  This paper elaborates on the sectoral-regional view of the business cycle
synchronization in the EU -- a necessary condition for the optimal currency
area. We argue that complete and tidy clustering of the data improves the
decision maker's understanding of the business cycle and, by extension, the
quality of economic decisions. We define the business cycles by applying a
wavelet approach to drift-adjusted gross value added data spanning over 2000Q1
to 2021Q2. For the application of the synchronization analysis, we propose the
novel soft-clustering approach, which adjusts hierarchical clustering in
several aspects. First, the method relies on synchronicity dissimilarity
measures, noting that, for time series data, the feature space is the set of
all points in time. Then, the ``soft'' part of the approach strengthens the
synchronization signal by using silhouette measures. Finally, we add a
probabilistic sparsity algorithm to drop out the most asynchronous ``noisy''
data improving the silhouette scores of the most and less synchronous groups.
The method, hence, splits the sectoral-regional data into three groups: the
synchronous group that shapes the EU business cycle; the less synchronous group
that may hint at cycle forecasting relevant information; the asynchronous group
that may help investors to diversify through-the-cycle risks of the investment
portfolios. The results support the core-periphery hypothesis.
