0300.Representing-data-with-models.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Representing data in a computer\n",
    "\n",
    "The core of data science and machine learning is **data**: we are interested in extracting knowledge from data.\n",
    "\n",
    "But how exactly do computers represent data? Let's find out exactly what an \"artificial intelligence\" has at its disposal to learn from."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data is represented as arrays\n",
    "\n",
    "Let's take a look at some fruit. Using the `Images.jl` library, we can load in some images:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "100×100 Array{RGB{N0f8},2} with eltype RGB{N0f8}:\n",
       " RGB{N0f8}(0.996,1.0,0.984)    …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.984,1.0,0.988)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.98,1.0,0.996)        RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.969,1.0,0.992)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.969,1.0,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.98,1.0,1.0)       …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.992,0.996,1.0)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.984,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.984,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,1.0)      …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.996,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)           RGB{N0f8}(1.0,1.0,1.0)\n",
       " ⋮                             ⋱  \n",
       " RGB{N0f8}(0.992,1.0,0.988)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.992,1.0,0.988)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.992,1.0,0.996)    …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.996,1.0,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.996,0.996,0.996)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,0.996)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,0.996)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,0.996)    …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.996,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)           RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)           RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)           RGB{N0f8}(1.0,1.0,1.0)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Images, FileIO\n",
    "\n",
    "apple = load(\"data/10_100.jpg\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "100×100 Array{RGB{N0f8},2} with eltype RGB{N0f8}:\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)  …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)  …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)  …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " ⋮                                               ⋱  \n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)  …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)  …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "banana = load(\"data/104_100.jpg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we have images of apples and bananas. We would eventually like to build a program that can automatically distinguish between the two. However, the computer doesn't \"see\" an apple or a banana; instead, it just sees numbers.\n",
    "\n",
    "An image is encoded in something called an **array**, which is like a container that has boxes or slots for individual pieces of data:\n",
    "\n",
    "An array is a bunch of numbers in connected boxes; the figure above shows a 1-dimensional array. Our images are instead 2-dimensional arrays, or matrices, of numbers, arranged something like this:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://raw.githubusercontent.com/JuliaComputing/JuliaAcademyData.jl/master/courses/Foundations%20of%20machine%20learning/data/array2d.png\" alt=\"attachment:array2d.png\" width=\"500\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, `apple` is an image, consisting of a 100x100 array of numbers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Matrix{RGB{N0f8}} (alias for Array{RGB{Normed{UInt8, 8}}, 2})"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "typeof(apple)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 100)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "size(apple)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×3 Matrix{Int64}:\n",
       " 1  2  3\n",
       " 4  5  6"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = [ 1 2 3;4 5 6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Matrix{Int64} (alias for Array{Int64, 2})"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "typeof(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "size(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can grab the datum stored in the box at row `i` and column `j` by *indexing* using square brackets: `[i, j]`. For example, let's get the pixel (piece of the image) in box $(40, 60)$, i.e. in the 40th row and 60th column of the image:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "100×100 Array{RGB{N0f8},2} with eltype RGB{N0f8}:\n",
       " RGB{N0f8}(0.996,1.0,0.984)    …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.984,1.0,0.988)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.98,1.0,0.996)        RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.969,1.0,0.992)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.969,1.0,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.98,1.0,1.0)       …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.992,0.996,1.0)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.984,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.984,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,1.0)      …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.996,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)           RGB{N0f8}(1.0,1.0,1.0)\n",
       " ⋮                             ⋱  \n",
