ewHjKeM+Wsx3jDsxzy+8RGsAcBwzOEMQGjDq4possx1DOfNGmZk5n/GsH9Sk7dvnWMuLcZXxvy1pqcXlIF5fOOJfT1VAAgBAWeNYkzz31SZ62gcZQXUu3f7RkUs+yclg/ZtTA17hKWM+WspBGvM4xtP6snzAKAOBJwBIFHKanU1jmK8CZCqnTuP9TD3i6lhj7CUMVJjlPNRqOfzEEfZhLqteqXQuw0ATWMOZ8NinNtZF+bNtM/27dJ738t6qAhPkfMR5/PiYtlWKczfBYA6kDQoYFzM0Hb9DfktW6TrruNGA+LD+by4WLZVLIExADSNpEEBY7gO2iwrIceuXT7IbPMw5xiGGmI1zufFxbKtQhyKDACxIeBsWArJKFAMQcRqJORYjayY8eJ8XlxM24q5/gAwGQLOhrUtc2Bbgy6CiGyx9HLUiSA8Xm07n0+CbQUA7UHA2bAiw3VSCdLaHHQRRGSLqZejLgTh8Wpq+GWM1wiGqgJAe5A0KHApJSwoI0lErJlrp6ZWZl7tMvPDtFJEVs/xxJJMBWHgGAIAhICkQRFLqWds0p6bmHtI29aTV3Rf0cuxWp1DDWPsGcNKKV0jAABpooczcCn1jE3acxNzz0/beiFi3lchqKMnv211MlUpXSMAAPGihzNiKfWMTdpzE/Pctrb15MW8r0JQR1ZMesaqUXevcUrXCABAmgg4A5dSJr9Jg67YG1ZtSq0f+75qA24KlK+JYf8pXSMAAGki4Axcaj1jkwRdsTas8no8Up4/F+u+akoTdYGbAuVrotc4tWsEACA9zOFEVGLLUps3T27bNmnXrrTnz8W2r5rS1FxK5nCWj/mUAIC2GjSHk4ATtWljAJKXPGfNGml5efXzJNVpnyYTLLXxmKwSybIAAG1FwInGtbU3Ja/HIw89Ie1Dr1g62nqeAwCALLVoXN7cpm3b0pq72C9vPtyaNaO9HuliLmU6mE8JAMBqBJyoRV7my+Xl6rM4Nikvec6ll5JUBx4JltLSpmzUAAAUQcCJWgzqrTl8WHrta+srS53yejyuuoqeEHj0igEAgJQxhxO1yJrb1G9hgUY2wkNiHQAAgMGYw4nGdXtx8uYuStWuVQeMo3ujZP9+n9hn//60h4ADAACUjYATYxt1sfr5eb/2ZJ68eZ5AU/KSXXFzBAAAoBgCToxl3J6f+XlpZib7d2TlLG7UYB/jybsJws0RAACAYgg4MZZJen6uuIKsnJNgmGd9WLIEAABgMgScGMskPT9k5ZwMwzzrw5IlAAAAkyHgxFgm7flhrbrxMcyzPtwcAQAAmAwBZyBim5OX1fNjJm3Z0kx52oRhnuUpctxxcwQAAGB8BJwVK9KgjXFO3vy8tG2bDzK7nPNZaEMudwoY5lmOGI87AACA2JhzrtIP2Lx5s1taWqr0M0LVbdD2zrebnl49JG9uzjd2+83O+h6VUMVa7hQsLvo5mwcO+J7NnTvpeRsV9RcAAKAcZrbHObc563f0cFaoaHKXWOfkxVrukA3rEe/+futW///duxnmOS7qLwAAQPUIOCtUtEEb65y8WMsdqmFDPBkCWi7qLwAAQPUIOCtUtEEb65y8WMsdqmE94iyHUi7qLwAAQPUIOCtUtEEb69ILsZY7VMN6xBkCWi7qLwAAQPVIGlQxkrugqGFJbEhyAwAAgBCRNKhBrOGHoob1iDMEFAAAALEh4AQCMWyIJ0NAAQAAEBuG1AIAAAAAxsaQWgAAAABA7Qg4gRZbXPTJiKam/E/W9AQAAECZCDgjQ4CAsiwuSpde6jPfOud/XnopdQoAAADlIeCMCAECyrRjh3T48MrnDh/2zwMAAABlIOCMCAECynTgwGjPAwAAAKMi4IwIAQJDisu0fv1ozwMAAACjIuAcIqQAp+0BAkOKy7VzpzQ9vfK56Wn/PAAAAFAGAs4BQgtw2h4gMKS4XPPz0tVXS7Ozkpn/efXV/nkAAACgDOacq/QDNm/e7JaWlir9jKrMzfkgs9/srLRvX92l8RYXfYB14IDv2dy5sz0BwtSUD/z7mUlHj9ZfHgAAAACSme1xzm3O+t1xdRcmJiHOmZyfb0+A2W/9+uwbAG0ZUgwAAADEhiG1A7R9zmQIeufQPvCAdPzxK3/fpiHFAAAAQGwIOAdo+5zJpvXPoT10yP+cmWHOIQAAABADhtQO0A1k2jpnsmlZSYKOHJFOPlk6eLCZMgEAAAAojqRBCBZJggAAAIDwDUoaxJBaBIs5tAAAAEDcCDgRLObQAgAAAHEj4ESw5ud9UqDZWZIEAQAAADEiaRCC1uZ1RwEAAIDY0cMJAAAAAKgEAScAAAAAoBIEnAAAAACAShBwAgAAAAAqQcAJAAAAAKgEAScAAAAAoBIEnAAAAACAShBwAgAAAAAqQcAJAAAAAKgEAScAAAAAoBIEnAAAAACAShBwAgAAAAAqUSjgNLM1ZvYiM3uhmR3X8/wvVFc0AAAAAEDMivZwXitpo6QNkv7BzJ7Uef6VlZQKAAAAABC944a/RJL0o865eUkys12SPmBmb6ysVAAAAACA6BXt4fwhM/shSXLOfVnSz0p6vaQzqyoYAAAAAARjcVGam5OmpvzPxcWmSxSFgT2cZrbGObcs6dcknSLpXklyzn3HzH5O0kuqLyIAAAAANGhxUbr0UunwYf///fv9/yVpfr65ckVgWA/n35jZyc65f3LO3dv7C+fcsnNuocKyAQAAAEDzduw4Fmx2HT7sn8dAwwLOWyV9ysx+tPuEmZ1tZp+stlgAAAAAEIgDB0Z7Hg8bGHA65/6zpPfIB50vNrPrJf2JpI/VUTgAAAAAmEgZcy/Xrx/teTysSNKgT0v6tqRFSV+R9Hjn3DsrLRUAAAAATKo793L/fsm5Y3MvRw06d+6UpqdXPjc9LW3ZQiKhIQYGnGb2EUk3SvozSS+S9BxJ51ZfLAAAAACYUFlzL+fnpauvlmZnJTP/c9s2adeuyYPZxJlzLv+XZm+T9Dbn3H2d/z9V0l9Ieodz7soiH7B582a3tLRURlkBAAAAoLipKR8M9jOTjh6d7L3n5nyQ2W92Vtq3b7L3joyZ7XHObc763bA5nG/oBpud/39W0k9Kenm5RQQAAACAkhWdeznOPE8SCRVSZA7nCs65eySdVUFZAAAAAKA8eXMvd+489v9x53mSSKiQkQNOSXLOfafsggAAAABAqbLmXl59tX++a9x5nkWCWQyew1kG5nACAAAACNYk8zwXF31geuCA79ncuXNlMNsSY8/hBAAAAICkjTI0tn+up+QTBB096n+2MNgchoATAAAAQHsVHRpb1pqeLUPACQAAAKC9iszzlMpb07NlmMMJAAAAAMNUuaZn5JjDCQAAAACTYBmUsRBwAgAAAMAwLIMyFgJOAAAAAOXozeK6bp1/dDO6xp5cp+hcT6zAHE4AAAAAk+tmce1PrNM1PU2AlijmcAIAAACoVlYW115kdG0lAk4AAAAAkztwoJzXICkEnAAAAAAmVyRbKxldW4eAEwAAAMDksrK49urP6NqbYCiFpELIRMAJAAAAYHL9WVxnZvwjK6Pr9u3S1q3S/v2Sc/7npZdWG3QS4DaCgBMAAADjK9KIp6HfHvPz0r590tGj0sGD/nH0qH+uG2wuLkrvfa8PNHtVmVSom0G3zgAXklgWBQAAAOPKWgajf+mLIq9Bu8zN+YAvi5kPUOv6zNlZHwxjIiyLAgAAgPJlLYPR30tV5DVtQU+vNyhTbVVJhfI+k6y5lSPgBAAASFmVQU6RRjwNfY8hncfkBZVmK5MK1fGZZM2tHAEnAABAqqoOcoo04mnoe/T0HpOVzdZMuuyy6oZZZ31mf9ZcVIKAEwAAIFVVBzlFGvE09D16eo/pz2Y7Oyvt3i1ddVW9n8k84lqQNAgAACBVU1OrM4FK5SZmWVz0AeyBA77XcufO1Y34Iq9JHUlrkLBBSYMIOAEAAFJFkBMOsvUiYWSpBQAAaCOGs4Zj0iGdZLgNH/soEwEnAABAqpi3Fpb5ed+zfPSo/zlKsEmG2+pNEjCyj3IxpBYAAAAIGUOjqzfJkOfFRWnbNml5efXvWrKPmMMJAAAAxKqO5E9tN25QnxWo9mrJPmIOJwAAAPIx9yxsrGVavXGXrclaeqgX+4iAEwAAoNWYexY+kj9V79RTR3u+a1BAyj6SRMAJAADQblk9NIcP++cRBpI/hSuvB3PNGvZRB3M4AQAA2oz5gcD4xwHrq0piDicAAADyMD8QGP84KLP3OdG51AScAACgGok2npLD/ECkYpJzziTHwbjrq/ZKeC41AScAAChfwo2n5DA/ECmY9JzT9HGQ8Fxq5nACAIDysVB9uhYXfSP4wAE/3HDnToJT1GNQ3Yv9nBP5XOpBcziPq7swAACgBcZd0w5h60+Q0u1Fkgg6Ua1hdS/2c8769dkBcwJzqRlSCwAAyldFIpqq5oSmPNe07O+W8LC/RqRc98o2rO7Fnvwq4bnUBJwAAKB8ZTeesuZnbd0qbd8+WTlTnmtaxXeLvRcpJCnXvSoMq3uxB2xNzyGtEHM4AQBANcqc65c3P8tM2r27/PeNZd7XIFV8t5S3V93YlqMpsr2YX9yYQXM4CTgBAED48hJqSJM10CNP1DFQFd+NRe7Lk3LdqwJ1L2iDAk6G1AIAgPANmoc1yXDO2Od9DVLFd0t42F/tUq57VaDuRYuAEwAAhG/nTt/IzDJJAz32eV+DVPXdyljkHmnXvapQ96JEwAkAAMI3Py9ddtnqoHPSBnrKvSYpf7cUsH/QEszhBAAA8UghKUgK3wEAejCHEwAApCH2IXUshYEmse4nGkDACQBASmhQhm3Y4vWxot6Fj5sdaAhDagEASAXLBoQvxaUwqHdxYN1PVIghtQAAtEGqvWcpSXEpDOpdmPp7nbOCTWmyZYWAAgg4AQBIRV7DMdQGZRuHYaa4FEZs9a4NsobPVrGsEFAAAScAAKmIqfesrfPJUlwKI6Z617S6brJk9To7V/6yQkABBJwA0DZt7FVqi5h6z9o8DDP2TLv9Yqp3TarzJkte77Jzad3sCB3XW0kEnADQLqH0KnERrkZMvWcMw0xHTPWuSXXeZMnrXe4mCErlZkfIQrneBoAstQDQJkWyFFa9KD0ZLSGRMRPtU2eGYs6zzWvZOY4stQAAb1ivUh13ZNs8lBLHMAwTbVPnXFd6netHVuBcBJwA0CbDGjx1BIMMpYxXmUOhaRBXi2Hr4an7JkuTc4XbVv/ICjwQAScAtElWg+f446UHHvANgzruyJLRMk5V9H6nljynCVkNe+aOhaktN1naVP+6x98FF5AVeADmcAJA2/TO0Tz1VOnb35aOHBn8N2XOOWFuUZxaNh8pCnnH0oknSocOrX49+yoeVc+lr1JbzhVZx1+W2dk49+OImMMJADimt1fp5JOHB5tl35Fty13+1DAUOjx5Q+Czgk2JfRWL2HsIB50rUhpqm3X89SMrsCQCTgBot0EN0CqDQYZSNmucRh9DocMzagDJvopDqInVip438urZqafGHUj3G3b8tXT4bBYCTgBos0FrtREMpmnc3pOqE56k1PMxTFnfNe/4nZkhA3DMQhxNMMp5I+9cIYUZSI9r0A0cRu6sQMAJAG3G0hQrhRL0VFmOcXtPqhwKHfsQwlGU+V3zjt8rrmDYesxCHE0wynkj71xx333Z7x3rUO+8429hYbKbtaFch8rknKv0sWnTJgcACNjCgnOzs86Z+Z8LC02XqBkLC85NTzvnwwD/mJ6uf3uUXY7+/dv7vr0PszK/xWjyyjU721yZqlL2d+X4TU8o56JeZpOfN1I8zss+/kLc9wVJWnI58SBZagEAkMLJrFhmObKyKJr5ZkwZ71+WqansMpn5od0padN3xfhCy1JbxnmJDOXDhXIdGgNZagEAGCaUeVNlliNrGFyIa8OFOISwKm36rhhfaInVyph+QYby4UK5DpWMgBMAACmcQKDMcuQ1UpwLq9HXprnEbfquSEdZwWJogXRoQrkOlYyAEwAAKZxAoMxyDMpCHFKjr009H236dYBWTwAAFY1JREFUrkgLwWL1QrkOlYyAEwAQlqYy9IUSCJRZjpgaL21qzLbpuwIoLpTrUMlIGgQARYWWxCFFJJUoH/UWQOw4jwVvUNIgAk4A4QvhQkMgVI+IM/QBACrA9TcKBJwA4hXKhYZAqB4sGQEA6MX1NwosiwIgXlnLOhw+7J+vU6KpyoOTaIY+ADVpag44qsP1N3oEnADCFsqFhkCoHjEluUFzCCqQpTsiZv9+P1Ji/37/f+rHSrEdP1x/o0fACSBsoVxomgyEYmscTCLRDH0oEUEF8oQyIiZkMR4/3IiMHnM4AYRt0BxOqd5kQk0kLwplDisQCuZzIQ9zwIeL9fgJIXkgBmIOJ4B45fV4SfXfpW1i7bw237GPtWc31nLHIpRh9qmLsR6HMiImZLEeP21cuzbGYzAHASeA8GVdaNoSiMXaOMhT9AIa47AvKd5yx4Sgonqx1uMqhl4m1OiXxPETi1iPwRwEnADilFoglielxsEoF9BYbyjEWu6YMJ9rcsOCqFjr8aRzwPu3y/bt4TT6ywp8OX7iEOsxmIM5nADiFOs8lFGlNIdzlH0W61ysWMsdmzrnc6U2d6zIOaWN9Thru5hlb4e6rzNlXwdSq9MpivAYHDSHk4ATQJxSCsSGSaVxMMoFNNYbCrGWG9lSPM8UqaNtrMd53zlL3Y3+Nu6Ptotwn5M0CEB62rR8RirJEkYZHhzrsK+yy53a/LHYJDasTVKx6QixHn+TGGU6Rt1TGtoyhQTHJHYMEnCiPjScULZUArG2GOUCGusNhTLLnVjSiCil2NAvcuMn1uNvEqeeWux1TTT6q5zLT9ssTIkdgwypRT1SHJYEYHSpDA+uQ4RDqpKT4j7gepxt3Trp0KHVz590kv9dk+esqvYZdQElYkgtmpfisCQgZk3d1aZXurhJetdi67UItbyJDWuTlFzPSWnuuy/7+cOHmz9nVbXPaJuhJvRwoh55yUIkf/KkpwOoD3e14zBu71ps+zf08tIr3w4p9mYPE2EmVISLHk40b9A8g9jnJoV6Zx7Iw13tOIzbuxbb/g29vPTKt0OKvdnDpLTOM4JGwIl6ZJ3I+4XUwCiKpB6IUYqJUFI07jC62PZvbOVFmto41LiNQTYaQcCJevSfyPPE1sAI/c48kIW72vEYp3cttv0bW3mRrth6sycdYdVUkM3IsNYh4ER9ek/ks7PZr4mtgcGdecSIu9ppi23/xlZeIARljbCqO8iOeWQYgfLYCDjRjFQaGNyZR4zaOHSsTWLbv7GVFwhBrCOsYi13k4FyAoEuASeakUoDI5XAGe0Ty9CxBC60jYhl/3b1l1div8eOY7dasY6wirXcTQXKMfcI9yDgRHNiaxBlKTtw5gKdr+ptw7YPz/bt0tat0V9oo9P0sZBIA6vV2IfVi3WEVazlbipQjrVHuJ9zrtLHpk2bHIACFhacm552zl+e/WN62j/fdlVvG7Z9eBYWnDNbuU+6j9nZpkuXrhCOhdlZ9nuoFhb8fjDzP/PqBfuweiEcq+OItdxN1emsz+w+AiNpyeXEg/RwAqFI5S5WFareNjFv+6Z7o6qyY0f2guRSeXeUU912kwjhWIh1yF3qRum1ZB9Wr8mpSZOcO2OdUtXUFKo1a0Z7PlDm8i7oJdm8ebNbWlqq9DPQAouLvsFz4IAfdrFzZ/gnp1FNTWU3sM38sOM2q3rbxLrtuw3A3gBhejqOi/cweftE8g2U7jy/caW87SYRwrEwN+eDmX5l7HeMb5T9wj5MV5vPnU20RQctJVhxDDcqM9vjnNuc9Tt6OEPBnfZ8bZkLEuu8hjpUsW16j7mpnFNh6Ns+hN6oquRte7Ny7iinvO0mEcJ5iGRsYRql17Kt+7ANbbk2nzubyD2St4xg3vOBIuAMQVsCqnG15eTW1gt0EWVvm/5jbnl59Wti2PaDGoCxN3yy9rmZdNll5VzkGfKXLYTzUKxD7vrFfgz2G+VmRCr7cBRtactx7qxXCOfkMuRN7izrQdKgAphcP1he4hCzpktWPIFCU++XkjK3Td4xt2ZNXNs+73vMzMSZlKFflccD5918nIcmF2tilEFS/E5lass5JeXvGeq5L9Ry9dGApEHM4QxBCHNmQhbqXJA2z2OIXSrHXF4dPPFE6dCh1a9v+pgJSarHbxvmu8cg1OvWpKhf+VK5rgyT8rkzxe9VI+Zwhi6EOTMhC3U4QVuG+qYolWMub9jaffdlv54hT8ekOOSvLUP6YpDqsMMU1s+uSirXlWFSPHdKtOkqRsAZglADqlA0fXLLm4eTaoOiDVI65rIagG1p+EwqtcYzDaZwFD0GU5vn2WYpXVeGSe3cKdGmqxgBZwiaDqhi0NTJbVCPQRONehon5Uj9mGtTwwfH0GAKR5FjkB7ptKR+XUkdN2qrlTe5s6wHSYMQtUGT4+tOoFD150UyKR0FsT/bJ+VkHjEadgyyvxCz1K4xJMWamAYkDaKHs+3oMRtsUI9B3Xczqxwux5329KQ45AmD0bM9XJ3XvGHHYJk90lzLUacU2wz0UFcrLxIt60EPZ8C4mzNcSHegs8rRfUwqpO+JMKR297otQt9vTZYvtGteWefdOr9X6PUL9aDNgAxiWRRkSjVte5lCSpN93HHS8vLq59eskX7wg8neuy3p3FFMSPUe6Wi6XoV2zStre9T1vZrefwgHbQZkYFkUZCPBxHAhDbHICjYHPT8KJsujF9lOUYWm61Vo17yyri91fa+m919qYh4GTZsBIyLgbDNOGMWEMhdudna050cR89yvmC/aoQqtYY40ZPXCSfXVqxCveWVcX+r6XpwXyhP7HMiY2wxoBAFnm3HCiEuV+yukntxRxH7RDtWwBixBPka1uOjPLVnqCvhSvebV9b1CDNhjFXtvcaxtBjQnb3JnWQ+SBgWOBABxYX+tVDRxAdttNHlJSF75SudmZlZv71SSjQ2rJ9Sj8eUdq2b1Jw5KcR/W8b1CS7oUM7P84wGIlEgaBCBJRRIXkOhiPIuL/m77gQO+B2PLFmnXrtV35btiTzY2rJ5QjyaTd6xK+c8jPP3nhZ07J6//Vbxn6EJLYAWUgKRBQIgYlji5IkO8Yh+61JT+uWXXXZcfbErxz+MaVk+oR5PJO1bLmIMegracz8uYc9q7rdatky6+uH3TIlId3g3kIOCMVVsubqli7mE5ily0SXRRjmHbK/Z5XMPqCfVoMik3sCc9n7fpet6/rQ4dkh56aOVr2nAjhzmQaBkCzhgRrMQvxd6SJhpNRS7aJLoox6DtlULgMKyeUI8mk3IDe5Lzeduu51nbKksbbuSEkgEfqAEBZ4xSDFbaJrXekiYbTcMu2pP0rLSp52GYrO0oSTMzaQQOw+rJpD101KV0G9iTnM/bdj0veo3jRg6QFALOGKUWrLRRar0lITeaxu1ZaVvPwzBZ23FhQTp4MI3AYVg9maSHjrqUtknO5227nhfZJimMmACwAllqY0R2s/illvGySLbY2HCcoSzUpeZVmQm16Pk8qww7drSrbmRtq7VrpUc+UrrvvvZkqQUSRJba1KScfKEthvWWxDb8LrUeW6l9PQ+oDnWpWVX3MBfp/c4rw5Yt7bqeZ22rD3zAj5RIbag1gIfRwxmrNq5b1RYx9n7GWOZh6JVCWahLzQph+w8qQ7enk+s5gIjRw1mHunukUk2+gLDnQ+ZJMQMlIwlQFupSs0LoYR5UBq7nABJHwFkGEkKgTHU3jsq6WZJaoynFIBrNoC41K4Qh/yGUAQAaQsBZhhh7pBCuOhsm3CwZLLUguq1CmBNNXWpOCD3MIZQBABpCwFmGEIbrIB11Nky4WYJYFQ0iuanSHnl1IoQe5hDKAAANIWlQGUJISIC01JUUKsXlTJC+UZJUcX5uhxQTlwFARAYlDSLgLAMXOsSKxjhiNEq95aZKO3AuA4BGkaW2agyV8UKYJ4XRMK9oPNT1Zo0yjYFkLe0Q29QWziEAWoSAsyxtTwgRwjwpLuCj42bJ6EKo6203ShDJTZV2iOnGAucQAC1DwFkUwcxgTSef4QI+vrbfLBlV03UdowWR3FRph5huLHAOAdAyBJxFEMwMtriYPXdGqm84Exfw+rT95ktsQ/diVlbW0UluqrS9vsciphsLnEMAtAwBZxGhBzNNNoi6wXieuoYzcQGvBzdfyhm6RxAz3LC6VkfPPPU9LrGM1ohp+C8AlICAs4hhwUx/43H79voak003iLKC8a46hzOldAFvOhgZ9Pmh33wZpKztOunQvaaP2ViEUNcmKUPTxzHCFdPwXwAog3Ou0semTZtc9GZnnfNNw5WP2VnnFhacm57O/n33MT3tX1d32epglv+9q/rOWbL2Q5XbvSpNf49hn5+3v83qKd+4yt6uCwv+GDM7dh4oquljNhYh1LVxy9D0cYzwTXIOAYAASVpyOfEg63AWMWidzR078ucv9qpqLbCm15gLae2zxUW/Pw4c8D2bO3fWP6Rq0jI0vT2HfX7T5RtXSOVu+piNRQj7bNwyhFB2AABqxDqckxqUjKDoHMGq5hI2PZQ0pKFBTc/fKWOoZNNzUYd9fkj7exRNb9deTR+zsQihro1bhpDqGwAADSPgLCovmCnaSKyqMdl0oyymzIBVK2POWdPByLDPj3V/N71dezV9zMYihLo2bhlCqm8AADSMIbWTyhpu2687/LaqhlIIQ0lRzlDJQcO369inTX9+VUL7XhyzaQutvgEAUDGG1FYp6w74K19Z7135poeSwiujV6PpXp2mP78qoX0vjtm0hVbfAABoED2cIaC3Iw1N9WpQfwAAANAgejhDxpp8zSl7nbwmejWoPwAAAAgYPZxNI31+M1KZY0X9AQAAQMPo4QwZ6fObUUZG2RBQf4DqlD0KAgCAFiLgbBrp85uRSqBG/YkDgUt8soarX3CBtG4d+w8AgBEQcErNNgZZk68ZqQRq1J/wMc82TlmjICTp0CH2HwAAIyDgbLoxSPr8ZqQSqFF/wpfK8O22GTTagf0HAEBhJA0i6Up7sZwIhimjjkxN+ZtZ/cz8OpwIU961oYv9BwDAw0gaNEheg2JQQwNpmJ/3NxWOHvU/CTbRq6zRD6kM326brFEQvdh/AAAUQsC5Zs1ozwNoh7KGwqYyfLttusPVZ2ZW/479BwBAYQScy8ujPQ+gHcrKZMw823jNz0sHD0oLC+w/AADGxBxO5nACyMK5AQAAoBDmcA7CcDcAWTg3ZGNNUQAAMAICToa7AcjCuWG1ppeRAgAA0WFILQCgGIYZAwCADAypBVAOhlO2Q95+LiuREgAAaA0CTgDFtH04ZVuC7UH7mTVFAQDAiAg4ARRT1rqUMWpTsD1oP5NICQAAjIiAE+3Vlh6rsrR5OGWbgu1B+5lESgAAYEQEnGinNvVYlSXV4ZRFbjy0Kdgetp/n532CoKNH/U+CTQAAMAABJ9ophB6roj2sofTEpjicsuiNh1SD7Swp7mcAANAYAk60U9M9VkUDnZB6YlMcTln0xkObgrAU9zMAAGgM63CinZpeT7Do5zddztRNTflAvp+ZHzLaa3HRB6IHDviezZ07CcIAAADEOpzAak33WBXtYW26JzZ1owyVZe4iAADAyAg4UUwo8wjL0vSwwaKBTpvmDjah6RsPAAAAiSPgxHAhzSMsU5M9VkUDHQKiajV94wEAACBxzOHEcMwjrEbROYHMHQQAAEDAmMOJyTCPsBpFe1hTnDs46hDt1IZ0AwAAtMRxTRcAEVi/PruHk3mEGEd3iHZ3OZLuEG0pv4d3lNcDAAAgGPRwYrgi8wjpgUJRRde+HPf1AAAACAYBJ4Ybllgl1aRCqMaoQ7QZ0g0AABAtkgZhciQVwihGrS/ULwAAgKCRNAjHVDH0lR4ojGLUpV5YGgYAACBaBJxtUnTo66hBaV7yIJIKIcuoa1+yViYAAEC0GFLbJkWGJvZnBJV8b9KgBv44fwMAAAAgCQyphVdk6Os4GUHpgQIAAACQgXU426TIeprjzsecnyfABAAAALACPZxtUiT5CvMxAQAAAJSEgLNNigx9bXtG0Cqy+AIAAAAt1e6As43Bxfy8TxB09Kj/2T8Mtj8onZmRTjxR2ro1/W1UNIsvAAAAgELam6WWzKrDtW0bFcniCwAAAGCFQVlq2xtwElwM17ZtNDXlezb7mfkeYQAAAACrsCxKlnGzsbZJk9uoieHOJEwCAAAAStXegLONwcWoQVzRbVR2cNjUXMq2J0wCAAAAStbegLNtwcU4QVyRbVRFcLhjx8p5o5L//44d479nEUWy+AIAAAAorL1zOCUfFO3Y4YeIrl/vA6lUg4tx52MO20ZVzPNkLiUAAAAQDZIGobogror3bVuyIgAAACBiJA1CdXNWq3jftg13BgAAABJFwNkWeUHcli2TJfypIjhkLiUAAACQBALOVPVnjpVWB3Hbtkm7dk2W8Keq4HB+3g+fPXrU/yTYBAAAAKJDwNmribUfR1G0fHmZY6WVQdx115WTDZbgEAAAAEAGkgZ1dYO03gBsejqcoZyjlK9o0h2ywQIAAACYEFlqiwg9M+oo5SsaSIb+nQEAAAAEjyy1RRw4MNrzdRulfEUzx5INFgAAAECFCDi7qlo2pCyjlK9oIEk2WAAAAAAVIuDsCr23b5TyjRJIkvAHAAAAQEUIOLtC7+0btXwEkgAAAAAaRtIgAAAAAMDYSBoEAAAAAKgdAScAAAAAoBIEnAAAAACAShBwAgAAAAAqQcAJAAAAAKgEAScAAAAAoBIEnAAAAACAShBwAgAAAAAqQcAJAAAAAKgEAScAAAAAoBIEnAAAAACAShBwAgAAAAAqQcAJAAAAAKgEAScAAAAAoBIEnAAAAACASphzrtoPMPuGpP2VfggAAAAAoCmzzrkfzvpF5QEnAAAAAKCdGFILAAAAAKgEAScAAAAAoBIEnAAAAACAShBwAgAwATP7XTP7aM//325mf2dma5ssFwAAISBpEAAAEzCzGUl3STpH0jMlvUrSTzrn7m+yXAAAhICAEwCACZnZGyW9SNKj5IPNr5jZoyRdL+kMSc90zu1tsIgAADSCIbUAAEzu/0h6qqTfcs59pfPcYUnPk/ThxkoFAEDDCDgBAJiAmT1V0nsk7ZJ0cfd559wR59w3GisYAAABIOAEAGBMZvY4SX8p6TJJ2yU91czOabRQAAAEhIATAIAxmNkjJV0n6fecc3/hnDss6e2SdjZbMgAAwkHSIPz/7dwxEcMAEANBiZxxGJAZpDGK4AsK2UV2EXx7o5kHYKjtneTyNAiAf2ThBICRtt8kR5JP2/PlcwDgcRZOAAAAJiycAAAATAhOAAAAJgQnAAAAE4ITAACACcEJAADAhOAEAABgQnACAAAwITgBAACYEJwAAABM/ACMfhvSaaPCaAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m0 = 200  # no. of training examples for class 0\n",
    "\n",
    "\n",
    "# Generate class 0 data points randomly from a uniform distribution\n",
    "#    Here a & b are 2 dimensions for each data (feature) point\n",
    "a = np.random.rand(m0,1)\n",
    "b = 4 + a + np.random.rand(m0,1)\n",
    "\n",
    "\n",
    "# Concatenate the 2 dimensions of each feature to create the data matrix for class 0 \n",
    "X0 = np.concatenate((a, b), axis=1)\n",
    "\n",
    "# Create the target vector for class 0 (target is coded with zeros)\n",
    "X0_target = np.zeros((m0,), dtype=np.int).reshape(-1, 1)\n",
    "\n",
    "\n",
    "m1 = 200  # no. of training examples for class 1\n",
    "\n",
    "\n",
    "# Generate class 1 data points randomly from a uniform distribution\n",
    "#    Here c & d are 2 dimensions for each data (feature) point\n",
    "c = np.random.rand(m1,1)\n",
    "d = 6 + c + np.random.rand(m1,1)\n",
    "\n",
    "# Concatenate the 2 dimensions of each feature to create the data matrix for class 1\n",
    "X1 = np.concatenate((c, d), axis=1)\n",
    "\n",
    "\n",
    "# Create the target vector for class 1 (target is coded with ones)\n",
    "X1_target = np.ones((m1,), dtype=np.int).reshape(-1, 1)\n",
    "\n",
    "\n",
    "\n",
    "# All training examples for class 0 and 1\n",
    "X = np.append(X0, X1, axis=0)\n",
    "\n",
    "# All target values for class 0 & 1\n",
