Classification and the Geometric view of data

AH

Dealing with 2D numerical data

Classifying iris flowers

[Fisher, 1936]

Can flower samples be assigned to their proper sub-family purely on the basis of quantitative observation?

  • Linear discriminant classification

  • high-quality, annotated dataset

  • easily the most cited dataset in the ML literature

Agenda for the lab

  • Describing Fischer’s Iris dataset

  • Using python to analyse the Iris dataset

  • Histograms and scatter plots

Images from Wikipedia

Setosa

Wiki image

Versicolour

Wiki image

Virginica

Wiki image

Instance:

  • 150 samples/datapoints, each having over 4 numerical dimensions \(\mathcal{D_1,} \dots \mathcal{D_{4}}\)

  • an expert classification function over 3 categories

Solution:

a linear combination \(\mathcal{D_1} \times \dots \mathcal{D_{4}}\rightarrow \mathcal{D_5}\)

that respects the given classification.

Measure: agreement with the given classification.

The Iris dataset

n=150 samples manually assigned by Fisher.

d=5 dimensions, four measurements and the classification

k=3 classes: Setosa, Versicolour and Virginica, 50 instances each, all available from

The predictors

  • sepal length;
  • sepal width;
  • petal length, and
  • petal width.

All measurements are in cm.

Loading the dataset

The`iris.csv file is a comma separated file. To load the dataset into the memory we follow the following steps:

  1. Read the file using Pandas.
  2. For each row, split them by comma. This will create a list of strings for the row. Then map the strings into the float value.
  3. Map the classes to an integer value.
  4. Convert the row lists called as in the program into a numpy array.

Histogram

A graph consisting of rectangles whose area is proportional to the frequency of a feature and whose width is equal to the class interval denoted as bins

Scatter plot

A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data.

  • A 2D visualization of datapoints against Cartesian coordinates.

  • Normally, the measured variable is on the x-axis.

  • if time is available then it is always on the x-axis.

from sklearn import datasets
iris = datasets.load_iris()

print(iris['data'])

print(iris['target'])

An alternative solution

Self-study this interesting package ucimlrepo

pip install ucimlrepo
import pandas as pd
from ucimlrepo import fetch_ucirepo 
  
ID = 53

iris = fetch_ucirepo(ID) 
  
# data (as pandas dataframes) 
X = iris.data.features 
y = iris.data.targets 
  
print(iris.metadata) 
  
print(iris.variables)

Try visualising the data

Open the exercise files, read the code then run it.

  • exercise: plot the histogram of the sepal-width column

See the Matplotlib tutorial

  • exercise: plot the scatter plot of the sepal width against the sepal length

See the Matplotlib tutorial

Try at home