# Data Clusters

• Clusters are collections of similar data
• Clustering is a type of unsupervised learning
• The Correlation Coefficient describes the strength of a relationship.

## Clusters

Clusters are collections of data based on similarity.

Data points clustered together in a graph can often be classified into clusters.

In the graph below we can distinguish 3 different clusters:

## Identifying Clusters

Clusters can hold a lot of valuable information, but clusters come in all sorts of shapes, so how can we recognize them?

The two main methods are:

• Using Visualization
• Using an Clustering Algorithm

## Clustering

Clustering is a type of Unsupervised Learning.

Clustering is trying to:

• Collect similar data in groups
• Collect dissimilar data in other groups

## Clustering Methods

• Density Method
• Hierarchical Method
• Partitioning Method
• Grid-based Method

The Density Method considers points in a dense regions to have more similarities and differences than points in a lower dense region. The density method has a good accuracy. It also has the ability to merge clusters.
Two common algorithms are DBSCAN and OPTICS.

The Hierarchical Method forms the clusters in a tree-type structure. New clusters are formed using previously formed clusters.
Two common algorithms are CURE and BIRCH.

The Grid-based Method formulates the data into a finite number of cells that form a grid-like structure.
Two common algorithms are CLIQUE and STING

The Partitioning Method partitions the objects into k clusters and each partition forms one cluster.
One common algorithm is CLARANS.

## Correlation Coefficient

The Correlation Coefficient (r) describes the strength and direction of a linear relationship and x/y variables on a scatterplot.

The value of r is always between -1 and +1:

 -1 Perfect downhill Negative linear relationship. -0.7 Strong downhill Negative linear relationship. -0.5 Moderate downhill Negative linear relationship. -0.3 Weak downhill Negative linear relationship. 0 No linear relationship. 0.3 Weak uphill Positive linear relationship. 0.5 Moderate uphill Positive linear relationship. 0.7 Strong uphill Positive linear relationship. 1 Perfect uphill Positive linear relationship.

Perfect Uphill +1.00:

Perfect Downhill -1.00:

'

Strong Uphill +0.61:

No Relationship: