lab7c.Rmd

---
title: "Cluster Analysis (3)"
subtitle: "Advanced Clustering Methods"
author: "Luc Anselin^[University of Chicago, Center for Spatial Data Science -- anselin@uchicago.edu]"
date: "Latest update 11/19/2018"
output:
  bookdown::html_document2:
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    toc: yes
    toc_depth: 4
    includes:
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      before_body: "../doc_before.html"
      after_body: "../footer.html"
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  pdf_document:
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bibliography: "../workbook.bib"
bibliography-style: "apalike"
link-citations: true
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = FALSE)
```

<br>

## Introduction {-}
In this final chapter that deals with standard (non-spatial) clustering
techniques, we consider some more advanced partitioning methods. First, we cover two
variants of K-means, i.e., K-medians and K-medoids. These operate in the same
manner as K-means, but differ in the way the central point of each cluster is assigned.
For K-means, we recall this was the centroid. In contrast, for K-median the central point
is the median for each dimension, whereas for K-medoid it is the median location, i.e., the 
actual observation that minimizes the distance to all the points in the cluster.^[Note
that the centroid in the K-mean approach and the median in the K-median approach typically
are not actual observations, whereas in the K-medoid method, they are.]


### Objectives {-}

- Carry out k-median and k-medoid clustering

- Carry out and interpret the results of spectral clustering

- Carry out and interpret the results of HDBScan clustering


#### GeoDa functions covered {-}

* Clusters > K Medians
    + select variables
* Clusters > K Medoids
* Clusters > Spectral
* Clusters > HDBScan

<br>

### Getting started {-}
As before, with GeoDa launched and all previous projects closed, we again load the Guerry sample data set from the **Connect to Data Source** interface. We either load it from the sample data 
collection and then save the file in a working directory, or we use a previously saved version.  The process should yield the familiar themeless base map, showing the 85 French departments,
as in Figure \@ref(fig:guerrybase).

```{r guerrybase, out.width='80%',fig.align="center",fig.cap="French departments themeless map"}
knitr::include_graphics('./pics7c/0_547_themelessbasemap.png')
```

## K Medians {-}

### Principle {-}
K-medians is a variant of K-means clustering. As a partitioning method, it starts
by randomly assigning observations to K clusters. Each cluster is then characterized
by a central point. In contrast to K-means, the central point is not the average
(in multiattribute space), but instead the median of the cluster observations. 

K-medians is often
confused with K-medoids. However, there is a subtle difference. In the K-medians algorithm
as implemented in GeoDa, the cluster center is the point that corresponds to the median
along each variable dimension. As is the case for the average, this point does not
necessarily correspond to an actual observation. This is the main difference with
K-medoids, where the central point has to be one of the observations (see the next
section).

Once an initial assignment is carried out and the central point computed, observations
are assigned to the cluster whose central point is the closest. In contrast to the
K-means method, a Manhattan distance (absolute difference) metric is used in the assignment.
This makes the method more robust to the influence of outliers, since large
distances are penalized less.

In all other respects, the implementation and interpretation is the same as for 
K-means.

### Implementation {-}







#### Variable Settings Panel {-}

#### Cluster results {-}

### Options and sensitivity analysis {-}

## K Medoids {-}

### Principle {-}

@Hastieetal:09, pp. 515-520

@KaufmanRousseeuw:05, Chapter 2


### Implementation {-}

## Spectral Clustering  {-}

### Principle {-}

### Implementation {-}

## HDBScan Clustering {-}

### Principle {-}

### Implementation {-}


<br>

## References {-}