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Dec 15, 2012

Clustering – An unsupervised learning method

Typical machine learning has well-defined outcomes: A review is either positive or negative, a mammogram scan either shows breast cancer or not. With unsupervised learning, we don’t know the outcome. What we can do is simply grouping similar items together, and form clusters. This is so-called clustering method. 

Clustering does not require training or human labeling on training data, thus it is a very convenient tool to use when we have a large number of new data, which may be fundamentally different from old data. This happens on the Internet domain, where new documents appear daily. It also happens with E-commerce domain, where new products appear weekly or monthly.

Clustering gives us freedom to form groups without prior knowledge. Such freedom also presents problems: How many clusters do we form? How do we define similarity? Once clusters are formed, how do we verify their correctness?

We can arbitrarily decide on the number of clusters beforehand. Let’s call this number k. To start clustering, we randomly pick k data points and assume they are the centers of k clusters (called centroid). Then we calculate the distance of other data points to each of these centers. Each of these data points are assigned to the neighborhood of the centroid that it is closest to. Once all data points are assigned, we will have k clusters. In round 2, we re-calculate the centroid of each cluster (Mathematically it is the mean of all the data points in a cluster), and re-assign all data points to each of these clusters. In round 3, we will repeat the process. The process will end when all clusters are the same as the last round. 

Let's look at a simple example. Suppose we have 6 people's income as the following: 1, 2, 100, 101, 1000, 1050. Suppose we believe there are 3 possible clusters in this data (k=3). To start, we arbitrarily pick 3 data points as the centers of clusters. Let these initial k centroids be: 1, 100, 101.  The remaining 3 points are then assigned to the clusters of {1}, {100} and {1050}. Based on the shortest distance, we end up with {1, 2}, {100}, {101, 1000, 1050}. In Round 2, our new centroids are 1.5, 100 and 717. Based on these centroids, our new clusters are {1, 2}, {100, 101}, {1000, 1050}. In round 3, the new centroids are 1,5, 100.5, 1025. The new clusters are {1, 2}, {100, 101}, {1000, 1050}. They are the same as the last round, and we have found our clusters. 

The about clustering process is called K-means clustering. It is the most popular method for doing clustering. Another popular method is called Expectation Maximization (EM). We may discuss it in the future blog, if there is opportunity (when no other interesting topic pops up). 

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