delta_learning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "experienced-curtis",
   "metadata": {},
   "source": [
    "# Delta Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "commercial-hospital",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a0182b3",
   "metadata": {},
   "source": [
    "## Sequential"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "according-range",
   "metadata": {},
   "source": [
    "<strong style=\"color:orange\">!!! REMEMBER: θ in augmented notation becomes -θ !!!</strong>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "impaired-status",
   "metadata": {},
   "outputs": [],
   "source": [
    "class sequential_delta_learning:\n",
    "    \"\"\" Delta learning algorithm\n",
    "        Parameters\n",
    "        ----------\n",
    "        X: np.array\n",
    "            Feature vectors\n",
    "        y: np.array\n",
    "            Class vector\n",
    "        a: np.array\n",
    "            Initialised weights\n",
    "        alpha: float, optional\n",
    "            Learning rate (default is 0.1)\n",
    "        epochs: int, optional\n",
    "            Number of training epochs. -1 is until convergence (default is -1)\n",
    "        max_epochs: int, optional\n",
    "            Max number of training epochs (default is 500)\n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, X, y, a, alpha=0.1, epochs=-1, max_epochs=500):\n",
    "        self.X = X\n",
    "        self.y = y\n",
    "        self.a = a\n",
    "        self.alpha = alpha\n",
    "        self.epochs = epochs\n",
    "        self.max_epochs = max_epochs\n",
    "        \n",
    "    def step(self, x):\n",
    "        if x > 0:\n",
    "            return 1\n",
    "        elif x == 0:\n",
    "            return 0.5\n",
    "        else:\n",
    "            return 0\n",
    "        \n",
    "    def train(self):\n",
    "        \"\"\"\n",
    "        Performs the training\n",
    "        \"\"\"\n",
    "        if self.epochs == -1:\n",
    "            self.train_until_convergence()\n",
    "        else: \n",
    "            self.train_until_epoch()\n",
    "            \n",
    "    def train_until_convergence(self):\n",
    "        counter = 0\n",
    "        epoch = 0\n",
    "        while epoch < self.max_epochs:\n",
    "            print('=====================')\n",
    "            print('EPOCH ', str(epoch + 1))\n",
    "            print('=====================')\n",
    "            e = 0\n",
    "            for i, x in enumerate(self.X):\n",
    "                counter += 1\n",
    "                print('iteration: ', epoch+1, '-', i+1)\n",
    "                print('tot-iter: ', counter)\n",
    "                print('--------------------')\n",
    "                \n",
    "                datum = np.insert(x, 0, 1)\n",
    "                label = self.y[i]\n",
    "                \n",
    "                y_hat = self.step(np.dot(self.a, datum))\n",
    "                if y_hat != label:\n",
    "                    e += 1\n",
    "                \n",
    "                self.a = self.a + self.alpha * (label -1 * y_hat) * np.transpose(datum)\n",
    "                \n",
    "                print('y: ', label, '\\ty_hat: ', y_hat)\n",
    "                print('lab-hat', label -1 * y_hat)\n",
    "                print('boundary: ', self.a)\n",
    "                \n",
    "            epoch += 1\n",
    "            if e == 0:\n",
    "                break\n",
    "        return\n",
    "    \n",
    "    def train_until_epoch(self):\n",
    "        counter = 0\n",
    "        for epoch in range(self.epochs):\n",
    "            print('=====================')\n",
    "            print('EPOCH ', str(epoch + 1))\n",
