Considerando que meu homônimo está envolvido, é melhor eu responder a essa pergunta!
De acordo com a página da Memória Beta em Arik Soong , é explicado que ele era de Noonien Soong bisavô :
In The Worst of Both Worlds, the mirror universe version of Noonien Soong told Jean-Luc Picard that Arik Soong was his great-grandfather, indicating that the same filial relationship existed between Arik and Noonien Soong in the primary universe. Furthermore, the fact that the mirror Arik Soong was executed in 2155, as depicted in the novel Age of the Empress, would seem to indicate that he had fathered at least one child in both universes by that time.
Noonien Soong may have been named out of admiration that Arik had for Khan Noonien
Agora, de qualquer forma, significa que o próprio Noonien não era um aumento, mas potencialmente foi o fruto de um dos aumentos de Arik; os detalhes simplesmente não estão lá, estou com medo! Tenha em mente que isso tudo está fora de cânone.