The metal subgenres are from Wikipedia, and depending on your perspective, some of those aren't real genres. 'Classic metal' and 'Symphonic & Gothic Metal'... Symphonic is a descriptor that can be applied to any genre. For example, there's symphonic power metal and symphonic black metal. Same goes with Viking metal. Progressive, however, is both a genre and a descriptor. Dream Theater and Haken are 'progressive metal' bands, but you can also have a band like Atheist, which is a progressive death metal band.
Taxonomy, especially of music, is a really difficult thing to do. You have orthodox, revisionist, and post-revisionist ways of classifying things. I personally think it's most convenient to use post-revisionist buckets and give orthodox classification through history blurbs/slugs on an artist/album/song. An example - Slayer is a thrash metal band. But at the time, a lot of people would have called them a black metal band. That's because when Show No Mercy was released, black metal was an aesthetic and subject matter, not a sound. So in this map I'd place them under thrash and clarify the dispute.
My top-down perspective is: black metal, death metal, thrash metal, power metal, doom metal, heavy metal. 'Glam metal and hair metal' belong under rock genres. Those 60s/70s hard rock bands (e.g. Sir Lord Baltimore, Blue Cheer) that Wikipedia calls 'classic metal', are just hard rock. Metalcore, deathcore, crossover, crust, grindcore, are interesting cases as well. Metalcore is, arguably, death metal -> melodic death metal + []hardcore. Hardcore being under punk. If you place it under metal overall, people will complain that it's really punk-based. If you place it under punk, you'll get the complaint that it's so influenced by metal that it shouldn't be. Similar problems in taxonomy arise in a lot of modern black metal bands because post-rock has influenced many greatly.
Anyway, very cool site, one day I'll be a librarian.