    "y = np.concatenate((X0_target, X1_target), axis=0)\n",
    "\n",
    "\n",
    "# Create a 1D row vector ofthe target with float values\n",
    "y = y.ravel()*1.0\n",
    "#print(y)\n",
    "\n",
    "\n",
    "\n",
    "# Draw a scatter plot\n",
    "plt.figure(figsize=(16,8))\n",
    "plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bo\", label=\"Class 0\")\n",
    "plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"ro\", label=\"Class 1\")\n",
    "plt.title(\"Linearly Separable Data: No Outliers\", fontsize=18)\n",
    "plt.legend(loc=2)\n",
    "plt.xlabel(\"$x_1$\", fontsize=12)\n",
    "plt.ylabel(\"$x_2$\", rotation=90, fontsize=12)\n",
    "plt.xticks(())\n",
    "plt.yticks(())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train the Linear SVC Model\n",
    "\n",
    "We scale the data first. Then, train the model.\n",
    "\n",
    "For performing these two tasks we deine a pipeline object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "         steps=[('scaler',\n",
       "                 StandardScaler(copy=True, with_mean=True, with_std=True)),\n",
       "                ('linear_svc',\n",
       "                 LinearSVC(C=1, class_weight=None, dual=True,\n",
       "                           fit_intercept=True, intercept_scaling=1,\n",
       "                           loss='hinge', max_iter=1000, multi_class='ovr',\n",
       "                           penalty='l2', random_state=42, tol=0.0001,\n",
       "                           verbose=0))],\n",
       "         verbose=False)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scaler = StandardScaler()\n",
    "svm_clf = LinearSVC(C=1, loss=\"hinge\", random_state=42)\n",
    "\n",
    "scaled_svm_clf = Pipeline([\n",
    "        (\"scaler\", scaler),\n",
    "        (\"linear_svc\", svm_clf),\n",
    "    ])\n",
    "\n",
    "scaled_svm_clf.fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Understanding the Performance of the LinearSVC Model\n",
    "\n",
    "To know whether the model created hard margin classification or not, we need to **visualize the decision boundary and the two margins**.\n",
    "\n",
    "\n",
    "### Drawing Decision Boundary\n",
    "\n",
    "\n",
    "In the SVM, the decision boundary is **solely determined by the support vectors**. Thus, to draw the decision boundary, we need to get the support vectors.\n",
    "\n",
    "Unfortunately, the LinearSVC model does not give the support vectors directly (however, SVC does). Thus, we will have to compute the support vectors for drawing the decision boundary.\n",
    "\n",
    "Let's present the equations for calculating the support vectors.\n",
    "\n",
    "### Calculating The Support Vectors\n",
    "\n",
    "First, we state the decision rule for a single sample $\\vec{x}$:\n",
    "\n",
    "$\\vec{w^T}.\\vec{x} + b \\geq 1$, then class = positive (+1), otherwise negative (-1).\n",
    "\n",
    "The decision boundary is perpendicular to $\\vec{w}$ and its displacement from the origin is controlled by the bias $b$.\n",
    "\n",
    "\n",
    "For the entire dataset $\\vec{X}$ and class label $\\vec{t}$ (represents the class labels -1/+1 of each sample in the dataset), the decision rule can be written as follows.\n",
    "\n",
    "$\\vec{t} * (\\vec{X}.\\vec{w} + b) \\geq 1$\n",
    "\n",
    "For sample $i$, if $t_i = +1$ (belongs to positive class), then\n",
    "\n",
    "$\\vec{w}^T.\\vec{x}_i + b \\geq 1$\n",
    "\n",
    "However, if $t_i = -1$ (belongs to negative class), then\n",
    "\n",
    "$\\vec{w}^T.\\vec{x}_i + b \\leq -1$\n",
    "\n",
    "From the above decision rule we derive the fact that the support vectors that reside on the decision surface satisfy the following equation:\n",
    "\n",
    "$\\vec{t} * (\\vec{X}.\\vec{w} + b) < 1$\n",
    "\n",
    "We will use this equation to compute the support vectors. For this we need to get the weight coefficients ($\\vec{w}$) and bias ($b$). The LinearSVC model provides these weight values by the following two attributes.\n",
    "\n",
    "- coef_: Weights assigned to the features (coefficients in the primal problem). This is only available in the case of a linear kernel.\n",
    "\n",
    "- intercept_ : Constants in decision function.\n",
    "\n",
    "However, there is an issue.\n",
    "\n",
    "We used **scaled data** to train the LinearSVC model. For computing the support vectors we need the **unscaled weight parameters**.\n",
    "\n",
    "\n",
    "### Unscaling Weight Parameters\n",
    "\n",
    "To unscale the weight parameters, we do the following.\n",
    "\n",
    "$\\vec{w}_{unscaled} = \\vec{w}_{scaled}/std$\n",
    "\n",
    "$b_{unscaled} = b_{scaled} - (mean/std)*\\vec{w}_{scaled}$\n",
    " \n",
    "\n",
    "We can get:\n",
    "- the $\\vec{w}_{scaled}$ values from the coef_ attribute of the model.\n",
    "- the $\\vec{b}_{scaled}$ values from the intercept_ attribute of the model.\n",
