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Assignment 5 In this assignment we will design simple classifiers for the IRIS dataset

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Assignment 5

In this assignment we will design simple classifiers for the IRIS dataset. recall that this dataset contains 3 flowers (Iris Versi- color, Iris Setosa and Iris Virginica) and each flower has 4 fea- tures: sepal-length, sepal-width, petal-length and petal-width The histogram of pairwise relationships is shown on the last page. If we examine the histogram, we notice that it is easier to identify Setosa than the other two flowers. Therefore, we focus our analysis on just two flowers: Versicolor (label 0) and Virginica (label 1).

The IRIS dataset can be downloaded into a Pandas frame:

import numpy as np
import pandas as pdf

url = r"https://archive.ics.uci.edu/ml/" \+ r"machine -learning -databases/iris/iris.data"

data = pd.read_csv(url, names=[ "sepal -length", "sepal -width", "petal -length", "petal -width", "Class"])

In this assignment, we will consider two different approaches to classification:

1. Method I: construct very simple classifiers (”weak learners”) based on single feature. Combine weak classifiers in an ensemble.
2. Method II: construct density distribution for each feature and design a ”weak learner” based on density. Combine density-based classifiers in an ensemble.

For every classifier, you split data 50/50 into training and testing sets. You estimate parameters by using training set and compute performance measures by using the testing set.

Question 1:

1. download IRIS dataset, remove Setosa flowers and assign labels 0 to to Versicolor and 1 to Virginica.
2. for each label and feature compute statistical averages (from training set!) and put them in the following table:

                       Table 1: Statistical measurements

3. for each class, compute the correlation matrix for your 4 features. Which features have the highest and lowest correlations?
4. discuss your findings

Question 2:

1. generate histograms of pairwise relationships for a train- ing set (include these histograms in submitted homework). X rain. You can use ”pairplot” method of the seaborn package:

import seaborn as sns
features = ["sepal -length", "sepal -width", "petal -length", "petal -width"]

pair_plot = sns.pairplot(X_train[features])

plt.show()

2. examine the histograms and for each feature design a simple classifier (”weak learner”) for labels. Your classifier can only consist of simple comparison using that single feature. For example,

if petal_length > 10:
     label = 0

else:
       label = 1

You design 4 such classfiers, one for each of the 4 features. Apply each classifier to testing set, compute the confusion matrix and summarize them in a table below

      Table 2: Results for signle-feature ”weak” learners

 

3. discuss your findings and rank your ”weak” learners by ac- curacy (from most accurate to least accurate)

Question 3:

You construct ensemble classifiers by combining 3 ”weak learn- ers” together. For example, you take (1), (2) and (3). The output label is the majority decision. You will have 4 such ensemble classifiers - there are 4 distinct ways to choose 3 clas- sifiers out of 4.

1. For each such ensemble classifier, split data into training and test. Apply your classifiers on testing data, compute confusion matrix and summarize the results in a table below (note that no training is done, we are just combining the ”weak” learners).

 

Table 3: Result for ensembles of ”weak” learners

2. discuss your findings and rank your ensembles learners by accuracy (from most accurate to least accurate
3. compare ”weak learners” and ensemble results.

Question 4:

We will now design a density-based ”weak learner”. Assume that for each label each feature is distributed according to a normal distribution with mean μ and standard deviation σ. Split the data and use training data to compute (μ0,σ0) for class 0 and (μ1,σ1) for class 1. Given a flower in testing set with a feature value x, you compute p0(x) and p1(x) and pick up the label corresponding to the larger value

from scipy.stats import norm

p_0 = norm.pdf((x - mu_0)/sigma_0)

 p_1 = norm.pdf((x - mu_1)/sigma_1)

if p_0 >= p_1:
      label = 0

else:
       label = 1

1. you design 4 such density-based classfiers, one for each of the 4 features. For each classifier, compute the confusion matrix (from a testing set! as before) and summarize them in a table below

Table 4: Results for Density-based ”weak” learners

2. discuss your findings and rank your density-based ”weak” learners by accuracy (from most accurate to least accurate

Question 5:

You construct density-based ensemble classifiers by combining 3 density-based classifiers together. For example, you take (1), (2) and (3). The output label is the majority decision. You will have 4 such ensemble classifiers - there are 4 distinct ways

to choose 3 classifiers out of 4. Split your data again 50/50 into training and testing

1. For each such ensemble classifier, compute confusion matrix (on testing data!) and summarize the results in a table below

Table 5: Results for Density-based Ensembles

2. discuss your findings and rank your ensembles learners by accuracy (from most accurate to least accurate)
3. compare ”weak learners” and ensemble results.

Question 6

1. give a quick summary on comparing classifiers in Method I and Method II