    "            print('=====================')\n",
    "            for i, x in enumerate(self.X):\n",
    "                counter += 1\n",
    "                print('iteration: ', epoch+1, '-', i+1)\n",
    "                print('tot-iter: ', counter)\n",
    "                print('--------------------')\n",
    "                \n",
    "                datum = np.insert(x, 0, 1)\n",
    "                label = self.y[i]\n",
    "                \n",
    "                y_hat = self.step(np.dot(self.a, datum))\n",
    "                \n",
    "                self.a = self.a + self.alpha * (label -1 * y_hat) * np.transpose(datum)\n",
    "                \n",
    "                print('y: ', label, '\\ty_hat: ', y_hat)\n",
    "                print('lab-hat', label -1 * y_hat)\n",
    "                print('boundary: ', self.a)\n",
    "        return"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "insured-midwest",
   "metadata": {},
   "source": [
    "## Batch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "realistic-shame",
   "metadata": {},
   "outputs": [],
   "source": [
    "class batch_delta_learning:\n",
    "    \"\"\" Delta learning algorithm\n",
    "        Parameters\n",
    "        ----------\n",
    "        X: np.array\n",
    "            Feature vectors\n",
    "        y: np.array\n",
    "            Class vector\n",
    "        a: np.array\n",
    "            Initialised weights\n",
    "        alpha: float, optional\n",
    "            Learning rate (default is 0.1)\n",
    "        epochs: int, optional\n",
    "            Number of training epochs. -1 is until convergence (default is -1)\n",
    "        max_epochs: int, optional\n",
    "            Max number of training epochs (default is 500)\n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, X, y, a, alpha=0.1, epochs=-1, max_epochs=500):\n",
    "        self.X = X\n",
    "        self.y = y\n",
    "        self.a = a\n",
    "        self.alpha = alpha\n",
    "        self.epochs = epochs\n",
    "        self.max_epochs = max_epochs\n",
    "        \n",
    "    def step(self, x):\n",
    "        if x > 0:\n",
    "            return 1\n",
    "        elif x == 0:\n",
    "            return 0.5\n",
    "        else:\n",
    "            return 0\n",
    "    \n",
    "    def train(self):\n",
    "        \"\"\"\n",
    "        Performs the training\n",
    "        \"\"\"\n",
    "        if self.epochs == -1:\n",
    "            self.train_until_convergence()\n",
    "        else: \n",
    "            self.train_until_epoch()\n",
    "            \n",
    "    def train_until_convergence(self):\n",
    "        counter = 0\n",
    "        epoch = 0\n",
    "        while epoch < self.max_epochs:\n",
    "            print('=====================')\n",
    "            print('EPOCH ', str(epoch + 1))\n",
    "            print('=====================')\n",
    "            delta = 0\n",
    "            e = 0\n",
    "            for i, x in enumerate(self.X):\n",
    "                counter += 1\n",
    "                print('iteration: ', epoch+1, '-', i+1)\n",
    "                print('tot-iter: ', counter)\n",
    "                print('--------------------')\n",
    "                \n",
    "                datum = np.insert(x, 0, 1)\n",
    "                label = self.y[i]\n",
    "                \n",
    "                y_hat = self.step(np.dot(self.a, datum))\n",
    "                delta += (label -1 * y_hat) * datum\n",
    "                \n",
    "                if y_hat != label:\n",
    "                    e += 1\n",
    "                \n",
    "                print('y: ', label, '\\ty_hat: ', y_hat)\n",
    "                print('lab-hat', label -1 * y_hat)\n",
