notebooks/ML/Classic/CNN.ipynb

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   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from oli.math.math_utility import pretty_print_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Kernel & Convolution:\n",
    "- A kernel is a matrix of weights learned using backpropagation.\n",
    "- Represents a receptive field.\n",
    "- Is shifted by the stride along the input.\n",
    "- Output size is determined by the kernel size and the stride.\n",
    "- Applying a kernel to an input is called convolution.\n",
    "- Can be viewed as a dot product between the kernel and the input.\n",
    "- The outputs are called feature maps.\n",
    "    - The amount of feature maps is equal to the amount of kernels.\n",
    "    - They are also called channels.\n",
    "\n",
    "The following kernel is of size $W_{kernel} = 3$ and $H_{kernel} = 1$ There are 3 kernels in total leading to 3 feature maps (output channels). The stride is set to $s = 1$."
   ],
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  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Amount of kernels:  4\n",
      "Kernel width:  3\n",
      "Kernel height:  1\n",
      "Amount of strides:  2\n"
     ]
    }
   ],
   "source": [
    "X = np.array([5, 6, 6, 2, 5, 6])\n",
    "\n",
    "kernel_list = [\n",
    "    [1, -1, 1],\n",
    "    [0, 0, 1],\n",
    "    [0, 0, 0],\n",
    "    [1, 1, 1]\n",
    "]\n",
    "amout_of_kernels = len(kernel_list)\n",
    "kernel_width = len(kernel_list[0])\n",
    "kernel_height = 1\n",
    "amount_of_strides = int(len(X) / kernel_width)\n",
    "\n",
    "print(\"Amount of kernels: \", amout_of_kernels)\n",
    "print(\"Kernel width: \", kernel_width)\n",
    "print(\"Kernel height: \", kernel_height)\n",
    "print(\"Amount of strides: \", amount_of_strides)"
   ],
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   }
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X slice currently visible to the kernel:\n",
      "[\n",
      "  5 \n",
      "  6 \n",
      "  6 \n",
      "]\n",
      "Kernel:\n",
      "[\n",
      "  1 \n",
      "  -1 \n",
      "  1 \n",
      "]\n",
      "Convolution: 5\n",
      "\n",
      "X slice currently visible to the kernel:\n",
      "[\n",
      "  5 \n",
      "  6 \n",
      "  6 \n",
      "]\n",
      "Kernel:\n",
      "[\n",
      "  0 \n",
      "  0 \n",
      "  1 \n",
      "]\n",
      "Convolution: 6\n",
      "\n",
      "X slice currently visible to the kernel:\n",
      "[\n",
      "  5 \n",
      "  6 \n",
      "  6 \n",
      "]\n",
      "Kernel:\n",
      "[\n",
      "  0 \n",
      "  0 \n",
      "  0 \n",
      "]\n",
      "Convolution: 0\n",
      "\n",
      "X slice currently visible to the kernel:\n",
      "[\n",
      "  5 \n",
      "  6 \n",
      "  6 \n",
      "]\n",
      "Kernel:\n",
      "[\n",
      "  1 \n",
      "  1 \n",
      "  1 \n",
      "]\n",
      "Convolution: 17\n",
      "\n",
      "\n",
      "X slice currently visible to the kernel:\n",
      "[\n",
      "  6 \n",
      "  6 \n",
      "  2 \n",
      "]\n",
      "Kernel:\n",
      "[\n",
      "  1 \n",
      "  -1 \n",
      "  1 \n",
      "]\n",
      "Convolution: 2\n",
      "\n",
      "X slice currently visible to the kernel:\n",
      "[\n",
      "  6 \n",
      "  6 \n",
      "  2 \n",
      "]\n",
      "Kernel:\n",
      "[\n",
      "  0 \n",
      "  0 \n",
      "  1 \n",
      "]\n",
      "Convolution: 2\n",
      "\n",
      "X slice currently visible to the kernel:\n",
      "[\n",
      "  6 \n",
      "  6 \n",