    "- the data mean and std from scaler.mean_ and scaler.scale_.\n",
    "\n",
    "\n",
    "We define a function to compute the support vectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_support_vectors(svm_clf, scaler, X, y):\n",
    "    w_unscaled = svm_clf.coef_[0] / scaler.scale_\n",
    "\n",
    "\n",
    "    b_scaled = svm_clf.intercept_\n",
    "    #print(\"b_scaled: \", b_scaled)\n",
    "\n",
    "    # Following term is subtracted from the b_scaled\n",
    "    b_subtract = [(svm_clf.coef_[0]).T.dot(-scaler.mean_ / scaler.scale_)]\n",
    "    #print(\"b_subtract: \", b_subtract)\n",
    "\n",
    "    b_unscaled = np.array(b_scaled + b_subtract)\n",
    "    #print(\"b_unscaled: \", b_unscaled)\n",
    "\n",
    "    # Update the weight and intercept of the model with the unscaled weight parameters\n",
    "    svm_clf.intercept_ = np.array([b_unscaled])\n",
    "\n",
    "    svm_clf.coef_ = np.array([w_unscaled])\n",
    "    \n",
    "    \n",
    "    # Now compute the support vectors.\n",
    "\n",
    "    # The original class labels are 0 and 1.\n",
    "    # We need to transform them to -1 and 1.\n",
    "    t = y * 2 - 1\n",
    "\n",
    "\n",
    "    # Note that the data points are classified according to the following rule:\n",
    "    #  (t * (X.dot(w) + b) >= 1)\n",
    "    # Thus the support vectors will satisfy: (t * (X.dot(w) + b) < 1)\n",
    "\n",
    "    support_vectors_idx = (t * (X.dot(w_unscaled) + b_unscaled) < 1).ravel()\n",
    "\n",
    "    svm_clf.support_vectors_ = X[support_vectors_idx]\n",
    "\n",
    "\n",
    "    return svm_clf\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute the Support Vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Support Vectors:\n",
      "[[0.7337483  5.72579411]\n",
      " [0.96348912 5.95674182]\n",
      " [0.64390716 6.65207319]\n",
      " [0.70499668 6.71594282]\n",
      " [0.76499941 6.77956999]]\n"
     ]
    }
   ],
   "source": [
    "svm_clf = compute_support_vectors(svm_clf, scaler, X, y)\n",
    "\n",
    "print(\"Support Vectors:\")\n",
    "print(svm_clf.support_vectors_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Decision Bounday \n",
    "\n",
    "We provide two techniques for plotting the class decision boundary for a binary classification problem.\n",
    "\n",
    "1. Using the Support Vectors\n",
    "2. Using Class Prediction \n",
    "\n",
    "The 1st technique is handy for binary classification problems. It helps us to understand the math for constructing the decision boundary using support vectors.\n",
    "\n",
    "The 2nd technique is simple and easy to extend to non-linear dataset. We will use it more often."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Decision Bounday: Using the Support Vectors\n",
    "\n",
    "We will use the support vectors to \n",
    "- plot the decision boundary and\n",
    "- the two margins \n",
    "\n",
    "\n",
    "### Plot Decision Boundary\n",
    "The equation for the decision boundary for a single 2D data point is:\n",
    "\n",
    "$\\vec{w^T}.\\vec{x} = 0$\n",
    "\n",
    "$=> w_1*x_1 + w_2*x_2 + b = 0$\n",
    "\n",
    "$=> x_2 = -w_1/w_2 * x_1 - b /w_2$\n",
    "\n",
    "$=> x_2 = -(b + w_1*x_1)/w_2$\n",
    "\n",
    "By using a range of values for $x_1$, we will generate the range of $x_2$ values. Then, we will plot the decision boundary by using $x_1$ and $x_2$ values.\n",
    "\n",
    "\n",
    "### Plot the Two Margins\n",
    "\n",
    "We can write the equations for the two margins by using the following equation of the decision boundary for a single data point:\n",
    "\n",
    "$w_1*x_1 + w_2*x_2 + b = 0$\n",
    "\n",
    "The equations for two margins are:\n",
    "\n",
    "$w_1*x_1 + w_2*x_2 + b = +1$\n",
    "\n",
    "\n",
    "$w_1*x_1 + w_2*x_2 + b = -1$\n",
    "\n",
    "Let's consider the equation of the margin for the positive class (+1).\n",
    "\n",
    "$w_1*x_1 + w_2*x_2 + b = +1$\n",
    "\n",
    "$=> w_1*x_1 + w_2*x_2 - 1 + b = 0$\n",
    "\n",
    "$=> w_1*x_1 + w_2*(x_2 - \\frac{1}{w_2}) + b = 0$\n",
    "\n",
    "Thus, we obtain this margin by **shifting the decision boundary** by the amount $\\frac{1}{w_1}$.\n",
    "\n",
    "Similarly consider the equation of the margin for the negative class (-1).\n",
    "\n",
    "$w_1*x_1 + w_2*x_2 + b = -1$\n",
    "\n",
    "$=> w_1*x_1 + w_2*x_2 + 1 + b = 0$\n",
    "\n",
    "$=> w_1*x_1 + w_2*(x_2 + \\frac{1}{w_2}) + b = 0$\n",
    "\n",
    "Thus, we obtain this margin by shifting the decision boundary by the amount $\\frac{1}{w_2}$.\n",
    "\n",
    "\n",
    "In short, the **distance of the two margins from the decision boundary** is: $\\frac{1}{w_2}$\n",
    "\n",
    "\n",
    "### Helper Function to Plot Decision Boundary and Two Margins\n",
    "\n",
    "We define the following helper function to plot the decision boundary and the two margins.\n",
    "\n",
