Ch_02_Perceptron_GradientDescent_Adaline.ipynb

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    "***Reference:***<br>\n",
    "***Raschka, Sebastian; Liu, Yuxi (Hayden); Mirjalili, Vahid. Machine Learning with PyTorch and Scikit-Learn: Develop machine learning and deep learning models with Python. Packt Publishing.*** "
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    "# ***<u>Chapter 2</u>***\n",
    "\n",
    "\n",
    "## ***Training Simple Machine Learning Algorithm for Classification***\n",
    "\n",
    "***In this chapter, we will make use of two of the first algorithmically described machine learning algorithms for classification:*** \n",
    "- **the Perceptron** and \n",
    "- **Adaptive Linear Neurons**"
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    "### **MCP Neuron Model**\n",
    "*A nerve cell as a simple logic gate with binary outputs; multiple signals arrive at the dendrites, they are then integrated into the cell body, and, if the accumulated signal exceeds a certain threshold, an output signal is generated that will be passed on by the axon.*\n",
    "\n",
    "### **Perceptron Learning Rule**\n",
    "***It is based on MCP Neuron model which automatically learns the optimal weight coeffs. that would be multiplied with the i/p features in order to make the decision weather a neuron fires(transmits a signal) or not. In context of classification, such an algorithm predicts weather a new data point belongs to one class or the other.***"
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    "### ***Binary Classification***\n",
    "In context of  binary classification task with two classes: 0 and 1. We can then define a **decision function**, $\\sigma(Z)$, that takes a linear combination of input values, $x$, and a corresponding weight vector, $w$, where **z** is the so-called **net input**,  \n",
    "$z = w_1x_1 + w_2x_2 + \\cdots + w_mx_m:$ \n",
    "$$w = \\begin{bmatrix}\n",
    "w_1\\\\\n",
    "\\vdots\\\\\n",
    "w_m\n",
    "\\end{bmatrix}, \n",
    "x = \\begin{bmatrix}\n",
    "x_1\\\\\n",
    "\\vdots\\\\\n",
    "x_m\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "*Now if the net i/p is greater than a defined threshold $\\theta$, we predict class 1, and class 0 otherwise.* ***(unit step function)***\n",
    "$$\\sigma(z) = \n",
    "\\left\\{\n",
    "\\begin{array}{ll}\n",
    "1 & \\mbox{if z $\\geq$ $\\theta$},\\\\\n",
    "0 & \\mbox{otherwise}\n",
    "\\end{array}\n",
    "\\right.$$\n",
    "\n",
    "Modify the above equation as $z - \\theta \\geq 0$ and<br> define **bias unit** as $b = -\\theta$ and make it a part of net i/p as \n",
    "$$z = w_1x_1 + w_2x_2 + \\cdots + w_mx_m + b$$ $$ z = w^Tx + b$$ and the decison function(**unit step function**) changes as\n",
    "$$\\sigma(z) = \n",
    "\\left\\{\n",
    "\\begin{array}{ll}\n",
    "1 & \\mbox{if z $\\geq$ 0},\\\\\n",
    "0 & \\mbox{otherwise}\n",
    "\\end{array}\n",
    "\\right.$$\n",
    "\n",
    "\n",
    "Figure illustrates how the net input $z = w^Tx + b$ is squashed into a binary output (0 or 1) by the decision function of the perceptron (left subfigure) and how it can be used to discriminate b/w two classes separable by a linear decision boundary (right subfigure):\n",
    "![img01](Images/img01.png)\n",
    "**A threshold function producing a linear decision boundary for a binary classification problem**"
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    "### ***The Perceptron Learning Rule***\n",
    "\n",
    "1. ***Initialize the weights and bais unit to 0 or some small random numbers.***\n",
    "2. ***For each training example,*** $x^{(i)}$:\n",
    "    - ***Compute the o/p value,*** $\\hat{y}^{(i)}$\n",
    "    -  ***Update the weights & bias unit***(if o/p value is wrong)\n",
    "    \n",
    "- Here the o/p value is the class label 0 or 1 predicted by the unit step function as defined earlier.\n",
    "\n",
    "- Update of the bias unit & each weight - \n",
    "$$w_j := w_j + \\Delta{w_j}$$\n",
    "$$b := b + \\Delta{b}$$\n",
    "\n",
    "- The update values are computed as:\n",
    "$$\\Delta{w_j} = \\eta(y_{(i)} - \\hat{y}^{(i)}){x_j}^{(i)}$$\n",
    "$$\\Delta b = \\eta(y_{(i)} - \\hat{y}^{(i)})$$\n",
    "\n",
    "- $\\eta$ is the **learning rate** - b/w 0 and 1\n",
    "- $y^{(i)}$ - is **true class label** of the $i^{th}$ training example and $\\hat{y}^{(i)}$ is the **predicted class label**.\n",
    "\n",
    "- Basically in Perceptron the weight vector in updated when the algorithm makes wrong prediction."
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    "- **Convergance of perceptron is only guaranteed if the two classes are linearly seperable.<br>As the No. of mistakes made by perceptron can upper bounded**<br> <a href=\"https://drive.google.com/file/d/14n87kZlIbSw6qnFyGZDR14OLpPyUI6Pq/view?usp=sharing\">Proof of Convergence of Perceptron</a>\n",
    "\n",
    "- **Why only linearly seperable?**\n",
    "    - ***Since we are updating the weights every time there is a missclasification, so if the data-points are perfectly linearly seprable we might end up updating forever as in any given iteration if one point is correctly classified, there will be some other point that will have been misclassified. Thus the datapoints must be linearly separable.***\n",
    "<br></br>\n",
    "- **If the two classes can't be separated by linear decision boundary, set a max. num of passes over the training dataset(epochs) and/or a threshold for the no. of tolerated misclassifications--the perceptron would never stop updating the weights otherwise.**"
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    "import numpy as np\n",
    "\n",
    "class Perceptron:\n",
    "    \"\"\"Perceptron classifier.\n",
    "\n",
    "    Parameters\n",
    "    ------------\n",
    "    eta : float\n",
    "      Learning rate (between 0.0 and 1.0)\n",
    "    n_iter : int\n",
    "      Passes over the training dataset. \n",
    "    random_state : int\n",
    "      Random number generator seed for random weight initialization.\n",
    "\n",
    "    Attributes\n",
    "    -----------\n",
    "    w_ : 1d-array\n",
    "      Weights after fitting.\n",
    "    b_ : Scalar\n",
    "      Bias unit after fitting.\n",
    "    errors_ : list\n",
    "      Number of misclassifications (updates) in each epoch.\n",
    "    \"\"\"\n",
    "    def __init__(self, eta=0.01, n_iter=50, random_state=1):\n",
    "        self.eta = eta\n",
    "        self.n_iter = n_iter\n",
    "        self.random_state = random_state\n",
    "    \n",
    "    def fit(self, X, y):\n",
    "        \"\"\"Fit training data.\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        X : {array-like}, shape = [n_examples, n_features], X ∈ R^(n*d)\n",
    "          Training vectors, where n_examples is the number of examples and\n",
    "          n_features is the number of features.\n",
    "        y : array-like, shape = [n_examples]\n",
    "          Target values.\n",
    "\n",
    "        Returns\n",
    "        -------\n",
    "        self : object\n",
    "        \"\"\"\n",
    "        \n",
    "        #RandomState exposes a number of methods for generating random numbers drawn from a variety of probability distributions.\n",
    "        rgen = np.random.RandomState(seed=self.random_state)\n",
    "        \n",
    "        # here we are initializing the weight vector with mean=0, std_dev=0.01\n",
    "        self.w_ = rgen.normal(loc=0.0, scale=0.01, size=X.shape[1])\n",
    "        # initializing bias = 0\n",
    "        self.b_ = np.float_(0.)\n",
    "        self.errors_ = []\n",
    "        \n",
    "        for i in range(self.n_iter):\n",
    "            errors = 0\n",
    "            for x_i, target in zip(X,y):\n",
    "                update = self.eta * (target - self.predict(x_i))\n",
    "                self.w_ += update*x_i\n",
    "                self.b_ += update\n",
    "                errors += int(update!=0.0)\n",
    "            self.errors_.append(errors)\n",
    "        return self\n",
    "    \n",
    "    def net_input(self, X):\n",
    "        '''Calculate the net input'''\n",
    "        return np.dot(X,self.w_) + self.b_\n",
    "    \n",
    "    def predict(self, X):\n",
    "        '''Return class label after unit step'''\n",
    "        return np.where(self.net_input(X)>=0.0, 1, 0)"
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    "- Using above, we can now initialize new Perceptron objects with a given learning rate, eta, and the number of epochs, n_iter (passes over the training dataset).\n",
    "\n",
    "- Via fit method, initialize the bias self.b_ = 0 and weights in self.w_ to a vector, $R^m$, m = No. of dimensions(features) in the dataset\n",
    "\n",
    "- Notice, initial weight vector contains small random nums. drawn from a normal dist. with std_dev = 0.01\n",
    "\n",
    "- Technically, we could initialize the weights to zero (in fact, this is done in the original perceptron algorithm). However, if we did that, then the learning rate (eta) would have no effect on the decision boundary. If all the weights are initialized to zero, the learning rate parameter, eta, affects only the scale of the weight vector, not the direction.\n",
    "\n",
    "- self.errors_ list is made so that we can later analyze (the No. of misclassificatios in each epoch) how well the perceptron has performed during the training."
