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Recently, slow earthquakes (slow EQ) have received much attention relative to understanding the mechanisms underlying large earthquakes and to detecting their precursors. Low-frequency earthquakes (LFE) are a specific type of slow EQ. In the present paper, we reveal the relevance of LFEs to the 11 March 2011 Great Tohoku Earthquake (Tohoku-oki EQ) by means of cluster analysis. We classified LFEs in northern Japan in a data-driven manner, based on inter-time, the time interval between neighboring LFEs occurring within 10 km. We found that there are four classes of LFE that are characterized by median inter-times of 24 seconds, 27 minutes, 2.0 days, and 35 days, respectively. Remarkably, in examining the relevance of these classes to the Tohoku-oki EQ, we found that activity in the shortest inter-time class (median 24 seconds) diminished significantly at least three months before the Tohoku-oki EQ, and became completely quiescent 30 days before the event (p-value = 0.00014). Further statistical analysis implies that this class, together with a similar class of volcanic tremor, may have served as a precursor of the Tohoku-oki EQ. We discuss a generative model for these classes of LFE, in which the shortest inter-time class is characterized by a generalized gamma distribution with the product of shape parameters vκ = 1:54 in the domain of inter-time close to zero. We give a possible geodetic interpretation for the relevance of LFE to the Tohoku-oki EQ.