We present a data integration framework that uses non-negative matrix factorization of patient-similarity networks to integrate continuous multi-omics datasets for molecular subtyping. It is demonstrated to have the capability to handle missing data without using imputation and to be consistently among the best in detecting subtypes with differential prognosis and enrichment of clinical associations in a large number of cancers. When applying the approach to data from individuals with lower-grade gliomas, we identify a subtype with a significantly worse prognosis. Tumors assigned to this subtype are hypomethylated genome wide with a gain of AP-1 occupancy in demethylated distal enhancers. The tumors are also enriched for somatic chromosome 7 (chr7) gain, chr10 loss, and other molecular events that have been suggested as diagnostic markers for "IDH wild type, with molecular features of glioblastoma" by the cIMPACT-NOW consortium but have yet to be included in the World Health Organization (WHO) guidelines.