KMeans对不平衡数据进行聚类

Question

I have a set of data with 50 features (c1, c2, c3 ...), with over 80k rows.

Each row contains normalised numerical values (ranging 0-1). It is actually a normalised dummy variable, whereby some rows have only few features, 3-4 (ie 0 is assigned if there is no value). Most rows have about 10-20 features.

I used KMeans to cluster the data, always resulting in a cluster with a large number of members. Upon analysis, I noticed that rows with fewer than 4 features tends to get clustered together, which is not what I want.

Is there anyway balance out the clusters?

Answer 1

It is not part of the k-means objective to produce balanced clusters. In fact, solutions with balanced clusters can be arbitrarily bad (just consider a dataset with duplicates). K-means minimizes the sum-of-squares, and putting these objects into one cluster seems to be beneficial.

What you see is the typical effect of using k-means on sparse, non-continuous data. Encoded categoricial variables, binary variables, and sparse data just are not well suited for k-means use of means . Furthermore, you'd probably need to carefully weight variables, too.

Now a hotfix that will likely improve your results (at least the perceived quality, because I do not think it makes them statistically any better) is to normalize each vector to unit length (Euclidean norm 1). This will emphasize the ones of rows with few nonzero entries. You'll probably like the results more, but they are even much harder to interpret.