## Clustering – Part 2 – Assignment 2
## Second Submission

##   3, 5, 8, 9, 11, 14
##                                   Clustering - Part 2 - Assignment 2
## 1.   List the methods of clustering
##     •    Partitioning methods
##     •    Hierarchical methods 
##     •    Density-based methods
##     •    Grid-based methods
## 2.   What are partitioning methods?
##     •    They use the information on the distances between the cases (or observations) in the dataset to obtain the  ##        k “best” groups, according to a certain criterion. 
## 3.   What are hierarchical methods?
##     •    Is obtained by a hierarchy of alternative clustering solutions – known as  dendrograms. 
## 4. For a dendrogram, given the relationship,
##                                                                    h(d) ≤ h(g) ⟺ d ⊆ g ,
##               which node is higher on the tree, d or g?
##     •    g is higher 

## 5.   The dendrogram follows which approaches for the task of building the hierarchy of clustering solutions?
##     •    Dendrograms follow a divisive, or an agglomerative approach to the task of building the hierarchy 

## 6. Explain the divisive clustering approach.
##     •    you start with one, all inclusive cluster and, at each step, spit a cluster until only singleton clusters of ##        individual points remain
## 7. What are density-based methods?
##    • Clusters are dense regions in the data space, separated by regions of lower object density – A cluster is 
##      defined as a maximal set of density connected points – Discovers clusters of arbitrary shape
## 8. What are two criteria used to elevate a clustering solution?
##    • Compactness and Separation.
## 9. Explain agglomerative clustering.
##    • you start with the points as individual clusters and, at each step, merge the closest pair of clusters. What is ##      the goal of the hierarchical clustering methods?
##    • start with as many groups as there are cases (points, observations, etc.) in the dataset. At each iteration, ##         the pair of groups that is most similar is merged into a single group.

## 10. What is the goal of the hierarchical clustering methods?
##        • The goal of the hierarchical clustering methods is to obtain a hierarchy of possible solutions ranging from ##          one single group to n groups, where n is the number of observations in the dataset

## 11. What is data noise?
##        • When attempting to cluster parts of the data, which can be referred to as noise, can disturb the clustering ##          on the remaining domain points.
## 12. Based on agglomerative hierarchical clustering methods, name three criteria that select the pair of groups that ##     is most similar and is merged into a single group.
##        • The single linkage criterion 
##        • The complete linkage method,
##        • The average linkage 

## 13. Explain the single linkage criteria.
##     •    In single linkage, the distance between two clusters is the minimum distance between members of the two 
##      clusters

## 14. Which type of clustering is implemented in the function, hclust( )?
##     •    Agglomerative Hierarchical clustering
## 15. For the function, hclust( ), what are the first two arguments (in Torgo’s text)?
##     •    The function, hclust() – takes in the first argument the distance matrix* of the dataset while the second 
##        argument specifies the criterion (single, complete, …) used to    select the two groups for merging at each 
##        step.
## 16. Explain average linking.
##     •    In average linkage, the distance between two clusters is the average of all distances between members of the ##        two clusters