1. A speech processing apparatus comprising: an acquisition processor configured to acquire a speech, wherein a microphone array including a plurality of microphones to acquire the speech and to provide the acquired speech to the acquisition processor; a separation processor configured to separate the speech into a plurality of sections in accordance with a prescribed rule; a calculation processor configured to calculate a degree of similarity in each combination of the sections; an estimation processor configured to estimate, with respect to the each section, a direction of arrival of the speech; a correction processor configured to group the sections whose directions of arrival are mutually similar into a same group and correct the degree of similarity with respect to the combination of the sections in the same group; and a clustering processor configured to cluster the sections by using the corrected degree of similarity.