    "The weight vector $\\vec{w}$ and the intercept $b$ values can be obtained by using the following two model functions respectively: \n",
    " - coef_\n",
    "\n",
    "- intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def decision_boundary_support_vectors(svm_clf, X):\n",
    "    \n",
    "    xmin, xmax = X.min() - 1, X.max() + 1\n",
    "    \n",
    "    w = svm_clf.coef_[0]\n",
    "    b = svm_clf.intercept_[0]\n",
    "\n",
    "    # At the decision boundary, w1*x1 + w2*x2 + b = 0\n",
    "    # => x2 = -(b + w1* x1)/w1\n",
    "    x1 = np.linspace(xmin, xmax, 100)\n",
    "    \n",
    "    decision_boundary = -(b + w[0]*x1)/w[1]\n",
    "\n",
    "    shifting_factor_for_margin = 1/w[1]\n",
    "    upper_margin = decision_boundary + shifting_factor_for_margin\n",
    "    lower_margin = decision_boundary - shifting_factor_for_margin\n",
    "\n",
    "    svs = svm_clf.support_vectors_\n",
    "    plt.scatter(svs[:, 0], svs[:, 1], s=200, facecolors='g', label=\"Support Vectors\")\n",
    "    plt.plot(x1, decision_boundary, \"k-\", linewidth=2)\n",
    "    plt.plot(x1, upper_margin, \"k--\", linewidth=2)\n",
    "    plt.plot(x1, lower_margin, \"k--\", linewidth=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot Decision Boundary and the Margins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'LinearSVC' object has no attribute 'support_vectors_'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
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      "\u001b[0;32m<ipython-input-4-b14f5eb8dd40>\u001b[0m in \u001b[0;36mdecision_boundary_support_vectors\u001b[0;34m(svm_clf, X)\u001b[0m\n\u001b[1;32m     16\u001b[0m     \u001b[0mlower_margin\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdecision_boundary\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mshifting_factor_for_margin\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     17\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 18\u001b[0;31m     \u001b[0msvs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msvm_clf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msupport_vectors_\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     19\u001b[0m     \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mscatter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msvs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msvs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m200\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfacecolors\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'g'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"Support Vectors\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     20\u001b[0m     \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdecision_boundary\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"k-\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlinewidth\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mAttributeError\u001b[0m: 'LinearSVC' object has no attribute 'support_vectors_'"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16,8))\n",
    "plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bo\", label=\"Class 0\")\n",
    "plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"ro\", label=\"Class 1\")\n",
    "\n",
    "decision_boundary_support_vectors(svm_clf, X)\n",
    "\n",
    "plt.xlabel(\"x1\", fontsize=14)\n",
    "plt.ylabel(\"x2\", fontsize=14)\n",
    "plt.legend(loc=\"best\", fontsize=14)\n",
    "plt.title(\"Hard Margin Classifier\", fontsize=16)\n",
    "plt.axis([0, 1, 4, 8])\n",
    "plt.xticks(())\n",
    "plt.yticks(())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Decision Bounday: Using Class Prediction\n",
    "\n",
    "\n",
    "We can show the decision boundary by using **different colors for different class labels**.\n",
    "\n",
    "First, create a mesh grid of data points. Then, predict the class labels of these new data points.\n",
    "\n",
    "Finally using the contour plot, display the class-colored data points. Samples belonging to the same class will be coded with the same color. As a consequence we will be able to visualize the **boundary between the classes by the color variance**.\n",
    "\n",
    "\n",
    "To better display the class-colored data points, we will use a **filled contour plot by using the plt.contourf() function**. \n",
    "\n",
    "We may add a **plt.colorbar()** command, which automatically creates an additional axis with labeled color information for the plot.\n",
    "\n",
    "For predicting class labels, we use the \"predict()\" function of the model.\n",
    "\n",
    "#### Plotting the signed distance of the samples to the hyperplane\n",
    "\n",
    "To make this plot more interesting and informative, we can draw the **signed distance of the samples to the hyperplane**.\n",
    "\n",
    "The model provides these distance values by the function \"decision_function()\".\n",
