## Machine Learning Lesson of the Day: Clustering, Density Estimation and Dimensionality Reduction

I struggle to categorize unsupervised learning.  It is not an easily defined field, and it is also hard to find generalizations of techniques that are exhaustive and mutually exclusive.

Nonetheless, here are some categories of unsupervised learning that cover many of its commonly used techniques.  I learned this categorization from Mathematical Monk, who posted a great set of videos on machine learning on Youtube.

• Clustering: Categorize the observed variables $X_1, X_2, ..., X_p$ into groups that maximize some similarity criterion, or, equivalently, minimize some dissimilarity criterion.
• Density Estimation: Use statistical models to find an underlying probability distribution that gives rise to the observed variables.
• Dimensionality Reduction: Find a smaller set of variables that captures the essential variations or patterns of the observed variables.  This smaller set of variables may be just a subset of the observed variables, or it may be a set of new variables that better capture the underlying variation of the observed variables.

Are there any other categories that you can think of?  How would you categorize hidden Markov models?  Your input is welcomed and appreciated in the comments!

## Presentation Slides – Finding Patterns in Data with K-Means Clustering in JMP and SAS

My slides on K-means clustering at the Toronto Area SAS Society (TASS) meeting on December 14, 2012, can be found here.

This image is slightly enhanced from an image created by Weston.pace from Wikimedia Commons.

#### My Presentation on K-Means Clustering

I was very pleasured to be invited for the second time by the Toronto Area SAS Society (TASS) to deliver a presentation on machine learning.  (I previously presented on partial least squares regression.)  At its recent meeting on December 14, 2012, I introduced an unsupervised learning technique called K-means clustering.

I first defined clustering as a set of techniques for identifying groups of objects by maximizing a similarity criterion or, equivalently, minimizing a dissimilarity criterion.  I then defined K-means clustering specifically as a clustering technique that uses Euclidean proximity to a group mean as its similarity criterion.  I illustrated how this technique works with a simple 2-dimensional example; you can follow along this example in the slides by watching the sequence of images of the clusters toward convergence.  As with many other machine learning techniques, some arbitrary decisions need to be made to initiate the algorithm for K-means clustering:

1. How many clusters should there be?
2. What is the mean of each cluster?

I provided some guidelines on how to make these decisions in these slides.