A K-Means Approach to Clustering Disease Progressions

K-means algorithm has been a workhorse of unsupervised machine learning for many decades, primarily owing to its simplicity and efficiency. The algorithm requires availability of two key operations on the data, first, a distance metric to compare a pair of data objects, and second, a way to compute a representative (centroid) for a given set of data objects. These two requirements mean that k-means cannot be readily applied to time series data, in particular, to disease progression profiles often encountered in healthcare analysis. We present a k-means inspired approach to clustering disease progression data. The proposed method represents a cluster as a set of weights corresponding to a set of splines fitted to the time series data and uses the "goodness-of-fit" as a way to assign time series to clusters. We use the algorithm to group patients suffering from Chronic Kidney Disease (CKD) based on their disease progression profiles. A qualitative analysis of the representative profiles for the learnt clusters reveals that this simple approach can be used to identify groups of patients with interesting clinical characteristics. Additionally, we show how the representative profiles can be combined with patient's observations to obtain an accurate patient specific profile that can be used for extrapolating into the future.