    "                \n",
    "            self.a = self.a + self.alpha * delta\n",
    "            print('boundary: ', self.a)\n",
    "            \n",
    "            if e == 0:\n",
    "                break\n",
    "            epoch += 1\n",
    "        return\n",
    "            \n",
    "    def train_until_epoch(self):\n",
    "        counter = 0\n",
    "        for epoch in range(self.epochs):\n",
    "            print('=====================')\n",
    "            print('EPOCH ', str(epoch + 1))\n",
    "            print('=====================')\n",
    "            delta = 0\n",
    "            for i, x in enumerate(self.X):\n",
    "                counter += 1\n",
    "                print('iteration: ', epoch+1, '-', i+1)\n",
    "                print('tot-iter: ', counter)\n",
    "                print('--------------------')\n",
    "                \n",
    "                datum = np.insert(x, 0, 1)\n",
    "                label = self.y[i]\n",
    "                \n",
    "                y_hat = self.step(np.dot(self.a, datum))\n",
    "                delta += (label -1 * y_hat) * datum\n",
    "                \n",
    "                print('y: ', label, '\\ty_hat: ', y_hat)\n",
    "                print('lab-hat', label -1 * y_hat)\n",
    "                \n",
    "            self.a = self.a + self.alpha * delta\n",
    "            print('boundary: ', self.a)\n",
    "        return"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d6e94a2",
   "metadata": {},
   "source": [
    "## Examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "sweet-culture",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=====================\n",
      "EPOCH  1\n",
      "=====================\n",
      "iteration:  1 - 1\n",
      "tot-iter:  1\n",
      "--------------------\n",
      "y:  1 \ty_hat:  1\n",
      "lab-hat 0\n",
      "boundary:  [ 6.5 -5.5 -2.5]\n",
      "iteration:  1 - 2\n",
      "tot-iter:  2\n",
      "--------------------\n",
      "y:  1 \ty_hat:  0\n",
      "lab-hat 1\n",
      "boundary:  [ 7.5 -4.5 -0.5]\n",
      "iteration:  1 - 3\n",
      "tot-iter:  3\n",
      "--------------------\n",
      "y:  1 \ty_hat:  0\n",
      "lab-hat 1\n",
      "boundary:  [ 8.5 -2.5  0.5]\n",
      "iteration:  1 - 4\n",
      "tot-iter:  4\n",
      "--------------------\n",
      "y:  0 \ty_hat:  1\n",
      "lab-hat -1\n",
      "boundary:  [ 7.5  0.5 -0.5]\n",
      "iteration:  1 - 5\n",
      "tot-iter:  5\n",
      "--------------------\n",
      "y:  0 \ty_hat:  1\n",
      "lab-hat -1\n",
      "boundary:  [6.5 2.5 0.5]\n",
      "iteration:  1 - 6\n",
      "tot-iter:  6\n",
      "--------------------\n",
      "y:  0 \ty_hat:  0\n",
      "lab-hat 0\n",
      "boundary:  [6.5 2.5 0.5]\n",
      "=====================\n",
      "EPOCH  2\n",
      "=====================\n",
      "iteration:  2 - 1\n",
      "tot-iter:  7\n",
      "--------------------\n",
      "y:  1 \ty_hat:  1\n",
      "lab-hat 0\n",
      "boundary:  [6.5 2.5 0.5]\n",
      "iteration:  2 - 2\n",
      "tot-iter:  8\n",
      "--------------------\n",
      "y:  1 \ty_hat:  1\n",
      "lab-hat 0\n",
      "boundary:  [6.5 2.5 0.5]\n",
      "iteration:  2 - 3\n",
      "tot-iter:  9\n",
      "--------------------\n",
      "y:  1 \ty_hat:  1\n",
      "lab-hat 0\n",
      "boundary:  [6.5 2.5 0.5]\n",
      "iteration:  2 - 4\n",
      "tot-iter:  10\n",
      "--------------------\n",
      "y:  0 \ty_hat:  0\n",
      "lab-hat 0\n",
      "boundary:  [6.5 2.5 0.5]\n",
      "iteration:  2 - 5\n",
      "tot-iter:  11\n",
      "--------------------\n",
      "y:  0 \ty_hat:  1\n",
      "lab-hat -1\n",
      "boundary:  [5.5 4.5 1.5]\n",
      "iteration:  2 - 6\n",