       " RGB{N0f8}(0.992,1.0,0.988)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.992,1.0,0.988)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.992,1.0,0.996)    …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.996,1.0,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.996,0.996,0.996)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,0.996)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,0.996)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,0.996)    …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.996,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)           RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)           RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)           RGB{N0f8}(1.0,1.0,1.0)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "apple"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RGB{N0f8}\n",
      "  r: N0f8\n",
      "    i: UInt8 0x85\n",
      "  g: N0f8\n",
      "    i: UInt8 0x19\n",
      "  b: N0f8\n",
      "    i: UInt8 0x0d\n"
     ]
    }
   ],
   "source": [
    "dump(apple[40, 60])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGYAAABmCAIAAAC2vXM1AAAABGdBTUEAALGPC/xhBQAAAAFzUkdCAK7OHOkAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAO5JREFUeAHtwcFRxEAAxEB5LeKgiJ04KRPDPHwvdfv78837nosPePjjfZKRZCQZSUaSkWQkGUlGkpFkJBlJRpKRZCQZSUaSkWQkGUlGkpFkJBlJRpKRZCQZSUaSkWQkGUlGkpH39fAB9+F91/XF+yQjyUgykowkI8lIMpKMJCPJSDKSjCQjyUgykowkI8lIMpKMJCPJSDKSjCQjyUgykowkI8lIMpKMJCPPObzvXIcPuA/vk4wkI8lIMpKMJCPJSDKSjCQjyUgykowkI8lIMpKMJCPJSDKSjCQjyUgykowkI8lIMpKMJCPJSDKSjP4BYBYGlwsEcxwAAAAASUVORK5CYII=",
      "text/plain": [
       "3×3 Array{RGB{N0f8},2} with eltype RGB{N0f8}:\n",
       " RGB{N0f8}(0.639,0.129,0.122)  …  RGB{N0f8}(0.631,0.133,0.11)\n",
       " RGB{N0f8}(0.651,0.133,0.118)     RGB{N0f8}(0.655,0.149,0.129)\n",
       " RGB{N0f8}(0.659,0.141,0.125)     RGB{N0f8}(0.667,0.161,0.141)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "apple[18:20,29:31]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that Julia displays a coloured box! Julia, via the `Colors.jl` package, is clever enough to display colours in a way that is useful to us humans!\n",
    "\n",
    "So, in fact, an image is a 2D array, in which each element of the array is an object (a collection of numbers) describing a coloured pixel."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Colors as numbers\n",
    "\n",
    "How, then, are these colors actually stored? Computers store colors in RGB format, that is they store a value between 0 and 1 for each of three \"channels\": red, green, and blue. Here, 0 means none of that color and 1 means the brightest form of that color. The overall color is a combination of those three colors.\n",
    "\n",
    "For example, we can pull out the `red` value using the function `red` applied to the color. Since internally the actual value is stored in a special format, we choose to convert it to a standard floating-point number using the `Float64` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5215686274509804"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Float64(red(apple[40, 60]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×2 Matrix{Float32}:\n",
       " 0.570167  0.904002\n",
       " 0.338203  0.880797\n",
       " 0.3225    0.80016"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[ mean(float.(c.(img))) for c = [red,green,blue], img = [apple,banana] ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
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      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Plots\n",
    "histogram(float.(green.(apple[:])),color=\"red\",label=\"apple\", normalize=true, nbins=25)\n",
    "histogram!(float.(green.(banana[:])),color=\"yellow\",label=\"banana\",normalize=true, nbins=25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "100×100 Array{RGB{N0f8},2} with eltype RGB{N0f8}:\n",
       " RGB{N0f8}(0.996,1.0,0.984)    …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.984,1.0,0.988)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.98,1.0,0.996)        RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.969,1.0,0.992)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.969,1.0,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.98,1.0,1.0)       …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.992,0.996,1.0)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.984,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.984,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,1.0)      …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.996,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)           RGB{N0f8}(1.0,1.0,1.0)\n",
       " ⋮                             ⋱  \n",
       " RGB{N0f8}(0.992,1.0,0.988)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.992,1.0,0.988)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.992,1.0,0.996)    …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.996,1.0,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.996,0.996,0.996)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,0.996)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,0.996)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,0.996)    …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.996,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)           RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)           RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)           RGB{N0f8}(1.0,1.0,1.0)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "apple"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.61960787f0"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float(red(banana[50,20]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\"\n",
       "     width=\"25mm\" height=\"25mm\" viewBox=\"0 0 1 1\">\n",
       "    <rect width=\"1\" height=\"1\" fill=\"#9E831C\" stroke=\"none\"/>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "RGB{N0f8}(0.62,0.514,0.11)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "banana[50,20]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The RGB values are (0.5215686274509804, 0.09803921568627451, 0.050980392156862744)"