    "\n",
    "Using this function we compute the **signed distance of the samples from the grid to the hyperplane**.\n",
    "\n",
    "First we create a grid of $x_1$ values and a grid of $x_2$ values. The $x_1$ and $x_2$ values represent positions on the plot. We use the np.meshgrid function to create this grid.\n",
    "\n",
    "Then, we compute the **signed distance of the samples from the grid to the hyperplane** by using decision_function.\n",
    "\n",
    "Finally we create a contour plot of the signed distances on the grid.\n",
    "\n",
    "\n",
    "To generate class-colored decision bounday, we write the following function.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def decision_boundary_svc_class_colored(clf, X, plotDistanceFromHyperplane=False, colorBar=False):\n",
    "    \n",
    "    # Get the min and max value of feature x1\n",
    "    x1min, x1max = X[:,0].min() - 1, X[:, 0].max() + 1\n",
    "    \n",
    "    # Get the min and max value of feature x2\n",
    "    x2min, x2max = X[:,1].min() - 1, X[:, 1].max() + 1\n",
    "    \n",
    "    # Create the mesh grid\n",
    "    x1s = np.linspace(x1min, x1max, 100)\n",
    "    x2s = np.linspace(x2min, x2max, 100)\n",
    "    x1, x2 = np.meshgrid(x1s, x2s)\n",
    "    \n",
    "    \n",
    "    # Create pairs of new points from the grid\n",
    "    X_new = np.c_[x1.ravel(), x2.ravel()]\n",
    "    \n",
    "    \n",
    "    # Compute the class predictions for all new points\n",
    "    y_pred = clf.predict(X_new).reshape(x1.shape)\n",
    "    \n",
    "    \n",
    "    # Generate the contourf plot for the predictions\n",
    "    plt.contourf(x1, x2, y_pred, cmap=plt.cm.bwr, alpha=0.2)\n",
    "    \n",
    "    \n",
    "    if(plotDistanceFromHyperplane == True):\n",
    "    \n",
    "        # Compute the signed distance of a sample to the hyperplane for all new points\n",
    "        y_decision = clf.decision_function(X_new).reshape(x1.shape)\n",
    "\n",
    "        # Generate the contour plot for the distance of all points from the hyperplane and the two margins\n",
    "        plt.contour(x1, x2, y_decision, levels=[-1, 0, 1], alpha=0.5, linestyles=['--', '-', '--'], colors='black')\n",
    "        \n",
    "        \n",
    "        #plt.pcolormesh(x1, x2, -y_decision, cmap=plt.cm.RdBu)\n",
    "        \n",
    "        # Generate the contourf plot for the distance of all points from the hyperplane\n",
    "        plt.contourf(x1, x2, y_decision, cmap=plt.cm.bwr, alpha=0.2)\n",
    "    \n",
    "    \n",
    "    if(colorBar==True):\n",
    "        plt.colorbar()   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot The Decision Boundary Based on Class Predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16,8))\n",
    "plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bo\", label=\"Class 0\")\n",
    "plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"ro\", label=\"Class 1\")\n",
    "\n",
    "decision_boundary_svc_class_colored(svm_clf, X, plotDistanceFromHyperplane=True, colorBar=True)\n",
    "\n",
    "# We can plot the support vectors on the margin\n",
    "decision_boundary_support_vectors(svm_clf, X)\n",
    "\n",
    "plt.xlabel(\"x1\", fontsize=14)\n",
    "plt.ylabel(\"x2\", fontsize=14)\n",
    "plt.legend(loc=\"best\", fontsize=14)\n",
    "plt.title(\"Hard Margin Classifier\", fontsize=16)\n",
    "plt.axis([0, 1, 4, 8])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linearly Separable Data: Outlier\n",
    "\n",
    "There are two main issues with hard margin classification. \n",
    "\n",
    "- It only works if the data is linearly separable.\n",
    "- It is quite sensitive to outliers.\n",
    "\n",
    "If data has outliers, then it's not possible to find hard margin. To avoid this problem we use **Soft margin classifier**.\n",
    "\n",
    "Soft margin classifiers provide a more flexible model. The objective is to find a good balance between keeping the street as large as possible and limiting the margin violations (i.e., instances that end up in the middle of the street or even on the wrong side).\n",
    "\n",
    "In Scikit-Learn’s SVM classes, we can control this balance by using the C hyperparameter. \n",
    "- A smaller C value leads to a wider street but more margin violations. \n",
    "- A larger C value leads to a narrower street reducing violations.\n",
    "\n",
    "We will illustrate this using the synthetic dataset. We will build two LinearSVC models with small C (=1) and large C (=100) values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m0 = 200  # no. of training examples for class 0\n",
    "\n",
    "\n",
    "# Generate class 0 data points randomly from a uniform distribution\n",
    "#    Here a & b are 2 dimensions for each data (feature) point\n",
    "a = np.random.rand(m0,1)\n",
    "b = 4 + a + np.random.rand(m0,1)\n",
    "\n",
    "\n",