      "tot-iter:  12\n",
      "--------------------\n",
      "y:  0 \ty_hat:  0\n",
      "lab-hat 0\n",
      "boundary:  [5.5 4.5 1.5]\n",
      "=====================\n",
      "EPOCH  3\n",
      "=====================\n",
      "iteration:  3 - 1\n",
      "tot-iter:  13\n",
      "--------------------\n",
      "y:  1 \ty_hat:  1\n",
      "lab-hat 0\n",
      "boundary:  [5.5 4.5 1.5]\n",
      "iteration:  3 - 2\n",
      "tot-iter:  14\n",
      "--------------------\n",
      "y:  1 \ty_hat:  1\n",
      "lab-hat 0\n",
      "boundary:  [5.5 4.5 1.5]\n",
      "iteration:  3 - 3\n",
      "tot-iter:  15\n",
      "--------------------\n",
      "y:  1 \ty_hat:  1\n",
      "lab-hat 0\n",
      "boundary:  [5.5 4.5 1.5]\n",
      "iteration:  3 - 4\n",
      "tot-iter:  16\n",
      "--------------------\n",
      "y:  0 \ty_hat:  0\n",
      "lab-hat 0\n",
      "boundary:  [5.5 4.5 1.5]\n",
      "iteration:  3 - 5\n",
      "tot-iter:  17\n",
      "--------------------\n",
      "y:  0 \ty_hat:  0\n",
      "lab-hat 0\n",
      "boundary:  [5.5 4.5 1.5]\n",
      "iteration:  3 - 6\n",
      "tot-iter:  18\n",
      "--------------------\n",
      "y:  0 \ty_hat:  0\n",
      "lab-hat 0\n",
      "boundary:  [5.5 4.5 1.5]\n"
     ]
    }
   ],
   "source": [
    "X = np.array([[0.0, 2.0],\n",
    "              [1.0, 2.0],\n",
    "              [2.0, 1.0],\n",
    "              [-3.0, 1.0],\n",
    "              [-2.0, -1.0],\n",
    "              [-3.0, -2.0]\n",
    "             ])\n",
    "y = np.array([1, 1, 1, 0, 0, 0])\n",
    "a  = np.array([6.5, -5.5, -2.5])\n",
    "alpha = 1\n",
    "\n",
    "model = sequential_delta_learning(X, y, a, alpha=alpha, max_epochs=10)\n",
    "model.train()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "educated-doctor",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=====================\n",
      "EPOCH  1\n",
      "=====================\n",
      "iteration:  1 - 1\n",
      "tot-iter:  1\n",
      "--------------------\n",
      "y:  0 \ty_hat:  1\n",
      "lab-hat -1\n",
      "boundary:  [0.  1.  1.5]\n",
      "iteration:  1 - 2\n",
      "tot-iter:  2\n",
      "--------------------\n",
      "y:  1 \ty_hat:  0\n",
      "lab-hat 1\n",
      "boundary:  [1.  0.  1.5]\n",
      "iteration:  1 - 3\n",
      "tot-iter:  3\n",
      "--------------------\n",
      "y:  1 \ty_hat:  1\n",
      "lab-hat 0\n",
      "boundary:  [1.  0.  1.5]\n",
      "iteration:  1 - 4\n",
      "tot-iter:  4\n",
      "--------------------\n",
      "y:  0 \ty_hat:  1\n",
      "lab-hat -1\n",
      "boundary:  [ 0.  -1.   0.5]\n",
      "iteration:  1 - 5\n",
      "tot-iter:  5\n",
      "--------------------\n",
      "y:  1 \ty_hat:  0\n",
      "lab-hat 1\n",
      "boundary:  [ 1.  -1.  -0.5]\n",
      "=====================\n",
      "EPOCH  2\n",
      "=====================\n",
      "iteration:  2 - 1\n",
      "tot-iter:  6\n",
      "--------------------\n",
      "y:  0 \ty_hat:  0\n",
      "lab-hat 0\n",
      "boundary:  [ 1.  -1.  -0.5]\n",
      "iteration:  2 - 2\n",
      "tot-iter:  7\n",
      "--------------------\n",
      "y:  1 \ty_hat:  1\n",
      "lab-hat 0\n",
      "boundary:  [ 1.  -1.  -0.5]\n",
      "iteration:  2 - 3\n",
      "tot-iter:  8\n",
      "--------------------\n",
      "y:  1 \ty_hat:  1\n",
      "lab-hat 0\n",
      "boundary:  [ 1.  -1.  -0.5]\n",
      "iteration:  2 - 4\n",
      "tot-iter:  9\n",
      "--------------------\n",
      "y:  0 \ty_hat:  0\n",
      "lab-hat 0\n",
      "boundary:  [ 1.  -1.  -0.5]\n",
      "iteration:  2 - 5\n",
      "tot-iter:  10\n",
      "--------------------\n",
      "y:  1 \ty_hat:  1\n",
      "lab-hat 0\n",
      "boundary:  [ 1.  -1.  -0.5]\n"