   ]
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   "source": [
    "#### Applying Perceptron to iris dataset"
   ]
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   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal length in cm</th>\n",
       "      <th>sepal width in cm</th>\n",
       "      <th>petal length in cm</th>\n",
       "      <th>petal width in cm</th>\n",
       "      <th>class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
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      "text/plain": [
       "   sepal length in cm  sepal width in cm  petal length in cm  \\\n",
       "0                 5.1                3.5                 1.4   \n",
       "1                 4.9                3.0                 1.4   \n",
       "2                 4.7                3.2                 1.3   \n",
       "3                 4.6                3.1                 1.5   \n",
       "4                 5.0                3.6                 1.4   \n",
       "\n",
       "   petal width in cm        class  \n",
       "0                0.2  Iris-setosa  \n",
       "1                0.2  Iris-setosa  \n",
       "2                0.2  Iris-setosa  \n",
       "3                0.2  Iris-setosa  \n",
       "4                0.2  Iris-setosa  "
      ]
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   "source": [
    "s = \"https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data\"\n",
    "\n",
    "df = pd.read_csv(s, header=None, encoding='utf-8')\n",
    "df.columns = ['sepal length in cm','sepal width in cm','petal length in cm','petal width in cm','class']\n",
    "df.head()"
   ]
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# For perceptron we'll only consider only 2 categories and 2 flower types\n",
    "# Extracting Setosa(0), Versicolor(1) and sepal length & petal length\n",
    "\n",
    "# select setosa & versicolor\n",
    "y = df.iloc[0:100,4].values\n",
    "y = np.where(y=='Iris-setosa', 0, 1)\n",
    "\n",
    "# extract sepal length & petal length\n",
    "X = df.iloc[0:100, [0,2]].values\n",
    "\n",
    "\n",
    "# plot data\n",
    "\n",
    "plt.scatter(X[:50, 0], X[:50, 1], color='red', marker='o', label='Setosa')\n",
    "plt.scatter(X[50:100, 0], X[50:100, 1], color='blue', marker='s', label='Versicolor')\n",
    "\n",
    "plt.xlabel(\"Sepal Length[cm]\")\n",
    "plt.ylabel(\"Petal Length[cm]\")\n",
    "plt.legend()\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "838170e6-72c7-405b-b688-77a8a372a4ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZGUVFRQAApVIJB4eGL74lS5bg8uXL2LBhAwBg+fLlCAwMRL9+/VBTU4ONGzciMTERiYmJkm0H6ebKrdv4z8lCAL/OsG0JJoX4YGlnB1y+dRvbj1/GH4aa7uSfRETWQNI9NytXrkRpaSlGjRoFX19f7W3z5s3adQoLC5GX9+scPjU1NVi0aBH69++P6OhopKWlYceOHXj00Uel2ATSw/pDOajXiIgIdkdIF6XUcQzGRi7DrMZB/dakcVA/IiKpmcwJxR1FnxOSyHDKq+sQEb8PZVV1SJgZjrGNVxlZCnVVLSLj96O8ug5fPDcEo3t5SR2JiMiimN0JxWT5tvyUj7KqOgR7OlnkF7+LvS2mD2m4rL1pMlAiIpIGyw0ZXV29BmvTG77wZ0cFQWamg/bdzXMjAiETgLRfSnDmCgeLJCKSCssNGd3uM1dRcPM2XB1tMW2w/pf6m4uuro6YGNpw1R4H9SMikg7LDRnd6tSGy7+fGd4N9rZyidMY19zGy8KTTlzGVXWVxGmIiKwTyw0Z1dHcmziedwt2chmeiQiUOo7RDfTvjPBurqitF7EhI0fqOEREVonlhoxqTeNem6mD/ODpbB1TE8xp3Huz8XAeKmvqJE5DRGR9WG7IaPKuV2LX6YaBGZu+8K3B+L7e6ObuiNLbtUg8WiB1HCIiq8NyQ0azNl0FjQiM7OmJnt7OUsfpMHKZgOdHNIzAnJCmQr3GqoaSIiKSHMsNGUXp7VpsOZIPAJgbbTlTLejqsbCucLG3Qc71SuzLvip1HCIiq8JyQ0bxdWYeKmvq0dvHGVHdPaSO0+GcFDaYMbxh1vM1HNSPiKhDsdyQwdXWa7AuPQdAw6B9gmCZg/bdzcyIQNjIBGTm3MCJ/FtSxyEishosN2RwO04WokhdBU9nBaYM9JM6jmR8lPaYMqBh+9dwUD8iog7DckMGJYoi1qQ1XP49M6IbFDaWPWjf3cxuPN/oh1OFuHzrtsRpiIisA8sNGdThSzfw82U17G1lmDGsm9RxJNfPT4nI+9xRrxGxLp17b4iIOgLLDRlUQuNem8fCusLVyU7iNKZhTuPem28y81FWVStxGiIiy8dyQwZz8Vo59mYXQxCgHeeFgFE9vXCfpxPKquuw+ad8qeMQEVk8lhsymLWNJ82O7e2NYM9OEqcxHTKZgNlRDSM0f5Geg7p6jcSJiIgsG8sNGcSNihp82zjVwBwrHLTvbh4d3AXuTna4fOs2djZOSUFERMbBckMG8dXhXFTXaRDaRYlhQW5SxzE59rZyPN04qN/qVBVEkVMyEBEZC8sN3bOq2nqsz8gF0LDXxloH7bubZyK6wc5GhhP5t3A096bUcYiILBbLDd2zpBNXUFJeDV+lPSaF+kodx2R5dFLg0UFdAACrUy9JnIaIyHKx3NA9EUURCY1zJ82KDIStnP+k7mR2VMP5SLvPXEXu9QqJ0xARWSZ+E9E9Sb1QgnNXy+BkJ8cfhgZIHcfk9fB2xqhenhDFX68uIyIiw7rncqNWq7F9+3ZkZ2cbIg+ZmabDK08M8YfSwVbiNOZhTuNl4VuOFKC0koP6EREZmt7l5oknnsCKFSsAALdv30Z4eDieeOIJ9O/fH4mJiQYPSKbrbJEaqRdKIOOgfXoZ0d0dvX2ccbu2Hl9l5kodh4jI4uhdblJSUhAdHQ0A2LZtG0RRxK1bt/DJJ5/g73//u8EDkulqOtdmQogP/N0cJU5jPgRBwJzohr036w/loKaOg/oRERmS3uWmtLQUbm4N45js3LkT06ZNg6OjIx588EFcuHDB4AHJNBWXVeG7rCsAoP2iJt1NGeAHL2cFrqqr8Z+TV6SOQ0RkUfQuN/7+/sjIyEBFRQV27tyJmJgYAMDNmzdhb29v8IBkmr7MyEVNvQaDAzpjcICr1HHMjp2NDDMjAwEAazioHxGRQeldbhYuXIgZM2aga9eu8PX1xahRowA0HK4KDQ01dD4yQbdr6rHxcMO5InO516bdZgwLgIOtHGcK1ci4eF3qOEREFkPvcvPHP/4RGRkZWLt2LdLT0yGTNbxEcHAwz7mxEonHCnCzshb+bg6I6ecjdRyz1dnRDo+FdQUArOFl4UREBtOuS8HDw8Px4IMP4vLly6irqwMAPPjggxgxYoRBw5Hp0WhE7fgsz48IglzGqRbuxfNRQRAEYP/ZYvxSXCZ1HCIii6B3uamsrMTs2bPh6OiIfv36IS8vDwCwYMECvPfeewYPSKZl/9liXCqpgLO9DR4P95c6jtkL8nDCuD7eAICEtBxpwxARWQi9y82SJUtw4sQJHDx4sNkJxOPGjcPmzZsNGo5MT9OgfU8NC0AnhY3EaSxD03lLW48V4Hp5tcRpiIjMn97lZvv27VixYgWioqKazf7ct29fXLx40aDhyLScKijFj6obsJEJmNV4pQ/duyGBrujfVYnqOg02Hs6TOg4RkdnTu9xcu3YNXl5eLZZXVFQ0KztkedakNey1eai/L3yVDhKnsRy/HdTvy8M5qKqtlzgREZF507vcDBkyBDt27NDebyo0q1evRkREhOGSkUm5cus2dpwsBMBB+4xhYogP/JT2KCmvwXdZl6WOQ0Rk1vQ+aSI+Ph4TJkzAmTNnUFdXh48//hinT59GRkYGkpOTjZGRTMD6Qzmo04gYHuyGkC5KqeNYHFu5DM+NCMI7P2RjTaoKT4T7c08oEVE76b3nJjIyEunp6aisrMR9992H3bt3w9vbGxkZGQgLCzNGRpJYeXUdNmU2nAvCQfuMZ/pQf3RS2OBCcTkOnr8mdRwiIrOl956bkydPon///li/fn2Lx7Zv346pU6caIheZkC0/5aOsqg7Bnk4Y3avl+VZkGC72tpg+xB8JaSokpKr4d01E1E5677l54IEHcOnSpRbLExMTMWPGDIOEItNRrxGxNr1h0L7ZUUGQcdA+o5oVGQiZAKT9UoIzV9RSxyEiMkt6l5t58+Zh7NixKCws1C7bvHkznn32Waxbt86Q2cgE7DpdhIKbt+HqaItHB3WVOo7F83dzxMRQXwBAAqdkICJqF73Lzd/+9jdMmTIF48aNw40bN7Bp0yY899xz2LBhAx5//HFjZCQJrWkctO+Z4d3gYCeXOI11aDqvKenEZVxVV0mchojI/LRrbqmPP/4YgwcPxvDhwzF37lx8/fXXmDZtmqGzkcSO5t7EsbxbsJPL8HREN6njWI2B/p0R3s0VtfUiNmTkSB2HiMjs6HRCcVJSUotlU6dORXJyMp588kkIgqBdZ8qUKYZNSJJJaBy0b+ogP3g5299lbTKkOdHBOJJ7FBsP52H+6O5wtONUF0REuhJEURTvtpJMptsOHkEQUF9v2qOrqtVqKJVKlJaWwsXFxWCvW68Rkam6geKyKng522NokJtZzpjdtB1nC9V4+z9nIALYtXAkevk4Sx3NqtRrRIz5x0HkXq/E8yMCMcC/s1n/uyIiulf6fH/r9OugRqMxSLDfi4+Px9atW3H27Fk4ODggMjISS5cuRa9eve74vOTkZMTFxeH06dPw8/PDq6++itjYWKNk1MXOnwvx1vdnUFj66/kRvkp7vDG5LyaE+EqWS1+tbYedjQyqknKWmw4mlwkYHuSO3OuVWJueo11ujv+uiIg6WrvOuTGU5ORkzJ8/H4cPH8aePXtQV1eHmJgYVFRUtPkclUqFSZMmITo6GsePH8drr72GBQsWIDExsQOT/2rnz4WYt/FYs0IAAEWlVZi38Rh2/lzYxjNNS1vbUVOnMavtsBQ7fy7EliP5LZab278rIiIp6HRY6vcqKiqQnJyMvLw81NTUNHtswYIF7Q7TNClncnIyRo4c2eo6ixcvRlJSErKzs7XLYmNjceLECWRkZNz1PQx5WKpeIyJq6f4WheC3vJwV+HdshEkfSqjXiHjs8wxcK6tu9XEBgI/SHmmLx5j0dliKu/274udBRNbI4Ielfuv48eOYNGkSKisrUVFRATc3N5SUlMDR0RFeXl73VG5KS0sBAG5ubm2uk5GRgZiYmGbLHnjgASQkJKC2tha2trbNHquurkZ19a9f2mq14QZGy1TduGOxAYDismrc//5Bg72nFEQAhaVVyFTdQMR97lLHsXh3+3fFz4OI6M70Piz1yiuvYPLkybhx4wYcHBxw+PBh5ObmIiwsDB988EG7g4iiiLi4OERFRSEkJKTN9YqKiuDt7d1smbe3N+rq6lBSUtJi/fj4eCiVSu3N39+/3Rl/r7hMtzFIbGQCFDYyk73Z6Pjbv67bS/dG179nfh5ERK3Te89NVlYW/vWvf0Eul0Mul6O6uhrBwcFYtmwZZs6ciUcffbRdQV588UWcPHkSaWlpd13397MlNx1Za20W5SVLliAuLk57X61WG6zg6Hp59Jezh5n0b9gZF6/jydWH77oeLwfvGLr+PfPzICJqnd57bmxtbbUlwtvbG3l5DbNFK5VK7Z/19dJLLyEpKQkHDhxA1653HuLfx8cHRUVFzZYVFxfDxsYG7u4tC4RCoYCLi0uzm6EMDXKDr9Iebe33ENBwdcvQoLYPs5kCS9kOS8HPg4jo3uhdbgYNGoQjR44AAEaPHo2//e1v+Oqrr7Bw4UKEhobq9VqiKOLFF1/E1q1bsX//fgQFBd31OREREdizZ0+zZbt370Z4eHiL822MTS4T8MbkvgDQ4ouo6f4bk/ua/EmflrIdluJOn0cTfh5ERG3Tu9y8++678PVtGGPj//7v/+Du7o558+ahuLgY//rXv/R6rfnz52Pjxo3YtGkTnJ2dUVRUhKKiIty+fVu7zpIlS/Dss89q78fGxiI3NxdxcXHIzs7G2rVrkZCQgEWLFum7KQYxIcQXK58eDB9l80MEPkp7rHx6sNmMR2Ip22Ep2vo8AGDa4C78PIiI7qBdl4Ib7M1bOUcGAL744gvMmjULADBr1izk5OTg4MGD2seTk5PxyiuvaAfxW7x4sc6D+HGE4juzlO2wFL/9PE4VlGJNmgpdOjsg+X9HwUYu6TBVREQdSp/vb73LzZgxY7B161Z07ty5xZtOnToV+/fv1ztwRzJWuSEytqraekS+tx83Kmqw4qlBeKi/n9SRiIg6jD7f33r/6nfw4MEWA/cBQFVVFVJTU/V9OSLSkb2tHE8Pb5idfXWqChLudCUiMmk6Xwp+8uRJ7Z/PnDnT7Iql+vp67Ny5E126dDFsOiJq5pnh3fB58kWcyL+Fo7k3ER7IK6aIiH5P53IzcOBACIIAQRAwZsyYFo87ODjg008/NWg4ImrO01mBRwZ2weYj+ViTqmK5ISJqhc7lRqVq2A0eHByMzMxMeHp6ah+zs7ODl5cX5HK5UUIS0a9mRwdh85F87DpThNzrFejm7iR1JCIik6JzuenWreFYv0ajMVoYIrq7nt7OuL+nJ5LPX8MX6Tl4c0o/qSMREZkUvU8oXr9+PXbs2KG9/+qrr6Jz586IjIxEbm6uQcMRUevmRgcDALYcyUdpZa3EaYiITEu7BvFzcHAA0DBD94oVK7Bs2TJ4eHjglVdeMXhAImppRHd39PZxRmVNPTZltm/aEyIiS6V3ucnPz0f37t0BANu3b8djjz2GF154AfHx8bwUnKiDCIKAOY17b9YdUqGmjoeLiYia6F1uOnXqhOvXrwNomNNp3LhxAAB7e/tm0yYQkXFNHuALT2cFrqqrsePUFanjEBGZDL3Lzfjx4zFnzhzMmTMH58+fx4MPPggAOH36NAIDAw2dj4jaoLCRY1ZkIABgdQoH9SMiaqJ3ufnnP/+JiIgIXLt2DYmJiXB3dwcAHD16FE8++aTBAxJR254aGgB7WxnOFKqRcfG61HGIiEyCpBNnSoFzS5Gl+ev2n/Hl4VyM6e2FtbOGSB2HiMgo9Pn+1mmcm5MnTyIkJAQymazZNAyt6d+/v+5JieiePR8VhI0/5mL/2WL8UlyG7l7OUkciIpKUTuVm4MCBKCoqgpeXl3Yaht/u8Gm6LwgC6uvrjRaWiFoK8nDCuD7e2HPmKhLSchD/aKjUkYiIJKVTuVGpVNrpFlQqlVEDEZH+5kYHY8+Zq9h6rACLYnrCvZNC6khERJLRqdw0Tb3w+z8TkWkYEuiK/l2VOFlQio2H8/DyuB5SRyIikozOc0ulpKTotN7IkSPbHYaI2qdpUL8FXx/Hl4dz8D/3B8PelhPZEpF10rncjBo1CoIgAECb42nwnBsi6UwM8YGf0h5XSqvwXdZlTB8SIHUkIiJJ6DzOjaurK/z9/fHXv/4VFy5cwM2bN1vcbty4YcysRHQHtnIZnhsRBABYk8pB/YjIeulcbgoLC7F06VJkZGQgNDQUs2fPxqFDh+Di4gKlUqm9EZF0pg/1RyeFDS4UlyP5/DWp4xARSULncmNnZ4fp06dj165dOHfuHPr3748XX3wR/v7+eP3111FXV2fMnESkAxd7W0wf4g+gYe8NEZE10nv6BQDw9/fH3/72N+zduxc9e/bEe++9B7VabehsRNQOsyIDIROAtF9KkF3I/5dEZH30LjfV1dXYtGkTxo0bh5CQEHh4eGDHjh1wc3MzRj4i0pO/myMmhvoC4N4bIrJOOpebzMxMzJs3Dz4+Pvjggw8wZcoU5OfnY8uWLZgwYYIxMxKRnuZENZxYnHTiMorVVRKnISLqWDpfCj58+HAEBARgwYIFCAsLAwCkpaW1WG/KlCmGS0dE7TIowBXh3VxxJPcm1mfk4H8f6C11JCKiDqPzrOAy2d138pjDODecFZysxc6fCxG78Rg6O9ri0J/HwNFO599liIhMjj7f3zofltJoNHe9mXqxIbIm4/v6IMDNEbcqa5F4tEDqOEREHUbncvPaa68hMzPTmFmIyIDkMgHPjwgEACSkqaDRcFA/IrIOOpebK1eu4KGHHoKvry9eeOEF7NixA9XV1cbMRkT36PFwf7jY2yDneiX2Zl+VOg4RUYfQudysW7cOV69exZYtW9C5c2f86U9/goeHBx599FGsW7cOJSUlxsxJRO3gpLDBU8O6AQDWpPGycCKyDnqNcyMIAqKjo7Fs2TKcPXsWmZmZGD58OFavXo0uXbpg5MiR+OCDD3D58mVj5SUiPc2KDISNTECm6gZOFtySOg4RkdG1a4TiJn369MGrr76K9PR0FBQUYObMmUhNTcXXX39tqHxEdI98lPaYPMAPAAf1IyLroPOl4G1Rq9XYv38/evfujd69TX8sDV4KTtbo58uleOjTNMhlAlJeHY0unR2kjkREpBejXAre5IknnsCKFSsAALdv30Z4eDieeOIJhIaGIjExsX2JicioQrooERHsjnqNiPWHcqSOQ0RkVHqXm5SUFERHRwMAtm3bBlEUcevWLXzyySf4+9//bvCARGQYc0c2TMnw9Y95KKuqlTgNEZHx6F1uSktLtZNk7ty5E9OmTYOjoyMefPBBXLhwweABicgwRvX0QrCnE8qq67DlCAf1IyLLpXe58ff3R0ZGBioqKrBz507ExMQAAG7evAl7e3uDByQiw5DJBMyJCgYArE1Toa5eI3EiIiLj0LvcLFy4EDNmzEDXrl3h6+uLUaNGAWg4XBUaGmrofERkQI8O7gI3JztcvnUbO08XSR2HiMgo9C43f/zjH5GRkYG1a9ciPT1dO6FmcHAwz7khMnH2tnI8PbxhUL/VqSrc48WSREQmqd2XgtfU1EClUuG+++6DjY35zDbMS8HJ2l0rq8aIpftRU6fBt7ERCA90kzoSEdFdGfVS8MrKSsyePRuOjo7o168f8vLyAAALFizAe++9177ERNRhPJ0VeGRgFwAc1I+ILJPe5WbJkiU4ceIEDh482OwE4nHjxmHz5s0GDUdExjE7uuGy8F1nipB7vULiNEREhqV3udm+fTtWrFiBqKgoCIKgXd63b19cvHjRoOGIyDh6ejvj/p6eEEXgi/QcqeMQERmU3uXm2rVr8PLyarG8oqKiWdkhItM2N7rhsvAtR/JRWslB/YjIcuhdboYMGYIdO3Zo7zcVmtWrVyMiIsJwyYjIqEZ0d0dvH2dU1tRjU2ae1HGIiAxG73ITHx+P119/HfPmzUNdXR0+/vhjjB8/HuvWrcM777yj12ulpKRg8uTJ8PPzgyAI2L59+x3XP3jwIARBaHE7e/asvptBZPUEQcCcxr036w6pUFPHQf2IyDLoXW4iIyORnp6OyspK3Hfffdi9eze8vb2RkZGBsLAwvV6roqICAwYM0E7Eqatz586hsLBQe+vRo4dezyeiBpMH+MLTWYGr6mrsOHVF6jhERAbRrgFqQkNDsX79+nt+84kTJ2LixIl6P8/LywudO3e+5/cnsnYKGzlmRQbi/V3nsDpFhakDu/DcOSIye3rvuZHL5SguLm6x/Pr165DL5QYJdTeDBg2Cr68vxo4diwMHDtxx3erqaqjV6mY3IvrVU0MDYG8rw5lCNTIuXZc6DhHRPdO73LQ1oHF1dTXs7OzuOdCd+Pr6YtWqVUhMTMTWrVvRq1cvjB07FikpKW0+Jz4+HkqlUnvz9/c3akYic+PqZIfHwxr+X3BQPyKyBDoflvrkk08ANJyEuGbNGnTq1En7WH19PVJSUtC7d2/DJ/yNXr16oVevXtr7ERERyM/PxwcffICRI0e2+pwlS5YgLi5Oe1+tVrPgEP3O81FB2PhjLvafLcYvxeXo7tXp7k8iIjJROpebjz76CEDDnpvPP/+82SEoOzs7BAYG4vPPPzd8wrsYPnw4Nm7c2ObjCoUCCoWiAxMRmZ8gDyeM6+ONPWeuIiFNhfhHQ6WORETUbjqXG5WqYXf16NGjsXXrVri6uhotlD6OHz8OX19fqWMQmb05UUHYc+Yqth4rwKKYnnDvxF8KiMg86X211N1O4NVHeXk5fvnlF+19lUqFrKwsuLm5ISAgAEuWLMHly5exYcMGAMDy5csRGBiIfv36oaamBhs3bkRiYiISExMNlonIWg0NckP/rkqcLCjFxsN5eHkch1ggIvPUrkvBCwoKkJSUhLy8PNTU1DR77MMPP9T5dY4cOYLRo0dr7zedGzNz5kysW7cOhYWF2lnHAaCmpgaLFi3C5cuX4eDggH79+mHHjh2YNGlSezaDiH5DEATMjgrCy99k4cvDOfif+4Nhb9sxV0ASERmSILZ1+VMb9u3bhylTpiAoKAjnzp1DSEgIcnJyIIoiBg8ejP379xsrq0Go1WoolUqUlpbCxcVF6jhEJqW2XoP7lx3AldIqLJ0WiulDAqSOREQEQL/vb70vBV+yZAn+9Kc/4eeff4a9vT0SExORn5+P+++/H48//ni7QxOR9GzlMswaEQig4bJwPX/3ISIyCXqXm+zsbMycORMAYGNjg9u3b6NTp054++23sXTpUoMHJKKO9YehAXCyk+NCcTmSz1+TOg4Rkd70LjdOTk6orq4GAPj5+eHixYvax0pKSgyXjIgk4WJvqz0clZDGQf2IyPzoXW6GDx+O9PR0AMCDDz6IP/3pT3jnnXfw/PPPY/jw4QYPSEQd77kRgZAJQOqFEmQXcsoSIjIvepebDz/8EMOGDQMAvPnmmxg/fjw2b96Mbt26ISEhweABiajj+bs5YmJIw/hR3HtDROZG76ulzB2vliLSzfG8m3jks0OwlQtIXzwGXi72UkciIitm1KuliMg6DApwRVg3V9TWi9iQkSt1HCIinek0iJ+rqysEQdDpBW/cuHFPgYjIdMyNDsLR3JvY+GMu/jj6PjjatWvcTyKiDqXTT6rly5dr/3z9+nX8/e9/xwMPPICIiAgAQEZGBnbt2oW//vWvRglJRNIY39cHAW6OyLtRicRjl/HM8G5SRyIiuiu9z7mZNm0aRo8ejRdffLHZ8hUrVmDv3r3Yvn27IfMZHM+5IdLPunQV3vz+DII8nLAv7n7IZLrtxSUiMiSjnnOza9cuTJgwocXyBx54AHv37tX35YjIxD0e7g8XexuoSiqwN/uq1HGIiO5K73Lj7u6Obdu2tVi+fft2uLu7GyQUEZkOJ4UNnhrWcDhqDS8LJyIzoPfZgW+99RZmz56NgwcPas+5OXz4MHbu3Ik1a9YYPCARSW9WZCDWpF5CpuoGThbcQv+unaWORETUJr333MyaNQuHDh1C586dsXXrViQmJkKpVCI9PR2zZs0yQkQikpqP0h6TB/gBaJhQk4jIlHEQPyLSyc+XS/HQp2mQywSkvDoaXTo7SB2JiKyIPt/f7Rq0or6+Htu2bUN2djYEQUCfPn3w8MMPw8aGY2AQWaqQLkpEBLsj49J1rD+Ug9cm9ZE6EhFRq/RuIz///DMefvhhFBUVoVevXgCA8+fPw9PTE0lJSQgNDTV4SCIyDXNHBiHj0nV8/WMeXhrTHc72tlJHIiJqQe9zbubMmYN+/fqhoKAAx44dw7Fjx5Cfn4/+/fvjhRdeMEZGIjIRo3p6IdjTCWXVddhypEDqOERErdK73Jw4cQLx8fFwdXXVLnN1dcU777yDrKwsQ2YjIhMjkwmYExUMAFibpkJdvUbiRERELeldbnr16oWrV1sO5FVcXIzu3bsbJBQRma5HB3eBm5MdLt+6jV2nOagfEZkevcvNu+++iwULFuDbb79FQUEBCgoK8O2332LhwoVYunQp1Gq19kZElsfeVo6nG+eYWp16CVZ2wSURmQG9LwWXyX7tQ00zhTe9xG/vC4KA+vp6Q+U0GF4KTnTvrpVVY8TS/aip0yBxXgTCurlJHYmILJxRLwU/cOBAu4MRkWXwdFbgkYFdsPlIPlanqBD2DMsNEZkOvcvN/fffb4wcRGRmZkcHYfORfOw6U4Tc6xXo5u4kdSQiIgB6lJuUlJRWlyuVSnTv3h1OTvzBRmRNeno74/6enkg+fw1fpOfgzSn9pI5ERARAj3IzatSoNh+Ty+WYN28e/vGPf8DWloN6EVmLOdFBSD5/DVuO5OOVcT2hdOT/fyKSns5XS928ebPVm0qlwqZNm5CUlIT333/fmFmJyMREdfdAbx9nVNbUY1NmntRxiIgA6FFulEplq7du3brh8ccfx8cff4yvvvrKmFmJyMQIgoDZUUEAgHWHVKip46B+RCQ9vce5acuAAQOQm5trqJcjIjMxZaAfPJ0VuKquxo5TV6SOQ0RkuHJz5coVeHl5GerliMhMKGzkmBnRMKjfmlQVB/UjIskZpNwUFxfjL3/5C8aMGWOIlyMiMzNjWDfY28pw+ooaGZeuSx2HiKyczldLDRo0SDsC8W+VlpaioKAAffr0wTfffGPQcERkHlyd7PBYWFdsPJyHhFQVIu/zkDoSEVkxncvN1KlTW13u4uKC3r17IyYmBnK53FC5iMjMPD8iCF/9mId9Z4vxS3E5unt1kjoSEVkpncvNG2+8YcwcRGTmgj07YWxvb+zNvoq16Sq8+0io1JGIyEoZ7IRiIqK50Q2XhSceLcD18mqJ0xCRtWK5ISKDGRrkhtAuSlTXafDVjxzUj4ikwXJDRAYjCALmNO692ZCRg6raeokTEZE10qncqNVqY+cgIgsxKdQXvkp7lJTX4Lusy1LHISIrpFO5cXV1RXFxMQBgzJgxuHXrljEzEZEZs5XL8NyIQAAc1I+IpKFTuenUqROuX28YmOvgwYOora01aigiMm9/GBoAJzs5LhSXI/n8NanjEJGV0elS8HHjxmH06NHo06cPAOCRRx6BnZ1dq+vu37/fcOmIyCy52Nti+pAArE1XISFNhVG9ODULEXUcncrNxo0bsX79ely8eBHJycno168fHB0djZ2NiMzYcyMCse6QCqkXSpBdqEYfXxepIxGRlRBEPQ+Ijx49Gtu2bUPnzp2NFMm41Go1lEolSktL4eLCH7ZExjT/q2PYcaoQj4V1xQePD5A6DhGZMX2+v/W+FPzAgQPaYiOKIk8WJKI2NV0W/l3WZRSrqyROQ0TWol3j3GzYsAGhoaFwcHCAg4MD+vfvjy+//NLQ2YjIzA0KcEVYN1fU1ot494dsfJd1GRkXr6New1+KiMh49C43H374IebNm4dJkyZhy5Yt2Lx5MyZMmIDY2Fh89NFHer1WSkoKJk+eDD8/PwiCgO3bt9/1OcnJyQgLC4O9vT2Cg4Px+eef67sJRNSBwrt1BgBsz7qCl7/JwpOrDyNq6X7s/LlQ2mBEZLH0LjeffvopVq5ciaVLl2LKlCl4+OGHsWzZMnz22Wf45JNP9HqtiooKDBgwACtWrNBpfZVKhUmTJiE6OhrHjx/Ha6+9hgULFiAxMVHfzSCiDrDz50KsSlG1WF5UWoV5G4+x4BCRUeg8K3iTwsJCREZGtlgeGRmJwkL9flBNnDgREydO1Hn9zz//HAEBAVi+fDkAoE+fPjhy5Ag++OADTJs2Ta/3JiLjqteIeOv7M2jtAJQIQADw1vdnML6vD+QyoYPTEZEl03vPTffu3bFly5YWyzdv3owePXoYJFRbMjIyEBMT02zZAw88gCNHjrQ5sGB1dTXUanWzGxEZX6bqBgpL2z6JWARQWFqFTNWNjgtFRFZB7z03b731FqZPn46UlBSMGDECgiAgLS0N+/bta7X0GFJRURG8vb2bLfP29kZdXR1KSkrg6+vb4jnx8fF46623jJqLiFoqLtPt6ihd1yMi0pXee26mTZuGH3/8ER4eHti+fTu2bt0KDw8PZGZm4pFHHjFGxmYEofnu66ZL0X+/vMmSJUtQWlqqveXn5xs9IxEBXs72Bl2PiEhXeu+5AYCwsDBs3LjR0FnuysfHB0VFRc2WFRcXw8bGBu7u7q0+R6FQQKFQdEQ8IvqNoUFu8FXao6i0qtXzbgQAPkp7DA1y6+hoRGTh2jXOjVQiIiKwZ8+eZst2796N8PBw2NraSpSKiFojlwl4Y3JfAA1F5vdEAG9M7suTiYnI4CQtN+Xl5cjKykJWVhaAhku9s7KykJeXB6DhkNKzzz6rXT82Nha5ubmIi4tDdnY21q5di4SEBCxatEiK+ER0FxNCfLHy6cHwUbY89DS+rzcmhLQ8T46I6F6167CUoRw5cgSjR4/W3o+LiwMAzJw5E+vWrUNhYaG26ABAUFAQfvjhB7zyyiv45z//CT8/P3zyySe8DJzIhE0I8cX4vj7IVN1AcVkVCm5W4v1d53H44nWUV9ehk0LSH0NEZIH0njjT3HHiTCJpaTQixn2UjEvXKvDXh/pidlSQ1JGIyAwYdeJMIqJ7IZMJ2kLzRboKdfUaiRMRkaUxWLn57LPP8Pbbbxvq5YjIgk0b3BWujrYouHkbu05flToOEVkYg5WbxMRErFu3zlAvR0QWzN5WjmeGdwMArEm7JHEaIrI0Bis3+/btw6VL/CFFRLp5JiIQdnIZjufdwtFcTsFARIZzT+VGFEVY2fnIRGQgns4KTB3kBwBYk9py5nAiovZqV7nZsGEDQkND4eDgAAcHB/Tv3x9ffvmlobMRkYWbEx0MANh1ugh51yslTkNElkLvcvPhhx9i3rx5mDRpErZs2YLNmzdjwoQJiI2NxUcffWSMjERkoXp6O2NkT09oRGBtOvfeEJFh6D3OTVBQEN56661mIwcDwPr16/Hmm29CpTLtH1Ac54bItKReuIZnEjLhaCdHxp/HQunIqVSIqCWjjnNTWFiIyMjIFssjIyNRWFio78sRkZWL6u6B3j7OqKypx9c/5d39CUREd6F3uenevTu2bNnSYvnmzZvRo0cPg4QiIushCL8O6rcuPQc1dRzUj4jujd6Turz11luYPn06UlJSMGLECAiCgLS0NOzbt6/V0kNEdDdTBvph2a5zKFJX4YdThZg6qIvUkYjIjOm952batGn48ccf4eHhge3bt2Pr1q3w8PBAZmYmHnnkEWNkJCILp7CRY2ZEw6B+q1MvcYgJIronnDiTiEzCzYoaRLy3D1W1GmyaOwyR93lIHYmITAgnziQis+PqZIfHwroCABI4qB8R3QOdy41MJoNcLr/jzcZG71N4iIi0nh8RBEEA9p0txi/F5VLHISIzpXMb2bZtW5uPHTp0CJ9++imPkxPRPQn27ISxvb2xN/sq1qar8O4joVJHIiIzpHO5efjhh1ssO3v2LJYsWYLvv/8eM2bMwP/93/8ZNBwRWZ+50UHYm30ViUcL8KfxPeHeSSF1JCIyM+065+bKlSuYO3cu+vfvj7q6Ohw/fhzr169HQECAofMRkZUZGuSG0C5KVNdp8NWPHNSPiPSnV7kpLS3F4sWL0b17d5w+fRr79u3D999/j9BQ7jomIsMQBAFzohsG9duQkYOq2nqJExGRudG53CxbtgzBwcH4z3/+g6+//hqHDh1CdHS0MbMRkZWaFOoLX6U9SsprkJR1Reo4RGRmdB7nRiaTwcHBAePGjYNcLm9zva1btxosnDFwnBsi87Aq5SLe/eEsenp3wq6FIyEIgtSRiEhC+nx/63xC8bPPPssfLkTUYaYPCcDHey/g/NVypFwowf09PaWORERmQudys27dOiPGICJqTulgi+lDArA2XYU1qZdYbohIZxyhmIhM1nMjAiETgNQLJThbpJY6DhGZCZYbIjJZ/m6OmBjiCwBYwykZiEhHLDdEZNJmN14W/l3WZRSrqyROQ0TmgOWGiEza4ABXhHVzRW29iA0ZuVLHISIzwHJDRCZvTlTD3puNP+bidg0H9SOiO2O5ISKTF9PPB/5uDrhVWYtvjxVIHYeITBzLDRGZPLlMwPMjGvberE1TQaPRaexRIrJSLDdEZBaeCPeHs70NVCUV2He2WOo4RGTCWG6IyCw4KWzw1LAAAMCa1EsSpyEiU8ZyQ0RmY1ZkIGxkAn5U3cCpglKp4xCRiWK5ISKz4at0wEP9Gwf1S+PeGyJqHcsNEZmVOdHBAID/nCzElVu3JU5DRKaI5YaIzEpIFyWGB7uhXiNi/aEcqeMQkQliuSEiszO3ce/Npsw8lFfXSZyGiEwNyw0RmZ3RvbwQ7OmEsqo6bPkpX+o4RGRiWG6IyOzIZAJmN07JsDZdhbp6jcSJiMiUsNwQkVmaNrgrXB1tUXDzNnafuSp1HCIyISw3RGSW7G3leGZ4NwDAag7qR0S/wXJDRGbrmYhA2MllOJ53C0dzb0odh4hMBMsNEZktT2cFpg7yA8ApGYjoVyw3RGTWmgb123W6CHnXKyVOQ0SmgOWGiMxaT29njOzpCY3YcOUUEZHk5eazzz5DUFAQ7O3tERYWhtTU1DbXPXjwIARBaHE7e/ZsByYmIlMzN7rhsvAtR/JRertW4jREJDVJy83mzZuxcOFCvP766zh+/Diio6MxceJE5OXl3fF5586dQ2FhofbWo0ePDkpMRKYoqrsHevs4o7KmHl9n3vnnBxFZPknLzYcffojZs2djzpw56NOnD5YvXw5/f3+sXLnyjs/z8vKCj4+P9iaXyzsoMRGZIkH4dVC/dek5qKnjoH5E1kyyclNTU4OjR48iJiam2fKYmBgcOnTojs8dNGgQfH19MXbsWBw4cOCO61ZXV0OtVje7EZHlmTLQD57OChSpq/DDqUKp4xCRhCQrNyUlJaivr4e3t3ez5d7e3igqKmr1Ob6+vli1ahUSExOxdetW9OrVC2PHjkVKSkqb7xMfHw+lUqm9+fv7G3Q7iMg0KGzkmBnx66B+oihKnIiIpGIjdQBBEJrdF0WxxbImvXr1Qq9evbT3IyIikJ+fjw8++AAjR45s9TlLlixBXFyc9r5arWbBIbJQM4Z1w4oDv+D0FTUOX7qBiPvcpY5ERBKQbM+Nh4cH5HJ5i700xcXFLfbm3Mnw4cNx4cKFNh9XKBRwcXFpdiMiy+TqZIfHwroC4KB+RNZMsnJjZ2eHsLAw7Nmzp9nyPXv2IDIyUufXOX78OHx9fQ0dj4jM1PMjgiAIwL6zxbh4rVzqOEQkAUkPS8XFxeGZZ55BeHg4IiIisGrVKuTl5SE2NhZAwyGly5cvY8OGDQCA5cuXIzAwEP369UNNTQ02btyIxMREJCYmSrkZRGRCgj07YWxvb+zNvoqENBXefSRU6khE1MEkLTfTp0/H9evX8fbbb6OwsBAhISH44Ycf0K1bw0mBhYWFzca8qampwaJFi3D58mU4ODigX79+2LFjByZNmiTVJhCRCZoTHYS92VeReLQAi2J6wc3JTupIRNSBBNHKLilQq9VQKpUoLS3l+TdEFkoURUxZkY5Tl0sRN74nFozlQJ9E5k6f72/Jp18gIjI0QRAwp3FKhg0ZOaiqrZc4ERF1JJYbIrJIk0J94au0R0l5DZKyrkgdh4g6EMsNEVkkW7kMsyIDAQBr0jioH5E1YbkhIov1h6EBcLKT4/zVcqRcKJE6DhF1EJYbIrJYSgdbPDGkYURyDupHZD1YbojIoj0/IggyAUi9UIKzRZw4l8gasNwQkUXzd3PEhBAfAEBCqkriNETUEVhuiMjizYkOBgB8l3UFxWVVEqchImNjuSEiizc4wBWDAzqjpl6DLzNypY5DREbGckNEVmFu496bjYdzcbuGg/oRWTKWGyKyCjH9fODv5oCblbVIPFYgdRwiMiKWGyKyCnKZgOdHNEzJsDZNBY2Gg/oRWSqWGyKyGk+E+8PZ3gaXSiqw/2yx1HGIyEhYbojIajgpbPDUsAAAwGoO6kdksVhuiMiqzIoMhI1MwI+qGzhVUCp1HCIyApYbIrIqvkoHPNTfF0DDhJpEZHlYbojI6jQN6rfjZCGu3LotcRoiMjSWGyKyOiFdlBge7IY6jYj1h3KkjkNEBsZyQ0RWqWlQv02ZeSivrpM4DREZEssNEVml0b28EOzphLKqOmz5KV/qOERkQCw3RGSVZDIBs6MaB/VLV6Geg/oRWQyWGyKyWo8O6gpXR1sU3LyNXaeLpI5DRAbCckNEVsvBTo5nhncDAKzhoH5EFoPlhois2tMR3WAnl+FY3i0czb0pdRwiMgCWGyKyal7O9pg6yA8A994QWQqWGyKyerOjGi4L33W6CHnXKyVOQ0T3iuWGiKxeLx9njOzpCY3YcOUUEZk3lhsiIgBzGi8L33IkH6W3ayVOQ0T3guWGiAhAdA8P9PJ2RmVNPb7OzJM6DhHdA5YbIiIAgiBgdnTD3pt16TmorddInIiI2ovlhoio0cMD/eDRSYEidRV2nCyUOg4RtRPLDRFRI4WNHDMjGgf1S7sEUeSUDETmiOWGiOg3ZgzvBntbGX6+rMbhSzekjkNE7cByQ0T0G25Odpg2uCsAICGNg/oRmSOWGyKi32maLXxvdjEuXiuXOA0R6Yvlhojod4I9O2FcHy8AwNo0DupHZG5YboiIWjEnumFKhm+PFuBGRY3EaYhIHyw3REStGBbkhpAuLqiu0+Crw7lSxyEiPbDcEBG1QhAEzG3ce7M+IxdVtfUSJyIiXbHcEBG1YVKoL3yV9igpr0bSiStSxyEiHbHcEBG1wVYuw6zIQABAQqqKg/oRmQmWGyKiO/jD0AA42clx7moZUi+USB2HiHTAckNEdAdKB1s8McQfALA6lYP6EZkDlhsiort4fkQQZAKQeqEE54rKpI5DRHdhI3UAIiJT5+/miAkhPvjhVBHe/eEMHh3cFV7O9hga5Aa5TJA6XrvUa0Rkqm6guKzKrLeF22FaTGU7JC83n332Gd5//30UFhaiX79+WL58OaKjo9tcPzk5GXFxcTh9+jT8/Pzw6quvIjY2tgMTE5E1CvFT4odTRUg+X4Lk8w3n3vgq7fHG5L6YEOIrcTr97Py5EG99fwaFpVXaZea4LdwO02JK2yHpYanNmzdj4cKFeP3113H8+HFER0dj4sSJyMvLa3V9lUqFSZMmITo6GsePH8drr72GBQsWIDExsYOTE5E12flzId7fda7F8qLSKszbeAw7fy6UIFX77Py5EPM2Hmv2BQSY37ZwO0yLqW2HIEp4beOwYcMwePBgrFy5UrusT58+mDp1KuLj41usv3jxYiQlJSE7O1u7LDY2FidOnEBGRoZO76lWq6FUKlFaWgoXF5d73wgismj1GhFRS/e3+KH9W17OCvw7NsLkDyPUa0Q89nkGrpVVt7mOOWwLt8O03G07BAA+SnukLR5zT9uhz/e3ZIelampqcPToUfz5z39utjwmJgaHDh1q9TkZGRmIiYlptuyBBx5AQkICamtrYWtr2+I51dXVqK7+9S9crVYbID0RWYtM1Y07FhsAKC6rxv3vH+yYQEZmKdvC7TAdIoDC0ipkqm4g4j73DnlPycpNSUkJ6uvr4e3t3Wy5t7c3ioqKWn1OUVFRq+vX1dWhpKQEvr4tj+nFx8fjrbfeMlxwIrIqxWV3LjZNbGSCSf92DTT8hl2nufvOelPfFm6HadF1O3T9v2QIkp9QLAjNPzBRFFssu9v6rS1vsmTJEsTFxWnvq9Vq+Pv7tzcuEVkZL2d7ndb7cvawDvuttL0yLl7Hk6sP33U9U98Wbodp0XU7dP2/ZAiSnVDs4eEBuVzeYi9NcXFxi70zTXx8fFpd38bGBu7urX/wCoUCLi4uzW5ERLoaGuQGX6U92vqVS0DDFSFDg9w6Mla7WMq2cDtMiyluh2Tlxs7ODmFhYdizZ0+z5Xv27EFkZGSrz4mIiGix/u7duxEeHt7q+TZERPdKLhPwxuS+ANDih3fT/Tcm9zXpwwZNLGVbuB2mxRS3Q9JLwePi4rBmzRqsXbsW2dnZeOWVV5CXl6cdt2bJkiV49tlntevHxsYiNzcXcXFxyM7Oxtq1a5GQkIBFixZJtQlEZAUmhPhi5dOD4aNsvlvdR2mPlU8PNquxSCxlW7gdpsXUtkPSS8GBhkH8li1bhsLCQoSEhOCjjz7CyJEjAQCzZs1CTk4ODh48qF0/OTkZr7zyinYQv8WLF+s1iB8vBSei9jKV0VcNwVK2hdthWoy5Hfp8f0tebjoayw0REZH50ef7mxNnEhERkUVhuSEiIiKLwnJDREREFoXlhoiIiCwKyw0RERFZFJYbIiIisigsN0RERGRRWG6IiIjIorDcEBERkUWxkTpAR2sakFmtVkuchIiIiHTV9L2ty8QKVlduysrKAAD+/v4SJyEiIiJ9lZWVQalU3nEdq5tbSqPR4MqVK3B2doYgmN+kZB1BrVbD398f+fn5nH/LBPDzMC38PEwPPxPTYqzPQxRFlJWVwc/PDzLZnc+qsbo9NzKZDF27dpU6hllwcXHhDwoTws/DtPDzMD38TEyLMT6Pu+2xacITiomIiMiisNwQERGRRWG5oRYUCgXeeOMNKBQKqaMQ+HmYGn4epoefiWkxhc/D6k4oJiIiIsvGPTdERERkUVhuiIiIyKKw3BAREZFFYbkhIiIii8JyQ1rx8fEYMmQInJ2d4eXlhalTp+LcuXNSx6JG8fHxEAQBCxculDqK1bp8+TKefvppuLu7w9HREQMHDsTRo0eljmWV6urq8Je//AVBQUFwcHBAcHAw3n77bWg0GqmjWY2UlBRMnjwZfn5+EAQB27dvb/a4KIp488034efnBwcHB4waNQqnT5/ukGwsN6SVnJyM+fPn4/Dhw9izZw/q6uoQExODiooKqaNZvZ9++gmrVq1C//79pY5itW7evIkRI0bA1tYW//3vf3HmzBn84x//QOfOnaWOZpWWLl2Kzz//HCtWrEB2djaWLVuG999/H59++qnU0axGRUUFBgwYgBUrVrT6+LJly/Dhhx9ixYoV+Omnn+Dj44Px48dr53g0Jl4KTm26du0avLy8kJycjJEjR0odx2qVl5dj8ODB+Oyzz/D3v/8dAwcOxPLly6WOZXX+/Oc/Iz09HampqVJHIQAPPfQQvL29kZCQoF02bdo0ODo64ssvv5QwmXUSBAHbtm3D1KlTATTstfHz88PChQuxePFiAEB1dTW8vb2xdOlS/M///I9R83DPDbWptLQUAODm5iZxEus2f/58PPjggxg3bpzUUaxaUlISwsPD8fjjj8PLywuDBg3C6tWrpY5ltaKiorBv3z6cP38eAHDixAmkpaVh0qRJEicjAFCpVCgqKkJMTIx2mUKhwP33349Dhw4Z/f2tbuJM0o0oioiLi0NUVBRCQkKkjmO1vvnmGxw9ehRHjhyROorVu3TpElauXIm4uDi89tpryMzMxIIFC6BQKPDss89KHc/qLF68GKWlpejduzfkcjnq6+vxzjvv4Mknn5Q6GgEoKioCAHh7ezdb7u3tjdzcXKO/P8sNterFF1/EyZMnkZaWJnUUq5Wfn4+XX34Zu3fvhr29vdRxrJ5Go0F4eDjeffddAMCgQYNw+vRprFy5kuVGAps3b8bGjRuxadMm9OvXD1lZWVi4cCH8/Pwwc+ZMqeNRI0EQmt0XRbHFMmNguaEWXnrpJSQlJSElJQVdu3aVOo7VOnr0KIqLixEWFqZdVl9fj5SUFKxYsQLV1dWQy+USJrQuvr6+6Nu3b7Nlffr0QWJiokSJrNv//u//4s9//jP+8Ic/AABCQ0ORm5uL+Ph4lhsT4OPjA6BhD46vr692eXFxcYu9OcbAc25ISxRFvPjii9i6dSv279+PoKAgqSNZtbFjx+LUqVPIysrS3sLDwzFjxgxkZWWx2HSwESNGtBga4fz58+jWrZtEiaxbZWUlZLLmX2FyuZyXgpuIoKAg+Pj4YM+ePdplNTU1SE5ORmRkpNHfn3tuSGv+/PnYtGkTvvvuOzg7O2uPmSqVSjg4OEiczvo4Ozu3ON/JyckJ7u7uPA9KAq+88goiIyPx7rvv4oknnkBmZiZWrVqFVatWSR3NKk2ePBnvvPMOAgIC0K9fPxw/fhwffvghnn/+eamjWY3y8nL88ssv2vsqlQpZWVlwc3NDQEAAFi5ciHfffRc9evRAjx498O6778LR0RFPPfWU8cOJRI0AtHr74osvpI5Gje6//37x5ZdfljqG1fr+++/FkJAQUaFQiL179xZXrVoldSSrpVarxZdfflkMCAgQ7e3txeDgYPH1118Xq6urpY5mNQ4cONDqd8bMmTNFURRFjUYjvvHGG6KPj4+oUCjEkSNHiqdOneqQbBznhoiIiCwKz7khIiIii8JyQ0RERBaF5YaIiIgsCssNERERWRSWGyIiIrIoLDdERERkUVhuiIiIyKKw3BAREZFFYbkhIqskCAK2b98udQwiMgKWGyLqcLNmzYIgCC1uEyZMkDoaEVkATpxJRJKYMGECvvjii2bLFAqFRGmIyJJwzw0RSUKhUMDHx6fZzdXVFUDDIaOVK1di4sSJcHBwQFBQEP797383e/6pU6cwZswYODg4wN3dHS+88ALKy8ubrbN27Vr069cPCoUCvr6+ePHFF5s9XlJSgkceeQSOjo7o0aMHkpKStI/dvHkTM2bMgKenJxwcHNCjR48WZYyITBPLDRGZpL/+9a+YNm0aTpw4gaeffhpPPvkksrOzAQCVlZWYMGECXF1d8dNPP+Hf//439u7d26y8rFy5EvPnz8cLL7yAU6dOISkpCd27d2/2Hm+99RaeeOIJnDx5EpMmTcKMGTNw48YN7fufOXMG//3vf5GdnY2VK1fCw8Oj4/4CiKj9OmTucSKi35g5c6Yol8tFJyenZre3335bFEVRBCDGxsY2e86wYcPEefPmiaIoiqtWrRJdXV3F8vJy7eM7duwQZTKZWFRUJIqiKPr5+Ymvv/56mxkAiH/5y1+098vLy0VBEMT//ve/oiiK4uTJk8XnnnvOMBtMRB2K59wQkSRGjx6NlStXNlvm5uam/XNERESzxyIiIpCVlQUAyM7OxoABA+Dk5KR9fMSIEdBoNDh37hwEQcCVK1cwduzYO2bo37+/9s9OTk5wdnZGcXExAGDevHmYNm0ajh07hpiYGEydOhWRkZHt2lYi6lgsN0QkCScnpxaHie5GEAQAgCiK2j+3to6Dg4NOr2dra9viuRqNBgAwceJE5ObmYseOHdi7dy/Gjh2L+fPn44MPPtArMxF1PJ5zQ0Qm6fDhwy3u9+7dGwDQt29fZGVloaKiQvt4eno6ZDIZevbsCWdnZwQGBmLfvn33lMHT0xOzZs3Cxo0bsXz5cqxateqeXo+IOgb33BCRJKqrq1FUVNRsmY2Njfak3X//+98IDw9HVFQUvvrqK2RmZiIhIQEAMGPGDLzxxhuYOXMm3nzzTVy7dg0vvfQSnnnmGXh7ewMA3nzzTcTGxsLLywsTJ05EWVkZ0tPT8dJLL+mU729/+xvCwsLQr18/VFdX4z//+Q/69OljwL8BIjIWlhsiksTOnTvh6+vbbFmvXr1w9uxZAA1XMn3zzTf44x//CB8fH3z11Vfo27cvAMDR0RG7du3Cyy+/jCFDhsDR0RHTpk3Dhx9+qH2tmTNnoqqqCh999BEWLVoEDw8PPPbYYzrns7Ozw5IlS5CTkwMHBwdER0fjm2++McCWE5GxCaIoilKHICL6LUEQsG3bNkydOlXqKERkhnjODREREVkUlhsiIiKyKDznhohMDo+WE9G94J4bIiIisigsN0RERGRRWG6IiIjIorDcEBERkUVhuSEiIiKLwnJDREREFoXlhoiIiCwKyw0RERFZlP8HETJ7dbw0YyQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Here we can clearly see that data is linearly seperable, thus perceptron should classify correcly\n",
    "\n",
    "ppn = Perceptron(eta=0.1, n_iter=10)\n",
    "ppn.fit(X,y)\n",
    "\n",
    "plt.plot(range(1, len(ppn.errors_)+1), ppn.errors_, marker='o')\n",
    "plt.xlabel(\"Epochs\")\n",
    "plt.ylabel(\"No. of Updates/Mistakes\")\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "216a15e6-998f-4031-a001-6b18762f9cc8",
   "metadata": {},
   "source": [
    "#### A function for plotting decision regions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9eeadf04-b099-4321-aca7-4dd19bbe13bd",
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib.colors import ListedColormap\n",
    "\n",
    "\n",
    "def plot_decision_regions(X, y, classifier, resolution=0.02):\n",
    "\n",
    "    # setup marker generator and color map\n",
