"TOKYO (Kyodo) -- A Chinese frigate and an unidentified foreign submerged submarine were spotted Thursday just outside Japanese territorial waters near the Senkaku Islands [near Miyako Island] in the East China Sea, the Defense Ministry said, prompting Tokyo to protest to Beijing over the sailing..."
The Japanese Navy has almost automatically assumed (or decided to announce) that because a Chinese (Type 054 or 054A) frigate was detected, the submarine must also be Chinese.
My alternative theory is that the Chinese Navy spotted a North Korean (NK) submarine. China wishing to avoid another Cheonan Incident pursued the NK sub to warn-off that sub. The Cheonan Incident was when a NK submarine torpedoed a South Korean surface ship in 2010. An NK sub would also be a threat to Japanese surface ships.
The Chinese frigate's actions is part of China's new policy of pressuring NK to be less belligerent in its actions and threats. China wishes to de-escalate NK vs (South Korea, Japan, US) tensions.
Photo of the Chinese submarine that was forced or decided to surface in Japan's Senkaku Islands area, January 11, 2018.
Comments, with links, received from readers since the first vague Japanese reports, strongly indicate it was a Chinese submarine that surfaced and showed the Chinese flag (above). The submarine appears to be a Type 093 (NATO designation "Shang" class SSN).
Another conclusion is that Japan is utilising its undersea sensor array to detect NK and Chinese submarines. See array MAP B below. The array includes seafloor hydrophones and other sensors, which is strung from the Japanese home islands, via Okinawa (main) Island and via Miyako (in Japan's Senkakus) Island etc.
MAP A - Neatly illustrates the Japanese Senkakus vs Chinese Diaoyu Islands territorial dispute Significantly Taiwan is also in dispute against Japan. Taiwan calling them the Tiaoyutai Islands. (Map coutesy Malaysia Chronicle, January 18, 2018)
The Chinese action could be a freedom of navigation exercise (FONOPS) against Japan's disputed Senkakus territorial claim. This may also be a Chinese method to test Japan's anti-submarine defences (including sensitivity of the Japanese seafloor SOSUS-IUSS array in detecting the Chinese sub). The Chinese frigate could also detect counter-moves by Japanese patrolling Soryu or Oyashio class submarines.
MAP B is from page 54 “Map 4. The US ‘Fish Hook’ Undersea Defense Line” in Desmond Ball and Richard Tanter, The Tools of Owatatsumi Japan’s Ocean Surveillance and Coastal Defence Capabilities (2015, ANU Press) http://press-files.anu.edu.au/downloads/press/p309261/pdf/book.pdf?referer=444. The map may depict past or current locations of the eastern Asia - inner western Pacific SOSUS-IUSS seafloor array.