A k-means method for trends of time series: An application to time series of COVID-19 cases in Japan

A k-means method style clustering algorithm is proposed for trends of multivariate time series. The usual k-means method is based on distances or dissimilarity measures among multivariate data and centroids of clusters. Some similarity or dissimilarity measures are also available for multivariate time series. However, suitability of dissimilarity measures depends on the properties of time series. Moreover, it is not easy to define the centroid for time series. The k-medoid clustering method can be applied to time series using one of dissimilarity measures without using centroids. However, the k-medoid method becomes restrictive if appropriate medoids do not exist. In this paper, the centroid is defined as a common trend and a dissimilarity measure is also introduced for trends. Based on these centroids and dissimilarity measures, a k-means method style algorithm is proposed for a multivariate trend. The proposed method is applied to the time series of COVID-19 cases in each prefecture of Japan.