Abstract

The well-known Iris data set has been studied applying partial ordering methodology. Previous studies, e.g., applying supervision learning such as neural networks (NN) and support-vector machines (SVM) perfectly distinguish between the three Iris subgroups, i.e., Iris Setosa, Iris Versicolour and Iris Virginica, respectively, in contrast to, e.g., K-means clustering that only separates the full Iris data set in two clusters. In the present study applying partial ordering methodology further discloses the difference between the different classification methods. The partial ordering data appears to be in perfect agreement with the results of the K-means clustering, which means that the clear separation in the three Iris subsets applying NN and SVM is neither recognized by clustering nor by partial ordering methodology.

Highlights

  • One of the most often applied datasets in machine learning studies test cases is the Iris dataset [1, 2]

  • The plants are characterized by four indicators, i.e., Sepal length (SepalL), Sepal width (SepalW), Petal length (PetalL) and Petal width (PetalW), respectively, all in cm

  • We find that supervised learning, like neural network and support-vector machines (SVM), nicely classify the 3 classes Iris Setosa (i-set), Iris Versicolour (i-ver) and Iris Virginica (i-vir)

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Summary

Introduction

One of the most often applied datasets in machine learning studies test cases is the Iris dataset [1, 2] This dataset includes 150 entries comprising 3 x 50 entries for three subspecies of class of iris plant, i.e., Iris Setosa (iset), Iris Versicolour (i-ver) and Iris Virginica (i-vir), respectively. By application of the cover-relation a graph is dataset [1] comprising 3 x 50 entries for three subspecies constructed This graph is, based on the three axioms of of class of iris plant, i.e., Iris Setosa (i-set), Iris partial order. Directed (due to the order relation) triangle free (due to the cover relation) and

Basic concepts of partial order
Dominance and separability
K-means clustering
The Hasse diagram - visual inspection
The subsets
Dominances and separabilities
Separability matrix as mean to visualize the classification
Internal structures
Subset-selection
Conclusions and outlook
PROMETHEE Method for Multiple Criteria

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