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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


  • 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


  • 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


K-means Clustering – Details

- Initial centroiInitial 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“


  • 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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