    "    markers = ('o', 's', '^', 'v', '<')\n",
    "    colors = ('red', 'blue', 'lightgreen', 'gray', 'cyan')\n",
    "    cmap = ListedColormap(colors[:len(np.unique(y))])\n",
    "\n",
    "    # plot the decision surface\n",
    "    x1_min, x1_max = X[:, 0].min() - 1, X[:, 0].max() + 1\n",
    "    x2_min, x2_max = X[:, 1].min() - 1, X[:, 1].max() + 1\n",
    "    \n",
    "    xx1, xx2 = np.meshgrid(np.arange(x1_min, x1_max, resolution),\n",
    "                           np.arange(x2_min, x2_max, resolution))\n",
    "    \n",
    "    lab = classifier.predict(np.array([xx1.ravel(), xx2.ravel()]).T)\n",
    "    lab = lab.reshape(xx1.shape)\n",
    "    \n",
    "    plt.contourf(xx1, xx2, lab, alpha=0.3, cmap=cmap)\n",
    "    plt.xlim(xx1.min(), xx1.max())\n",
    "    plt.ylim(xx2.min(), xx2.max())\n",
    "\n",
    "    # plot class examples\n",
    "    for idx, cl in enumerate(np.unique(y)):\n",
    "        plt.scatter(x=X[y == cl, 0], \n",
    "                    y=X[y == cl, 1],\n",
    "                    alpha=0.8, \n",
    "                    c=colors[idx],\n",
    "                    marker=markers[idx], \n",
    "                    label=f'Class {cl}', \n",
    "                    edgecolor='black')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4b294ad3-65d9-440e-a858-5943d4128ef8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_decision_regions(X, y, classifier=ppn)\n",
    "plt.xlabel('Sepal length [cm]')\n",
    "plt.ylabel('Petal length [cm]')\n",
    "plt.legend(loc='upper left')\n",
    "\n",
    "\n",
    "#plt.savefig('images/02_08.png', dpi=300)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e08445c-e61c-4d79-bda2-f4cd0b7b1525",
   "metadata": {},
   "source": [
    "### ***Adaline and the convergence of learning***\n",
    "\n",
    "- **ADAaptive LInear NEuron (Adaline)** - A type of *single layer neural network(NN)*\n",
    "\n",
    "- The key diff. b/w Adaline & Perceptron is that weights are updated based on a ***linear activation function*** rather than a *unit step function* like in perceptron.\n",
    "\n",
    "- In Adaline, the *linear activation function* is simply the **identity function** of the net i/p $(z = w^Tx + b)$ $$\\sigma(z) = z$$\n",
    "\n",
    "![Adaline_Perceptron](Images/Adaline_Perceptron.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b435518f-ed29-48b1-8e09-fa4e1bf47962",
   "metadata": {},
   "source": [
    "### ***Minimizing Loss function with Gradient Descent***\n",
    "\n",
    "- The objective is to minimize the **Mean Squared Error(MSE) [or the Objective Function/Loss Function]** b/w the calculated o/p and the true class label:$$L(\\textbf{w},b) = \\frac{1}{2n} \\sum_{i=1}^{n} \\left(y^{(i)} - \\sigma(z^{(i)})\\right)^{2}$$\n",
    "\n",
    "- The main advantage of this continuous linear activation function, in contrast to the unit step function, is that the loss function becomes differentiable. Another nice property of this loss function is that it is convex; thus, we can use a very simple yet powerful optimization algorithm called gradient descent.\n",
    "\n",
    "- So, we can the update as \n",
    "$$\\Delta w_j = -\\eta \\frac{\\partial L}{\\partial w_j} \\text{ and } \\Delta b = -\\eta \\frac{\\partial L}{\\partial b} $$\n",
    "\n",
    "$$w: = w + \\Delta w \\text{ , } b: = b + \\Delta b$$\n",
    "\n",
    "where\n",
    "\n",
    "$$\\frac{\\partial L}{\\partial w_j} = -\\frac{2}{n}\\sum_{i} \\left(y^{(i)} - \\sigma(z^{(i)}) \\right)x_{j}^{(i)}$$\n",
    "\n",
    "$$\\frac{\\partial L}{\\partial b} = -\\frac{2}{n}\\sum_{i} \\left(y^{(i)} - \\sigma(z^{(i)}) \\right)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "42048d3b-9f6d-42bd-b218-be528957553d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Implementing Adaline in Python\n",
    "\n",
    "class AdalineGD:\n",
    "    \"\"\"ADAptive LInear NEuron classifier.\n",
    "\n",
    "    Parameters\n",
    "    ------------\n",
    "    eta : float\n",
    "      Learning rate (between 0.0 and 1.0)\n",
    "    n_iter : int\n",
    "      Passes over the training dataset.\n",
    "    random_state : int\n",
    "      Random number generator seed for random weight\n",
    "      initialization.\n",
    "\n",
    "\n",
    "    Attributes\n",
    "    -----------\n",
    "    w_ : 1d-array\n",
    "      Weights after fitting.\n",
    "    b_ : Scalar\n",
    "      Bias unit after fitting.\n",
    "    losses_ : list\n",
    "      Mean squared eror loss function values in each epoch.\n",
    "    \"\"\"\n",
    "    def __init__(self, eta=0.01, n_iter=50, random_state=1):\n",
    "        self.eta = eta\n",
    "        self.n_iter = n_iter\n",
    "        self.random_state = random_state\n",
    "    \n",
    "    def fit(self, X,y):\n",
    "        \"\"\" Fit training data.\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        X : {array-like}, shape = [n_examples, n_features]\n",
    "          Training vectors, where n_examples is the number of examples and\n",
    "          n_features is the number of features.\n",
    "        y : array-like, shape = [n_examples]\n",
    "          Target values.\n",
    "\n",
    "        Returns\n",
    "        -------\n",
    "        self : object\n",
    "        \"\"\"\n",
    "        rgen = np.random.RandomState(self.random_state)\n",
    "        self.w_ = rgen.normal(loc=0.0, scale=0.01, size=X.shape[1])\n",
    "        self.b_ = np.float_(0.)\n",
    "        self.losses_ = []\n",
    "        \n",
    "        for i in range(self.n_iter):\n",
    "            net_input = self.net_input(X)\n",
    "            output = self.activation(net_input)\n",
    "            errors = y-output\n",
    "            self.w_ += self.eta*2.0*X.T.dot(errors)/X.shape[0]\n",
    "            self.b_ += self.eta*2.0*errors.mean()\n",
    "            loss = (errors**2).mean() # Mean Squared Error\n",
    "            self.losses_.append(loss)\n",
    "            \n",
    "        return self\n",
    "            \n",
    "    \n",
    "    def net_input(self, X):\n",
    "        \"\"\"Calculate net input\"\"\"\n",
    "        return np.dot(X, self.w_) + self.b_\n",
    "    \n",
    "    def activation(self, X):\n",
    "        \"Compute linear activation sigma(z) = z\"\n",
    "        return X\n",
    "    \n",
    "    def predict(self, X):\n",
    "        \"\"\"Return class label after unit step\"\"\"\n",
