Hierarchical Clustering on Iris Data

Motivation, references, and the bulk of explanation of methods are detailed in report.pdf.

Only the .ipynb file has been uploaded (no .py version). Python code written in a Jupyter notebook (using Python 3.7.3).

Dependencies

Libraries that must be installed to run all code are: matplotlib, numpy, scipy, and scikit-learn, all of which can be installed with pip. If not already installed, this block of code can be pasted into a cell above the imports of the notebook:

!pip install numpy
!pip install matplotlib
!pip install scikit-learn
!pip install scipy

Running the program

Assuming all necessary dependencies have been installed, run all cells to make sure all functions are available; all cells except for the last should run in under a minute, while the last cell will take around 2 minutes to run. Running all cells will additionally run three "playground" cells which give example usage of the functions discussed below.

The primary function of interest to run is cluster_and_analyze which will cluster the data based on the parameters as well as display the dendrogram and list the purity, Rand index, and normalized mutual information measures of the clustering. cluster_and_analyze takes the following parameters:

• normalized: boolean value, when True will normalize the data
• distance_func: function, should be one of the functions defined in the section Cluster Similarity Functions of the notebook
• distance_metric: function, should be one of the functions defined in the section Distance Functions of the notebook
• use_weights: 1D number array of length 4, optional, by default [1,1,1,1], specifies the weights to use on the measures sepal length, sepal width, petal length, and petal width, in that order

The notebook also includes the varying of weights. There are two interesting functions to run in this section.

1. greedy_optimize runs a greedy "optimization" of the four weights, whose explanation can be found in the Methods section of the report. greedy_optimize takes the following parameters:

   • clust_sim: function, should be one of the functions defined in the section Cluster Similarity Functions of the notebook
   • dist_metric: function, should be one of the functions defined in the section Distance Functions of the notebook
   • threshold: float value, the stopping condition for the function based on the difference of cluster evaluation values between each iteration
   • clust_eval: function, should be one of the functions defined in the section Cluster Evaluation Functions of the notebook

2. plot_weight_range plots the cluster evaluation measures based on the parameters specified below:

   • use_weights: 1D number array of length 4, specifies the weights to use on the measures sepal length, sepal width, petal length, and petal width, in that order
   • weight_index: the index of use_weights to which weight_range will apply (making the value at this index defined in use_weights arbitrary)
   • weight_range: a list of values that specifies how the value of use_weights at the desired weight_index will vary. i.e. passing in range(0,5) will use 0, then 1, then 2, then 3, then 4 for use_weights[weight_index] during clustering
   • clust_sim: function, should be one of the functions defined in the section Cluster Similarity Functions of the notebook
   • dist_metric: function, should be one of the functions defined in the section Distance Functions of the notebook

Library versions

Matplotlib: 3.3.2

Numpy: 1.16.4

SciPy: 1.2.1

SKLearn/SciKit-Learn: 0.21.2