Data-Analytics_Iris_Data

Analytics performed on the fisher iris dataset

Average and variance of each feature for the total population and for each class for a normal dataset

	Population	Species Setosa	Species Versicolor	Species Virginica
Sepal length Mean	5.84	5.01	5.94	6.59
Sepal length Variance	0.68	0.12	0.26	0.4
Sepal width Mean	3.06	3.43	2.77	2.97
Sepal width Variance	0.19	0.14	0.1	0.1
Petal length Mean	3.76	1.46	4.26	5.55
Petal length Variance	3.1	0.03	0.22	0.3
Petal width Mean	1.2	0.25	1.33	2.03
Petal width Variance	0.58	0.01	0.04	0.07

Average and variance of each feature for a noisy dataset

	Population	Species Setosa	Species Versicolor	Species Virginica
Sepal length Mean	5.86	4.96	5.97	6.61
Sepal length Variance	0.95	0.21	0.58	0.73
Sepal width Mean	3.08	3.48	2.82	2.95
Sepal width Variance	0.95	0.21	0.6	0.73
Petal length Mean	3.76	1.45	4.28	5.56
Petal length Variance	3.26	0.05	0.38	0.48
Petal width Mean	1.22	0.24	1.32	2.09
Petal width Variance	0.65	0.02	0.09	0.12

T-Statistics for normal and noisy datasets

Normal dataset

Flower Parameter	Species	T-Statistic	P-Value
Sepal length	Setosa	-16.797	5.72e-22
Sepal width		6.914	9.0e-09
Petal length		-93.486	6.913e-57
Petal width		-63.966	7.06e-49
Sepal length	Veriscolor	1.269	2.10e-01
Sepal width		-6.475	4.32e-08
Petal length		7.554	9.24e-10
Petal width		4.529	3.80e-05
Sepal length	Virginica	8.281	7.12e-11
Sepal width		-1.827	7.38e-02
Petal length		22.985	6.73e-28
Petal width		21.283	2.09e-26

Noisy dataset

Flower Parameter	Species	T-Statistic	P-Value
Sepal length	Setosa	-13.233	8.49e-18
Sepal width		5.425	1.78e-06
Petal length		-75.570	2.17e-52
Petal width		-44.837	1.92e-41
Sepal length	Veriscolor	1.006	3.20e-01
Sepal width		-3.798	4.02e-04
Petal length		5.833	4.22e-07
Petal width		2.480	1.66e-02
Sepal length	Virginica	6.119	1.54e-07
Sepal width		-2.370	2.18e-02
Petal length		18.183	1.99e-23
Petal width		17.840	4.49e-23

One-way analysis of variation (ANOVA1) analysis for both the original and noisy datasets

Generating F-statistics and p-values for each feature to select the two features that provide the best distinction between the classes. Using Null Hypothesis: Means of all three group (i.e Species are Identical, which means that all species have the same sepal, petal, length and width)

PCA Parameter	F Statistic	P-Value < Alpha	Null Hypothesis
Sepal Length	119.265	True	Reject
Sepal Width	49.160	True	Reject
Petal Length	1180.161	True	Reject
Petal Width	960.007	True	Reject

We reject the null hypothesis and accept the alternative hypothesis proven by the F-statistice and p- values. This provides the following most prominent scatter graphs showing the 2 most prominent features being petal length and width and the 2 least prominent features being sepal width and length.

Principal Component Analysis

Determining what fraction of total variance in the set is represented by each principal component. Generate two scatterplots, first of the two most prominent principal components, and then of the two least prominent principal component for the original and noisy datasets in the image below.

PCA Parameter	Original Variance Fraction	Noisy Variance Fraction
Sepal Length	0.730	0.675
Sepal Width	0.229	0.225
Petal Length	0.037	0.080
Petal Width	0.005	0.020

Gaussian Mixture cluster analysis

Using the cores of the two most prominent principal components, the following distributions are found.