     ]
    }
   ],
   "source": [
    "X = np.array([[2.0, -1.0],\n",
    "              [-1.0, 0.0],\n",
    "              [0.0, 0.0],\n",
    "              [1.0, 1.0],\n",
    "              [0.0, -1.0],\n",
    "             ])\n",
    "y = np.array([0, 1, 1, 0, 1])\n",
    "a  = np.array([1.0, 3.0, 0.5])\n",
    "alpha = 1\n",
    "\n",
    "model = sequential_delta_learning(X, y, a, alpha=alpha, max_epochs=20)\n",
    "model.train()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "trained-wesley",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=====================\n",
      "EPOCH  1\n",
      "=====================\n",
      "iteration:  1 - 1\n",
      "tot-iter:  1\n",
      "--------------------\n",
      "y:  1 \ty_hat:  0\n",
      "lab-hat 1\n",
      "iteration:  1 - 2\n",
      "tot-iter:  2\n",
      "--------------------\n",
      "y:  0 \ty_hat:  1\n",
      "lab-hat -1\n",
      "boundary:  [-1.5  1. ]\n",
      "=====================\n",
      "EPOCH  2\n",
      "=====================\n",
      "iteration:  2 - 1\n",
      "tot-iter:  3\n",
      "--------------------\n",
      "y:  1 \ty_hat:  0\n",
      "lab-hat 1\n",
      "iteration:  2 - 2\n",
      "tot-iter:  4\n",
      "--------------------\n",
      "y:  0 \ty_hat:  0\n",
      "lab-hat 0\n",
      "boundary:  [-0.5  1. ]\n",
      "=====================\n",
      "EPOCH  3\n",
      "=====================\n",
      "iteration:  3 - 1\n",
      "tot-iter:  5\n",
      "--------------------\n",
      "y:  1 \ty_hat:  0\n",
      "lab-hat 1\n",
      "iteration:  3 - 2\n",
      "tot-iter:  6\n",
      "--------------------\n",
      "y:  0 \ty_hat:  1\n",
      "lab-hat -1\n",
      "boundary:  [-0.5  0. ]\n",
      "=====================\n",
      "EPOCH  4\n",
      "=====================\n",
      "iteration:  4 - 1\n",
      "tot-iter:  7\n",
      "--------------------\n",
      "y:  1 \ty_hat:  0\n",
      "lab-hat 1\n",
      "iteration:  4 - 2\n",
      "tot-iter:  8\n",
      "--------------------\n",
      "y:  0 \ty_hat:  0\n",
      "lab-hat 0\n",
      "boundary:  [0.5 0. ]\n",
      "=====================\n",
      "EPOCH  5\n",
      "=====================\n",
      "iteration:  5 - 1\n",
      "tot-iter:  9\n",
      "--------------------\n",
      "y:  1 \ty_hat:  1\n",
      "lab-hat 0\n",
      "iteration:  5 - 2\n",
      "tot-iter:  10\n",
      "--------------------\n",
      "y:  0 \ty_hat:  1\n",
      "lab-hat -1\n",
      "boundary:  [-0.5 -1. ]\n",
      "=====================\n",
      "EPOCH  6\n",
      "=====================\n",
      "iteration:  6 - 1\n",
      "tot-iter:  11\n",
      "--------------------\n",
      "y:  1 \ty_hat:  0\n",
      "lab-hat 1\n",
      "iteration:  6 - 2\n",
      "tot-iter:  12\n",
      "--------------------\n",
      "y:  0 \ty_hat:  0\n",
      "lab-hat 0\n",
      "boundary:  [ 0.5 -1. ]\n",
      "=====================\n",
      "EPOCH  7\n",
      "=====================\n",
      "iteration:  7 - 1\n",
      "tot-iter:  13\n",
      "--------------------\n",
      "y:  1 \ty_hat:  1\n",
      "lab-hat 0\n",
      "iteration:  7 - 2\n",
      "tot-iter:  14\n",
      "--------------------\n",
      "y:  0 \ty_hat:  0\n",
      "lab-hat 0\n",
      "boundary:  [ 0.5 -1. ]\n"
     ]
    }
   ],
   "source": [
    "X = np.array([[0.0],\n",
    "              [1.0],\n",
    "             ])\n",
    "y = np.array([1, 0])\n",
    "a  = np.array([-1.5, 2])\n",
    "alpha = 1\n",
    "\n",
    "model = batch_delta_learning(X, y, a, alpha=alpha, max_epochs=10)\n",
    "model.train()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "unavailable-arthur",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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