     ]
    }
   ],
   "source": [
    "pixel = apple[40, 60]\n",
    "\n",
    "red_value   = Float64( red(pixel) )\n",
    "green_value = Float64( green(pixel) )\n",
    "blue_value  = Float64( blue(pixel) )\n",
    "\n",
    "print(\"The RGB values are ($red_value, $green_value, $blue_value)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the red value is high while the others are low, this means that at pixel `(40, 60)`, the picture of the apple is very red. If we do the same at one of the corners of the picture, we get the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The RGB values are (0.996078431372549, 1.0, 0.984313725490196)"
     ]
    }
   ],
   "source": [
    "pixel = apple[1, 1]\n",
    "\n",
    "red_value   = Float64( red(pixel) )\n",
    "green_value = Float64( green(pixel) )\n",
    "blue_value  = Float64( blue(pixel) )\n",
    "\n",
    "print(\"The RGB values are ($red_value, $green_value, $blue_value)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "100×100 Array{RGB{N0f8},2} with eltype RGB{N0f8}:\n",
       " RGB{N0f8}(0.996,1.0,0.984)    …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.984,1.0,0.988)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.98,1.0,0.996)        RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.969,1.0,0.992)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.969,1.0,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.98,1.0,1.0)       …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.992,0.996,1.0)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.984,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.984,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,1.0)      …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.996,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)           RGB{N0f8}(1.0,1.0,1.0)\n",
       " ⋮                             ⋱  \n",
       " RGB{N0f8}(0.992,1.0,0.988)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.992,1.0,0.988)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.992,1.0,0.996)    …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.996,1.0,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.996,0.996,0.996)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,0.996)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,0.996)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,0.996)    …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.996,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)           RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)           RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)           RGB{N0f8}(1.0,1.0,1.0)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "apple"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that every color is bright, which corresponds to white."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Working on an image as a whole\n",
    "\n",
    "In Julia, to apply a function to the whole of an array, we place a `.` between the function name and the left parenthesis (`(`), so the following gives us the `red` value of every pixel in the image:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5701670588235295"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "redpartofapple = Float64.(red.(apple))\n",
    "mean(redpartofapple)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Plots.GRBackend()"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
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      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "histogram(redpartofapple[:],color=:red,label=\"redness in the apple\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that we get a 2D array (matrix) back."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Julia's [mathematical standard library](https://docs.julialang.org/en/v1/base/math/#Mathematics) has many mathematical functions built in. One of them is the `mean` function, which computes the average value. If we apply this to our apple:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5701670588235295"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean(Float64.(red.(apple)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we see that the value indicates that the average amount of red in the image is a value between the amount of red in the apple and the amount of red in the white background.\n",
    "\n",
    "*Somehow we need to teach a computer to use this information about a picture to recognize that there's an apple there!*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A quick riddle\n",
    "\n",
    "Here's a quick riddle. Let's check the average value of red in the image of the banana."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.904001568627451"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean(Float64.(red.(banana)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Oh no, that's more red than our apple? This isn't a mistake and is actually true! Before you move onto the next exercise, examine the images of the apple and the banana very carefully and see if you can explain why this is expected."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1\n",
    "\n",
    "What is the average value of blue in the banana?\n",
    "\n",
    "(To open a new box use <ESC>+b (b is for \"below\", what do you think a does?))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Solution\n",
    "\n",
    "We can calculate the average value of blue in the banana via"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8001596078431373"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean(Float64.(blue.(banana)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is approximately `0.8`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 2\n",
    "\n",
    "Does the banana have more blue or more green?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Solution\n",
    "\n",