    "        return np.where(self.activation(self.net_input(X)) >= 0.5, 1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d1a6286b-29a4-429f-9f9e-9c26a6788d41",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(10, 4))\n",
    "\n",
    "ada1 = AdalineGD(n_iter=15, eta=0.1).fit(X, y)\n",
    "\n",
    "ax[0].plot(range(1, len(ada1.losses_) + 1), np.log10(ada1.losses_), marker='o')\n",
    "ax[0].set_xlabel('Epochs')\n",
    "ax[0].set_ylabel('log(Mean squared error)')\n",
    "ax[0].set_title('Adaline - Learning rate 0.1')\n",
    "\n",
    "ada2 = AdalineGD(n_iter=15, eta=0.0001).fit(X, y)\n",
    "ax[1].plot(range(1, len(ada2.losses_) + 1), ada2.losses_, marker='o')\n",
    "ax[1].set_xlabel('Epochs')\n",
    "ax[1].set_ylabel('Mean squared error')\n",
    "ax[1].set_title('Adaline - Learning rate 0.0001')\n",
    "\n",
    "# plt.savefig('images/02_11.png', dpi=300)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b794991-c05b-4f51-a4bb-242ce0a425d5",
   "metadata": {},
   "source": [
    "- Left chart shows that if learning rate eta is too large, then instead of minimizing the loss fuction, the MSE becomes larger in every epoch, becoz we overshoot the global minima.\n",
    "\n",
    "- On the other hand, we can see that the loss decreases on the right plot, but the chosen learning rate, is so small that the algorithm would require a very large number of epochs to converge to the global loss minimum.\n",
    "\n",
    "![gd](Images/gd.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "349bcd02-c8a6-4a8d-859d-163a24dd9fb9",
   "metadata": {},
   "source": [
    "### ***Improving Gradient Descent through feature scaling***\n",
    "\n",
    "- Gradient descent is one of the many algorithms that benefit from feature scaling. \n",
    "\n",
    "- We will use a ***feature scaling method called standardization.*** This normalization procedure helps gradient descent learning to converge more quickly; however, it does not make the original dataset normally distributed. \n",
    "\n",
    "- ***Standardization shifts the mean of each feature so that it is centered at zero and each feature has a standard deviation of 1 (unit variance).***\n",
    "\n",
    "- To standardize the jth feature $$x_{j}^{'} = \\frac{x_j - \\mu_j}{\\sigma_j}$$ Here, $x_j$ is a vector consisting of the $j^{th}$ feature values of all training examples, n, and this standardization technique is applied to each feature, j, in our dataset.\n",
    "\n",
    "- One of the reasons why standardization helps with gradient descent learning is that it is easier to find a learning rate that works well for all weights (and the bias). If the features are on vastly different scales, a learning rate that works well for updating one weight might be too large or too small to update the other weight equally well. Overall, using standardized features can stabilize the training such that the optimizer has to go through fewer steps to find a good or optimal solution (the global loss minimum)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d4d54968-db7b-4846-a28d-f698103729ab",
   "metadata": {},
   "outputs": [],
   "source": [
    "# standardize features\n",
    "X_std = np.copy(X)\n",
    "X_std[:, 0] = (X[:, 0] - X[:, 0].mean()) / X[:, 0].std()\n",
    "X_std[:, 1] = (X[:, 1] - X[:, 1].mean()) / X[:, 1].std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9b51cf15-bedf-418d-876e-4a04e0d9dae5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ada_gd = AdalineGD(n_iter=20, eta=0.5)\n",
    "ada_gd.fit(X_std, y)\n",
    "\n",
    "plot_decision_regions(X=X_std, y=y, classifier=ada_gd)\n",
    "plt.title('Adaline - Gradient descent')\n",
    "plt.xlabel('Sepal length [standardized]')\n",
    "plt.ylabel('Petal length [standardized]')\n",
    "plt.legend(loc='upper left')\n",
    "plt.tight_layout()\n",
    "#plt.savefig('images/02_14_1.png', dpi=300)\n",
    "plt.show()\n",
    "\n",
    "plt.plot(range(1, len(ada_gd.losses_) + 1), ada_gd.losses_, marker='o')\n",
    "plt.xlabel('Epochs')\n",
    "plt.ylabel('Mean squared error')\n",
    "\n",
    "plt.tight_layout()\n",
    "#plt.savefig('images/02_14_2.png', dpi=300)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a41a2855-c557-4a1c-b0c5-d6c1a87a1232",
   "metadata": {},
   "source": [
    "### ***Large scale ML and Stochastic Gradient Descent(SGD)***\n",
    "\n",
    "- When we have large scale datasets, we used SGD.\n",
    "\n",
    "- A popular alternative to the batch gradient descent algorithm is *stochastic gradient descent (SGD), which is sometimes also called iterative or online gradient descent.*\n",
    "\n",
    "- Instead of updating the weights based on the sum of the accumulated errors over all training examples,<br><br> $\\Delta w_j = \\frac{2\\eta}{n}\\sum_{i} \\left(y^{(i)} - \\sigma(z^{(i)}) \\right)x_{j}^{(i)}$ <br><br> we update the parameters incrementally for each training excample, for instance: <br><br> $\\Delta w_j = \\eta \\left(y^{(i)} - \\sigma(z^{(i)})\\right)x_{j}^{(i)}, \\Delta b = \\eta \\left(y^{(i)} - \\sigma(z^{(i)})\\right)$\n",
    "\n",
    "- **Although SGD can be considered as an approximation of gradient descent, it typically reaches convergence much faster because of the more frequent weight updates.**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "793b1a5d-ce84-4324-8d57-4cb0e8a7622a",
   "metadata": {},
   "source": [
    "- **Adjust the learning rate during training**\n",
    "\n",
    "- in SGD, the fixed learning rate, $\\eta$, is often replaced by an **adaptive learning rate** *that decreases over time,*<br>for example:<br> $\\frac{c_1}{\\text{[no. of iterations] } + c_2}$<br> where $c_1$ and $c_2$ are constants.\n",
    "\n",
    "- Note that SGD does not reach the global loss minimum but an area very close to it. And using an adaptive learning rate, we can achieve further annealing to the loss minimum.\n",
    "\n",
    "- Another advantage of SGD is that we can use it for online learning. In online learning, our model is trained on the fly as new training data arrives. This is especially useful if we are accumulating large amounts of data, for example, customer data in web applications. Using online learning, the system can immediately adapt to changes, and the training data can be discarded after updating the model if storage space is an issue."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "389d8969-6e5f-4872-ab60-dc24a9255d63",
   "metadata": {},
   "source": [
    "#### ***Mini-batch Gradient Descent***\n",