      "  2 \n",
      "]\n",
      "Kernel:\n",
      "[\n",
      "  0 \n",
      "  0 \n",
      "  0 \n",
      "]\n",
      "Convolution: 0\n",
      "\n",
      "X slice currently visible to the kernel:\n",
      "[\n",
      "  6 \n",
      "  6 \n",
      "  2 \n",
      "]\n",
      "Kernel:\n",
      "[\n",
      "  1 \n",
      "  1 \n",
      "  1 \n",
      "]\n",
      "Convolution: 14\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for i in range(0, amount_of_strides):\n",
    "    current_visible_x = X[i:i + kernel_width]\n",
    "    for kernel in kernel_list:\n",
    "        pretty_print_matrix(current_visible_x, \"X slice currently visible to the kernel:\")\n",
    "        pretty_print_matrix(kernel, \"Kernel:\")\n",
    "        print(\"Convolution:\", np.tensordot(current_visible_x, kernel, axes=1))\n",
    "        print()\n",
    "    print()"
   ],
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  },
  {
   "cell_type": "markdown",
   "source": [
    "### 2D Convolution:"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3, 3)\n",
      "(3, 3)\n"
     ]
    },
    {
     "data": {
      "text/plain": "array(8)"
     },
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   "source": [
    "test_x = np.array([\n",
    "    [1, 0, 1],\n",
    "    [0, 1, 0],\n",
    "    [1, 0, 1]\n",
    "])\n",
    "test_kernel = np.array([\n",
    "    [2, 0, 2],\n",
    "    [2, 2, 2],\n",
    "    [0, 2, 2]\n",
    "])\n",
    "print(test_x.shape)\n",
    "print(test_kernel.shape)\n",
    "np.tensordot(test_x, test_kernel, axes=2)"
   ],
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  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Amount of kernels:  3\n",
      "Kernel width:  3\n",
      "Kernel height:  3\n",
      "Amount of strides x:  2\n",
      "Amount of strides y:  2\n"
     ]
    }
   ],
   "source": [
    "X = np.array([\n",
    "    [2, 0, 2, 2, 0],\n",
    "    [2, 2, 2, 2, 2],\n",
    "    [0, 2, 2, 2, 0],\n",
    "    [0, 2, 2, 2, 0],\n",
    "    [0, 0, 2, 0, 0]\n",
    "])\n",
    "\n",
    "kernel_list = [\n",
    "    np.array([\n",
    "        [1, 0, 1],\n",
    "        [0, 1, 0],\n",
    "        [1, 0, 1]\n",
    "    ]),\n",
    "    np.array([\n",
    "        [0, 1, 0],\n",
    "        [1, 0, 1],\n",
    "        [0, 1, 0]\n",
    "    ]),\n",
    "    np.array([\n",
    "        [1, 0, 1],\n",
    "        [0, 1, 0],\n",
    "        [1, 0, 1]\n",
    "    ])\n",
    "]\n",
    "\n",
    "amout_of_kernels = len(kernel_list)\n",
    "kernel_height = len(kernel_list[0])\n",
    "kernel_width = len(kernel_list[0][0])\n",
    "stride = 2\n",
    "amount_of_strides_x = int((len(X) - kernel_width) / stride) + 1\n",
    "amount_of_strides_y = int((len(X[0]) - kernel_height) / stride) + 1\n",
    "\n",
    "print(\"Amount of kernels: \", amout_of_kernels)\n",
    "print(\"Kernel width: \", kernel_width)\n",
    "print(\"Kernel height: \", kernel_height)\n",
    "print(\"Amount of strides x: \", amount_of_strides_x)\n",
    "print(\"Amount of strides y: \", amount_of_strides_y)"
   ],
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  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X slice currently visible to the kernel:\n",
      "[\n",
      "  2 0 2 \n",
      "  2 2 2 \n",
      "  0 2 2 \n",
      "]\n",
      "Kernel:\n",
      "[\n",
      "  1 0 1 \n",
      "  0 1 0 \n",
      "  1 0 1 \n",
      "]\n",
      "Convolution:  8\n",
      "\n",
      "X slice currently visible to the kernel:\n",
      "[\n",
      "  2 0 2 \n",
      "  2 2 2 \n",
      "  0 2 2 \n",
      "]\n",
      "Kernel:\n",
      "[\n",
      "  0 1 0 \n",
      "  1 0 1 \n",
      "  0 1 0 \n",
      "]\n",
      "Convolution:  6\n",
      "\n",
      "X slice currently visible to the kernel:\n",
      "[\n",
      "  2 0 2 \n",
      "  2 2 2 \n",
      "  0 2 2 \n",
      "]\n",
      "Kernel:\n",
      "[\n",
      "  1 0 1 \n",
      "  0 1 0 \n",
      "  1 0 1 \n",
      "]\n",
      "Convolution:  8\n",
      "\n",
      "\n",
      "X slice currently visible to the kernel:\n",
      "[\n",
      "  0 2 2 \n",
      "  2 2 2 \n",
      "  2 2 2 \n",
      "]\n",
      "Kernel:\n",
      "[\n",
      "  1 0 1 \n",
      "  0 1 0 \n",
      "  1 0 1 \n",
      "]\n",
      "Convolution:  8\n",
      "\n",
      "X slice currently visible to the kernel:\n",
      "[\n",
      "  0 2 2 \n",
      "  2 2 2 \n",
      "  2 2 2 \n",
      "]\n",
      "Kernel:\n",
      "[\n",
      "  0 1 0 \n",
      "  1 0 1 \n",
      "  0 1 0 \n",
      "]\n",
      "Convolution:  8\n",
      "\n",
      "X slice currently visible to the kernel:\n",
      "[\n",
      "  0 2 2 \n",
      "  2 2 2 \n",
      "  2 2 2 \n",
      "]\n",
      "Kernel:\n",
      "[\n",
      "  1 0 1 \n",
      "  0 1 0 \n",
      "  1 0 1 \n",
      "]\n",
      "Convolution:  8\n",
      "\n",
      "\n",
      "X slice currently visible to the kernel:\n",
      "[\n",
      "  2 2 2 \n",
      "  0 2 2 \n",
      "  0 2 2 \n",
      "]\n",
      "Kernel:\n",
      "[\n",
      "  1 0 1 \n",
      "  0 1 0 \n",
      "  1 0 1 \n",
      "]\n",
      "Convolution:  8\n",
      "\n",
      "X slice currently visible to the kernel:\n",
      "[\n",
      "  2 2 2 \n",
      "  0 2 2 \n",
      "  0 2 2 \n",
      "]\n",
      "Kernel:\n",
      "[\n",
      "  0 1 0 \n",
      "  1 0 1 \n",
      "  0 1 0 \n",
      "]\n",
      "Convolution:  6\n",
      "\n",
      "X slice currently visible to the kernel:\n",
      "[\n",
      "  2 2 2 \n",
      "  0 2 2 \n",
      "  0 2 2 \n",
      "]\n",
      "Kernel:\n",
      "[\n",
      "  1 0 1 \n",
      "  0 1 0 \n",
      "  1 0 1 \n",
      "]\n",
      "Convolution:  8\n",
      "\n",
      "\n",
      "X slice currently visible to the kernel:\n",
      "[\n",
      "  2 2 2 \n",
      "  2 2 2 \n",
      "  2 2 2 \n",
      "]\n",
      "Kernel:\n",
      "[\n",
      "  1 0 1 \n",
      "  0 1 0 \n",
      "  1 0 1 \n",
      "]\n",
      "Convolution:  10\n",
      "\n",
      "X slice currently visible to the kernel:\n",
      "[\n",
      "  2 2 2 \n",
      "  2 2 2 \n",
      "  2 2 2 \n",
      "]\n",
      "Kernel:\n",
      "[\n",
      "  0 1 0 \n",
      "  1 0 1 \n",
      "  0 1 0 \n",
      "]\n",
      "Convolution:  8\n",
      "\n",
      "X slice currently visible to the kernel:\n",
      "[\n",
      "  2 2 2 \n",
      "  2 2 2 \n",
      "  2 2 2 \n",
      "]\n",
      "Kernel:\n",
      "[\n",
      "  1 0 1 \n",
      "  0 1 0 \n",
      "  1 0 1 \n",
      "]\n",
      "Convolution:  10\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for y in range(0, amount_of_strides_y):\n",
    "    for x in range(0, amount_of_strides_x):\n",
    "        current_visible = X[y:y + kernel_height, x:x + kernel_width]\n",
    "        for kernel in kernel_list:\n",
    "            pretty_print_matrix(current_visible, \"X slice currently visible to the kernel:\")\n",
    "            pretty_print_matrix(kernel, \"Kernel:\")\n",
    "            print(\"Convolution: \", np.tensordot(current_visible, kernel, axes=2))\n",
    "            print()\n",
    "        print()"
   ],
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