    "The average value of green in the banana is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8807972549019609"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean(Float64.(green.(banana)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which gives approximately `0.88`. The banana has more green on average."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modeling data 1\n",
    "\n",
    "Machine learning and data science is about modeling data. **Modeling** is the representation of an idea with some parameters and  a mathematical representation which we will encode in software. All machine learning methods are about training a computer to fit a model to some data. Even the fanciest neural networks are simply choices for models. In this notebook, we will begin to start building our first computational model of data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modeling data is hard!\n",
    "\n",
    "Let's pick up where we left off in notebook 1 with fruit. We were left with a riddle: when we load images of apples and bananas,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "100×100 Array{RGB{N0f8},2} with eltype RGB{N0f8}:\n",
       " RGB{N0f8}(0.996,1.0,0.984)    …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.984,1.0,0.988)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.98,1.0,0.996)        RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.969,1.0,0.992)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.969,1.0,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.98,1.0,1.0)       …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.992,0.996,1.0)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.984,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.984,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,1.0)      …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.996,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)           RGB{N0f8}(1.0,1.0,1.0)\n",
       " ⋮                             ⋱  \n",
       " RGB{N0f8}(0.992,1.0,0.988)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.992,1.0,0.988)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.992,1.0,0.996)    …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.996,1.0,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(0.996,0.996,0.996)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,0.996)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,0.996)       RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.992,0.996)    …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,0.996,1.0)         RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)           RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)           RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)           RGB{N0f8}(1.0,1.0,1.0)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# using Pkg; Pkg.add(\"Images\")\n",
    "using Images, Statistics\n",
    "\n",
    "apple = load(\"data/10_100.jpg\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "100×100 Array{RGB{N0f8},2} with eltype RGB{N0f8}:\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)  …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)  …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)  …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " ⋮                                               ⋱  \n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)  …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)  …  RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)\n",
       " RGB{N0f8}(1.0,1.0,1.0)  RGB{N0f8}(1.0,1.0,1.0)     RGB{N0f8}(1.0,1.0,1.0)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "banana = load(\"data/104_100.jpg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and then compare their average value for the color red, we end up with something that is perhaps surprising:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"The average value of red in the apple is 0.5701670588235295, while the average value of red in the banana is 0.904001568627451.\""
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "apple_red_amount = mean(Float64.(red.(apple)))\n",
    "banana_red_amount = mean(Float64.(red.(banana)));\n",
    "\n",
    "\"The average value of red in the apple is $apple_red_amount, \" *\n",
    "\"while the average value of red in the banana is $banana_red_amount.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the banana's mean red value is higher than the apple's, even though the apple looks much redder. Can you guess why?\n",
    "\n",
    "There are actually two reasons. One of the reasons is the background: the image of the banana has a lot more white background than the apple, and that white background has a red value of 1! In our minds we ignore the background and say \"the banana is bright yellow, the apple is dark red\", but a computer just has a bundle of numbers and does not know where it should be looking.\n",
    "\n",
    "The other issue is that \"bright yellow\" isn't a color that exists in a computer. The computer has three colors: red, green, and blue. \"Bright yellow\" in a computer is a mixture of red and green, and it just so happens that to get this color yellow, it needs more red than the apple!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"The amount of red in the apple at (60, 60) is 0.4470588235294118, while the amount of red in the banana at (60, 60) is 0.6666666666666666.\""
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"The amount of red in the apple at (60, 60) is $(Float64(red(apple[60, 60]))), \" *\n",
    "\"while the amount of red in the banana at (60, 60) is $(Float64(red(banana[60, 60]))).\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\"\n",
       "     width=\"25mm\" height=\"25mm\" viewBox=\"0 0 1 1\">\n",
       "    <rect width=\"1\" height=\"1\" fill=\"#720D05\" stroke=\"none\"/>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "RGB{N0f8}(0.447,0.051,0.02)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "apple[60,60]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\"\n",