    "\n",
    "***A compromise between full batch gradient descent and SGD is so-called mini-batch gradient descent. Mini-batch gradient descent can be understood as applying full batch gradient descent to smaller subsets of the training data, for example, 32 training examples at a time. The advantage over full batch gradient descent is that convergence is reached faster via mini-batches because of the more frequent weight updates.***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2f250f94-ef7f-4153-9380-8a7b91be7746",
   "metadata": {},
   "outputs": [],
   "source": [
    "class AdalineSGD:\n",
    "    \"\"\"ADAptive LInear NEuron classifier.\n",
    "\n",
    "    Parameters\n",
    "    ------------\n",
    "    eta : float\n",
    "      Learning rate (between 0.0 and 1.0)\n",
    "    n_iter : int\n",
    "      Passes over the training dataset.\n",
    "    shuffle : bool (default: True)\n",
    "      Shuffles training data every epoch if True to prevent cycles.\n",
    "    random_state : int\n",
    "      Random number generator seed for random weight\n",
    "      initialization.\n",
    "\n",
    "\n",
    "    Attributes\n",
    "    -----------\n",
    "    w_ : 1d-array\n",
    "      Weights after fitting.\n",
    "    b_ : Scalar\n",
    "        Bias unit after fitting.\n",
    "    losses_ : list\n",
    "      Mean squared error loss function value averaged over all\n",
    "      training examples in each epoch.\n",
    "\n",
    "        \n",
    "    \"\"\"\n",
    "    def __init__(self, eta=0.01, n_iter=10, shuffle=True, random_state=None):\n",
    "        self.eta = eta\n",
    "        self.n_iter = n_iter\n",
    "        self.w_initialized = False\n",
    "        self.shuffle = shuffle\n",
    "        self.random_state = random_state\n",
    "        \n",
    "    def fit(self, X, y):\n",
    "        \"\"\" Fit training data.\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        X : {array-like}, shape = [n_examples, n_features]\n",
    "          Training vectors, where n_examples is the number of examples and\n",
    "          n_features is the number of features.\n",
    "        y : array-like, shape = [n_examples]\n",
    "          Target values.\n",
    "\n",
    "        Returns\n",
    "        -------\n",
    "        self : object\n",
    "\n",
    "        \"\"\"\n",
    "        self._initialize_weights(X.shape[1])\n",
    "        self.losses_ = []\n",
    "        for i in range(self.n_iter):\n",
    "            if self.shuffle:\n",
    "                X, y = self._shuffle(X, y)\n",
    "            losses = []\n",
    "            for xi, target in zip(X, y):\n",
    "                losses.append(self._update_weights(xi, target))\n",
    "            avg_loss = np.mean(losses)\n",
    "            self.losses_.append(avg_loss)\n",
    "        return self\n",
    "\n",
    "    def partial_fit(self, X, y):\n",
    "        \"\"\"Fit training data without reinitializing the weights\"\"\"\n",
    "        if not self.w_initialized:\n",
    "            self._initialize_weights(X.shape[1])\n",
    "        if y.ravel().shape[0] > 1:\n",
    "            for xi, target in zip(X, y):\n",
    "                self._update_weights(xi, target)\n",
    "        else:\n",
    "            self._update_weights(X, y)\n",
    "        return self\n",
    "\n",
    "    def _shuffle(self, X, y):\n",
    "        \"\"\"Shuffle training data\"\"\"\n",
    "        r = self.rgen.permutation(len(y))\n",
    "        return X[r], y[r]\n",
    "    \n",
    "    def _initialize_weights(self, m):\n",
    "        \"\"\"Initialize weights to small random numbers\"\"\"\n",
    "        self.rgen = np.random.RandomState(self.random_state)\n",
    "        self.w_ = self.rgen.normal(loc=0.0, scale=0.01, size=m)\n",
    "        self.b_ = np.float_(0.)\n",
    "        self.w_initialized = True\n",
    "        \n",
    "    def _update_weights(self, xi, target):\n",
    "        \"\"\"Apply Adaline learning rule to update the weights\"\"\"\n",
    "        output = self.activation(self.net_input(xi))\n",
    "        error = (target - output)\n",
    "        self.w_ += self.eta * 2.0 * xi * (error)\n",
    "        self.b_ += self.eta * 2.0 * error\n",
    "        loss = error**2\n",
    "        return loss\n",
    "    \n",
    "    def net_input(self, X):\n",
    "        \"\"\"Calculate net input\"\"\"\n",
    "        return np.dot(X, self.w_) + self.b_\n",
    "\n",
    "    def activation(self, X):\n",
    "        \"\"\"Compute linear activation\"\"\"\n",
    "        return X\n",
    "\n",
    "    def predict(self, X):\n",
    "        \"\"\"Return class label after unit step\"\"\"\n",
    "        return np.where(self.activation(self.net_input(X)) >= 0.5, 1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "eb680b64-cab3-4bbd-8749-8a48ef848069",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ada_sgd = AdalineSGD(n_iter=15, eta=0.01, random_state=1)\n",
    "ada_sgd.fit(X_std, y)\n",
    "\n",
    "plot_decision_regions(X_std, y, classifier=ada_sgd)\n",
    "plt.title('Adaline - Stochastic gradient descent')\n",
    "plt.xlabel('Sepal length [standardized]')\n",
    "plt.ylabel('Petal length [standardized]')\n",
    "plt.legend(loc='upper left')\n",
    "\n",
    "plt.tight_layout()\n",
    "# plt.savefig('figures/02_15_1.png', dpi=300)\n",
    "plt.show()\n",
    "\n",
    "plt.plot(range(1, len(ada_sgd.losses_) + 1), ada_sgd.losses_, marker='o')\n",
    "plt.xlabel('Epochs')\n",
    "plt.ylabel('Average loss')\n",
    "\n",
    "# plt.savefig('figures/02_15_2.png', dpi=300)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2456a75-508f-4f39-a5bc-f2f9ea83dc8a",
   "metadata": {},
   "source": [
    "## **Summary**\n",
    "\n",
    "1. Perceptron\n",
    "2. Adaline \n",
    "3. Gradient Descent & Schoastic Gradient Descent"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a41f4dad-850e-42fe-b8b7-94faf14bb641",
   "metadata": {},
   "source": [
    "***Reference:***<br>\n",
    "***Raschka, Sebastian; Liu, Yuxi (Hayden); Mirjalili, Vahid. Machine Learning with PyTorch and Scikit-Learn: Develop machine learning and deep learning models with Python. Packt Publishing.*** "
   ]
  }
 ],
 "metadata": {
  "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": "3.10.9"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {},
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}