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Here we first learn about clustering.

**What is Clustering?**

How do I group these documents by topic?

How do I group my customers by purchase patterns?

Sort items into groups by similarity:

Items in a cluster are more similar to each other than they are to items in other clusters.

Need to detail the properties that characterize “similarity”

•Not a predictive method; finds similarities, relationships

Our Example: K-means Clustering

**What is Cluster Analysis?**

Finding groups of objects such that the objects in a group will be similar (or related) to one another and different from (or unrelated to) the objects in other groups.

**Types of Clusters: Well-Separated**

**Well-Separated Clusters: **

A cluster is a set of points such that any point in a cluster is closer (or more similar) to every other point in the cluster than to any point not in the cluster.

**Types of Clusters: Center-Based**

**Center-based**

A cluster is a set of objects such that an object in a cluster is closer (more similar) to the “center” of a cluster, than to the center of any other cluster

The center of a cluster is often a centroid, the average of all the points in the cluster, or a medoid, the most “representative” point of a cluster

**K-Means Clustering - What is it?**

Used for clustering numerical data, usually a set of measurements about objects of interest.

Input: numerical. There must be a distance metric defined over the variable space.

Euclidian distance

Output: The centers of each discovered cluster, and the assignment of each input to a cluster.

**Centroid**

**What Euclidian Distance?**

**K-means Clustering**

Characteristics

Partitional clustering approach

Each cluster is associated with a centroid (center point)

Each point is assigned to the cluster with the closest centroid

Number of clusters, K, must be specified

The basic algorithm is very simple

Algorithm:

**K-means Clustering – Details**

- Initial centroi•Initial centroids are often chosen randomly.

Clusters produced vary from one run to another.

- The centroid is (typically) the mean of the points in the cluster.

- ‘Closeness’ is measured by **Euclidean distance**, cosine similarity, correlation, etc.

- K-means will converge for common similarity measures mentioned above.

- Most of the convergence happens in the first few iterations.

- Often the stopping condition is changed to ‘Until relatively few points change clusters’

Complexity is O( n * K * I * d )

n = number of points, K = number of clusters, I = number of iterations, d = number of attributesds are often chosen randomly.

**Use Cases**

Often an exploratory technique:

Discover structure in the data

Summarize the properties of each cluster

Sometimes a pre-step to classification:

"Discovering the classes“

Examples

The height, weight and average lifespan of animals

Household income, yearly purchase amount in dollars, number of household members of customer households

Patient record with measures of BMI, HBA1C, HDL

**Diagnostics – Evaluating the Model**

Do the clusters look separated in at least some of the plots when you do pair-wise plots of the clusters?

Pair-wise plots can be used when there are not many variables

Do you have any clusters with few data points?

Try decreasing the value of K

Are there splits on variables that you would expect, but don't see?

Try increasing the value K

Do any of the centroids seem too close to each other?

Try decreasing the value of K

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