I have a dataset with two cardinal attributes of comparable scale. I wish to divide the data points into 4 clusters, so as to have complete segmentation by attribute 1, while minimizing the variance within attribute 2.
E.g.: If plotting attribute 1 on the x-axis and attribute 2 on the y-axis, the resulting clusters should represent vertical cuts through the data set, which are sized horizontally so as to minimize the variance in attribute 2.
The only approach I have come up with so far is to employ k-means clustering and scale up attribute 1 so as to be the dominant factor in the distance function.
Any other suggestions for suitable unsupervised learning / clustering algorithms?
