{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Fisher Discriminant - Iris data set\n",
"\n",
"### Authors: \n",
"- Christian Michelsen (Niels Bohr Institute)\n",
"- Troels C. Petersen (Niels Bohr Institute)\n",
"\n",
"### Date: \n",
"- 16-11-2018 (latest update)\n",
"\n",
"***\n",
"\n",
"Python macro for analysing the famous Anderson-Fisher Iris data set from Gaspe Peninsula. Edgar Anderson took 50 samples of three species (Setosa, Versicolor, and Virginica) of Iris at the Gaspe Peninsula, and measured four distinguishing features on each flower:\n",
"\n",
"- Sepal Length\n",
"- Sepal Width\n",
"- Petal Length\n",
"- Petal Width\n",
"\n",
"Using these measurements, Ronald Fisher was able to make a classification scheme, for which he invented the Fisher Linear Discriminant.\n",
"\n",
"\n",
"### References:\n",
"- Glen Cowan, Statistical Data Analysis, pages 51-57\n",
"- http://en.wikipedia.org/wiki/Iris_flower_data_set\n",
"- http://en.wikipedia.org/wiki/Linear_discriminant_analysis\n",
"\n",
"***\n",
"\n",
"First, we import the modules we want to use:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# First, import the modules you want to use:\n",
"import numpy as np # Matlab like syntax for linear algebra and functions\n",
"import matplotlib.pyplot as plt # Plots and figures like you know them from Matlab\n",
"from numpy.linalg import inv"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"lines_to_next_cell": 2
},
"outputs": [],
"source": [
"r = np.random # Random generator\n",
"r.seed(42) # Set a random seed (but a fixed one)\n",
"save_plots = False # For now, don't save plots (once you trust your code, switch on)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Functions\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def get_covariance_offdiag(X, Y):\n",
" return np.cov(X, Y, ddof=1)[0, 1]\n",
"\n",
"\n",
"def calc_separation(x, y):\n",
" \n",
" mean_x = np.mean(x)\n",
" mean_y = np.mean(y)\n",
" \n",
" std_x = np.std(x, ddof=1)\n",
" std_y = np.std(y, ddof=1)\n",
" \n",
" d = np.abs((mean_x - mean_y)) / np.sqrt(std_x**2 + std_y**2)\n",
" \n",
" return d"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Define parameters:\n",
"\n",
"Define path to datafile"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"filename = \"DataSet_AndersonFisherIris.txt\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Set the variable and species names along with the number of variavles and number of species:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"var_name = [ \"Sepal Length\", \"Sepal Width\", \"Petal Length\", \"Petal Width\" ] #Variable name\n",
"spec_name = [ \"Setosa\" , \"Versicolor\" , \"Virginica\" ] #Species name\n",
"\n",
"nvar = len(var_name) # Sepal Length, Sepal Width, Petal Length, Petal Width\n",
"nspec = len(spec_name) # Setosa, Versicolor, Virginica"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Set the range for the histograms to plot and the number of bins:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"xmin = [3.5, 1.7, 0.0, 0.0] #Range for different variables\n",
"xmax = [8.5, 4.7, 7.5, 3.0]\n",
"nbin = [ 25, 30, 25, 30] #Number of bins for different variables"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Set the colors and markers to use for each species:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"colors = ['Red', 'Green', 'Blue']\n",
"markers = ['o', '^', 's']"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Loop over and read data from input\n",
"\n",
"Now we open the file and save the data in the variable called `data`: "
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"lines_to_next_cell": 2
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Read data: 5.10 3.50 1.40 0.20 0 \n",
"Read data: 4.90 3.00 1.40 0.20 0 \n",
"Read data: 4.70 3.20 1.30 0.20 0 \n",
"Read data: 4.60 3.10 1.50 0.20 0 \n",
"Read data: 5.00 3.60 1.40 0.20 0 \n"
]
}
],
"source": [
"data = [] # Container for all variables\n",
"with open(filename, 'r') as file:\n",
" counter = 0\n",
"\n",
" for line in file:\n",
"\n",
" data.append(line.strip().split()) # Read line -> Convert to list\n",
" for ivar in range(nvar): \n",
" data[-1][ivar] = float(data[-1][ivar]) # First nvar values are floats\n",
" \n",
" data[-1][-1] = int(data[-1][4]) - 1 # Last one is an integer width species type: 1,2,3\n",
" # Start counting at 0, to match your lists : 0,1,2\n",
" #Print some numbers as a sanity check\n",
" if counter < 5 : \n",
" print(f\"Read data: {data[-1][0]:5.2f} {data[-1][1]:5.2f} {data[-1][2]:5.2f} {data[-1][3]:5.2f} {data[-1][4]:d} \")\n",
" counter += 1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Below we show the numpy version of the above cell:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"lines_to_next_cell": 2
},
"outputs": [],
"source": [
"# Numpy version:\n",
"data = np.loadtxt(filename)\n",
"data[:, -1] -= 1 # Subtract one from all the last integers in the data:\n",
" # Last one is an integer width species type: 1,2,3\n",
" # Start counting at 0, to match your lists : 0,1,2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To introduce the notation that is very common in Machine Learning, we split the data up into the independent variable (input variables / features / columns) `X` and the dependent variable (output variable) `y`:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"# X is the independent variable / input variables / features / columns\n",
"X = data[:, :-1]\n",
"# y is the dependent variable / output variable \n",
"y = data[:, -1].astype(int)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here the capital `X` refers to the fact that `X` is a matrix (2D-array) and `y` is a vector (1D-array)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Display data:\n",
"\n",
"Now we plot the data as histograms for each variable with each species colored according to: Setosa, Versicolor, and Virginica:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
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\n",
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