Why Does Subsequence Time-Series Clustering Produce Sine Waves?

Data mining and machine leaning communities were surprised when Keogh et al. (2003) pointed out that the k-means cluster centers in subsequence time-series clustering become sinusoidal pseudopatterns for almost all kinds of input time-series data. Understanding this mechanism is an important open problem in data mining. Our new theoretical approach (based on spectral clustering and translational symmetry) explains why the cluster centers of k-means naturally tend to form sinusoidal patterns.