Cerebral amoebiasis is not caused by
Naegleria
Acanthamoeba
Dientamoeba
Balamuthia
Three free living amoebae are neuropathogenic (encephalitis)

Naegleria fowleri causes primary amoebic meningoencephalitis.  
Acanthamoeba causes granulomatous amoebic encephalitis.
Balamuthia mandrillaris causes amoebic meningoencephalitis.