       "     width=\"25mm\" height=\"25mm\" viewBox=\"0 0 1 1\">\n",
       "    <rect width=\"1\" height=\"1\" fill=\"#AA961B\" stroke=\"none\"/>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "RGB{N0f8}(0.667,0.588,0.106)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "banana[60,60]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a clear example that modeling data is hard!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A note on string interpolation\n",
    "\n",
    "In the last two input cells, we *interpolated a string*. This means that when we write the string using quotation marks (`\"  \"`), we insert a placeholder for some **value** we want the string to include. When the string is evaluated, the value we want the string to include replaces the placeholder. For example, in the following string,\n",
    "\n",
    "```julia\n",
    "mystring = \"The average value of red in the apple is $apple_red_amount\"\n",
    "```\n",
    "\n",
    "`$apple_red_amount` is a placeholder for the value stored in the variable `apple_red_amount`. Julia knows that we want to use the value bound to the variable `apple_red_amount` and *not* the word \"apple_red_amount\" because of the dollar sign, `$`, that comes before `apple_red_amount`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1\n",
    "\n",
    "Execute the following code to see what the dollar sign does:\n",
    "\n",
    "```julia\n",
    "mypi = 3.14159\n",
    "println(\"I have a variable called mypi that has a value of $mypi.\")\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "I have a variable called mypi that has a value of 3.14159.\n"
     ]
    }
   ],
   "source": [
    "mypi = 3.14159\n",
    "println(\"I have a variable called mypi that has a value of $mypi.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 2\n",
    "\n",
    "Alter and execute the code that creates `mystring` below\n",
    "\n",
    "```julia\n",
    "apple_blue_amount = mean(Float64.(blue.(apple)))\n",
    "mystring = \"The average amount of blue in the apple is apple_blue_amount\"\n",
    "```\n",
    "\n",
    "so that `println(mystring)` prints a string that reports the mean value of blue coloration in our image of an apple."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Solution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Add a `$` in front of `apple_blue_amount`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"The average amount of blue in the apple is 0.32250000000000006.\""
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "apple_blue_amount = mean(Float64.(blue.(apple)))\n",
    "mystring = \"The average amount of blue in the apple is $apple_blue_amount.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Take some time to think about the data\n",
    "\n",
    "Apples and bananas are very different, but how could we use the array of RGB values (which is how the images are represented in the computer, as we saw in notebook 1) to tell the difference between the two? Here are some quick ideas:\n",
    "\n",
    "- We could use the shape of the object in the image. But how can we encode ideas about shape from an array?\n",
    "- We could use the size of the object in the image. But how do we calculate that size?\n",
    "- We could use another color, or combinations of colors, from the image. Which colors?\n",
    "\n",
    "Let's go with the last route. The banana is yellow, which is a combination of red and green, while the apple is red. This means that the color that clearly differentiates between the two is not red, but green!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"The average value of green in the apple is 0.3382027450980393, while the average value of green in the banana is 0.8807972549019609.\""
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "apple_green_amount = mean(Float64.(green.(apple)))\n",
    "banana_green_amount = mean(Float64.(green.(banana)));\n",
    "\n",
    "\"The average value of green in the apple is $apple_green_amount, \" *\n",
    "\"while the average value of green in the banana is $banana_green_amount.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The processes that we just went through are assigned fancy names: feature selection and data munging.\n",
    "\n",
    "**Feature selection** is the process of subsetting the data to a more relevant and informative set. We took the full image data and decided to select out the green channel.\n",
    "\n",
    "**Data munging** is transforming the data into a format more suitable for modeling. Here, instead of keeping the full green channel, we transformed it down to a single data point: the average amount of green."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Building a model\n",
    "\n",
    "We want to model the connection between \"the average amount of green\" and \"is an apple or banana\".\n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/JuliaComputing/JuliaAcademyData.jl/master/courses/Foundations%20of%20machine%20learning/data/data_flow.png\" alt=\"Drawing\" style=\"width: 800px;\"/>\n",
    "\n",
    "This model is a mathematical function which takes in our data and spits out a number that we will interpret as \"is an apple\" or \"is a banana\".\n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/JuliaComputing/JuliaAcademyData.jl/master/courses/Foundations%20of%20machine%20learning/data/what_is_model.png\" alt=\"Drawing\" style=\"width: 500px;\"/>\n",
    "\n",
    "\n",
    "We will interpret the output of the function as \"is an apple\" if the output is close to 0, and \"is a banana\" if it's close to 1. Anything in the middle is something we are unsure about. Here we're using a mathematical function to perform a **classification**.\n",
    "\n",
    "Knowing how to declare and work with functions will allow us to model our data in the coming sections, so this is the subject of the next notebook!"
   ]
  }
 ],
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