    "# Concatenate the 2 dimensions of each feature to create the data matrix for class 0 \n",
    "X0 = np.concatenate((a, b), axis=1)\n",
    "\n",
    "# Create the target vector for class 0 (target is coded with zeros)\n",
    "X0_target = np.zeros((m0,), dtype=np.int).reshape(-1, 1)\n",
    "\n",
    "\n",
    "m1 = 200  # no. of training examples for class 1\n",
    "\n",
    "\n",
    "# Generate class 1 data points randomly from a uniform distribution\n",
    "#    Here c & d are 2 dimensions for each data (feature) point\n",
    "c = np.random.rand(m1,1)\n",
    "d = 5.2 + c + np.random.rand(m1,1)\n",
    "\n",
    "# Concatenate the 2 dimensions of each feature to create the data matrix for class 1\n",
    "X1 = np.concatenate((c, d), axis=1)\n",
    "\n",
    "\n",
    "# Create the target vector for class 1 (target is coded with ones)\n",
    "X1_target = np.ones((m1,), dtype=np.int).reshape(-1, 1)\n",
    "\n",
    "\n",
    "\n",
    "# All training examples for class 0 and 1\n",
    "X = np.append(X0, X1, axis=0)\n",
    "\n",
    "# All target values for class 0 & 1\n",
    "y = np.concatenate((X0_target, X1_target), axis=0)\n",
    "\n",
    "\n",
    "# Create a 1D row vector ofthe target with float values\n",
    "y = y.ravel()*1.0\n",
    "#print(y)\n",
    "\n",
    "\n",
    "# Draw a scatter plot\n",
    "plt.figure(figsize=(16,8))\n",
    "plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bo\", label=\"Class 0\")\n",
    "plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"ro\", label=\"Class 1\")\n",
    "plt.title(\"Linearly Separable Data: Outliers\", fontsize=18)\n",
    "plt.legend(loc=2)\n",
    "plt.xlabel(\"$x_1$\", fontsize=12)\n",
    "plt.ylabel(\"$x_2$\", rotation=90, fontsize=12)\n",
    "plt.xticks(())\n",
    "plt.yticks(())\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scale the Data and Train Two Linear SVC Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "         steps=[('scaler',\n",
       "                 StandardScaler(copy=True, with_mean=True, with_std=True)),\n",
       "                ('linear_svc',\n",
       "                 LinearSVC(C=100, class_weight=None, dual=True,\n",
       "                           fit_intercept=True, intercept_scaling=1,\n",
       "                           loss='hinge', max_iter=1000, multi_class='ovr',\n",
       "                           penalty='l2', random_state=42, tol=0.0001,\n",
       "                           verbose=0))],\n",
       "         verbose=False)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scaler = StandardScaler()\n",
    "\n",
    "\n",
    "svm_clf1 = LinearSVC(C=1, loss=\"hinge\", random_state=42)\n",
    "svm_clf2 = LinearSVC(C=100, loss=\"hinge\", random_state=42)\n",
    "\n",
    "scaled_svm_clf1 = Pipeline([\n",
    "        (\"scaler\", scaler),\n",
    "        (\"linear_svc\", svm_clf1),\n",
    "    ])\n",
    "\n",
    "\n",
    "scaled_svm_clf2 = Pipeline([\n",
    "        (\"scaler\", scaler),\n",
    "        (\"linear_svc\", svm_clf2),\n",
    "    ])\n",
    "\n",
    "scaled_svm_clf1.fit(X, y)\n",
    "scaled_svm_clf2.fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute The Support Vectors for Two Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "svm_clf1 = compute_support_vectors(svm_clf1, scaler, X, y)\n",
    "svm_clf2 = compute_support_vectors(svm_clf2, scaler, X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot Decision Boundary and the Margins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(18,6))\n",
    "plt.subplot(121)\n",
    "\n",
    "\n",
    "plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bo\", label=\"Class 0\")\n",
    "plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"ro\", label=\"Class 1\")\n",
    "\n",
    "decision_boundary_svc_class_colored(svm_clf1, X, plotDistanceFromHyperplane=True, colorBar=False)\n",
    "\n",
    "# We can plot the support vectors on the margin\n",
    "decision_boundary_support_vectors(svm_clf1, X)\n",
    "\n",
    "plt.xlabel(\"x1\", fontsize=14)\n",
    "plt.ylabel(\"x2\", fontsize=14)\n",
    "plt.legend(loc=\"best\", fontsize=14)\n",
    "plt.title(\"Soft Margin Classifier: $C = {}$\".format(svm_clf1.C), fontsize=16)\n",
    "plt.axis([0.4, 1, 4, 8])\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bo\", label=\"Class 0\")\n",
    "plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"ro\", label=\"Class 1\")\n",
    "\n",
    "decision_boundary_svc_class_colored(svm_clf2, X, plotDistanceFromHyperplane=True, colorBar=False)\n",
    "\n",
    "# We can plot the support vectors on the margin\n",
    "decision_boundary_support_vectors(svm_clf2, X)\n",
    "\n",
    "plt.xlabel(\"x1\", fontsize=14)\n",
    "plt.ylabel(\"x2\", fontsize=14)\n",
    "#plt.legend(loc=\"best\", fontsize=14)\n",
    "plt.title(\"Soft Margin Classifier: $C = {}$\".format(svm_clf2.C), fontsize=16)\n",
    "plt.axis([0.4, 1, 4, 8])\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}