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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:

-1.00Perfect downhillNegative linear relationship.
-0.70Strong downhillNegative linear relationship.
-0.50Moderate downhillNegative linear relationship.
-0.30Weak downhillNegative linear relationship.
0No linear relationship.
+0.30Weak uphillPositive linear relationship.
+0.50Moderate uphillPositive linear relationship.
+0.70Strong uphillPositive linear relationship.
+1.00Perfect uphillPositive linear relationship.

Perfect Uphill +1.00:

Perfect Downhill -1.00:

'

Strong Uphill +0.61:

No Relationship: