Cop out. You refuse to answer the question because you know you can't. There are as many races as you want to see. Just because a bunch of people have decided that they refuse to answer a question because they can't, that doesn't mean it is a defensible position. It isn't. This is your 'turtles all the way down' moment. Scientists DO have an answer for how many species of sea cucumbers we have documented. They DO have an answer for how many subspecies of grey wolves there are. Why don't YOU have an answer? The rest of the scientific world isn't shy about this when it comes to taxonomic classification, but you have got cold feet all of a sudden.

I don't think its a cop out. You seem to be of the idea that we believe in a FIXED number of human races. Can you point to any modern geneticist that believe in race that says there is a FIXED number of human races? We can talk about the big ones like europeans, asians, africans, americans, oceanians but we can break each of these down into smaller races too.
The funny part about this is that just for entertainment, lets say I said we have 6 human races and then you run k=7 and show me that we now have 7 human races LOL, it wouldn't disprove the 6 human races. I will repeat it until you understand your misunderstanding: Its not the number of races thats important, its that the algo returns k RACIAL clusters. We didn't ask it to return RACIAL clusters. We asked it to return whatever clusters and it somehow chose to return RACIAL clusters. Out of all the millions of ways it could cluster human beings, it chose down racial lines. What a coincidence.

Nope. No conflation. I mean exactly what I said. Your first link contains data from studies that were conducted using STRUCTURE. They are landmark studies, often the first cited in these discussions, and cite them first you did.

My first link was the medium article about choosing the optimal k....

Of course race is real. I would never say something so ridiculous as 'race isn't real.' Race is one of the most consequential and painfully real things in the modern world, perhaps the single most consequential. But it isn't a scientific concept. It is a social construct emerging out of the biological reality of our intuitive, cognitive racial-classification modules. In fact, with reference to those modules, in a way, race IS biology. Not in the way people think of it, as a real attribute of human population genetics, but as a little part of our brain that has evolved to see race wherever we look, because so far it has proved adaptive.

I hope you're not referring to the sociology concept of race, where blacks = people with black skin from africa, southern india, australia, south america, because black skin != same race.
If this is not what you meant and I understood you correctly, then this is actually perfect, because this makes us able to translate from your paradigm into my paradigm. It opens a communication channel where we speak the same language.
"But it isn't a scientific concept. It is a social construct emerging out of the biological reality of our intuitive, cognitive racial-classification modules."
This is how we humans classify races. This is my preconceived ideas about racial groups. (Obviously a normie on the street wont have as good a classification as someone who works with different human populations. The race realists before DNA was discovered made a lot of different classifications of human races.

We can compare this with the biological reality.
"Not in the way people think of it, as a real attribute of human population genetics"

The clustering algorithms can help us see if our preconceived classifications match the clustering of genetic population data. If it does, then our preconceived classifications were correct, in the sense that it had a biological/genetic basis. If it does not, then it is evidence to support the hypothesis that the preconceived classifications do not have a biological/genetic basis.
We have found that they DO match with the biological reality.

Subspecies is an intermediary between 'species' and 'individual.'

'species' is an intermediary between 'animal' and 'individual'

Are there glimmers of inconsistency in species categories? Of course. There are discrepencies between biological, phylogenetic, cladistic species, etc.

Yes and how do you choose which type of "species" to use? That is a very arbitrary choice! Oh no...
Is a Tiger and a Lion even different species if they can produce offspring together? Wow, time to eliminate the entire concept of 'species'. Of course not.
Just so I'm not misunderstanding you; you don't reject 'subspecies' as a concept, right? You're just contesting if human beings have races or not.

Yes, it did. I have an excellent source for this. YOUR video. Didn't quite remember Josh saying that one bit, eh? ;)

Please be able to have an attention span of more than 1 comment back. If you use an algorithm to pick the optimal k, then you did not pick k. This algorithm could be using the elbow method for simplicity.
And if you remember I explained how the optimal k might change when we run the algorithm once, because of the randomized initial conditions of the kmeans algo. Well we can use other data analysis tools to increase the chance of finding the optimal k to any arbitrarily high percentage. So if you want to be 99,9999% sure that you are using the optimal k, then you can run the "optimal k algorithm" as a monte carlo algorithm.
There will be a risk of 0,000001% or whatever percentage risk that you tolerate that the MC algo will return, say, 8 clusters instead of 7 clusters (which was actually the optimal k)

I have been very generous in that I have willingly gone into the territory you chose, stats and ML, just to show that you will lose even on your home turf.

The reason I've went here is because of two reasons. 1: you mentioned k in an earlier post (which I know is a bogus argument) and 2: in your first reply to me, you displayed that you lacked an understanding of how the clustering actually works in the program that you're using, which led to you reaching some false conclusions and derive some misconceptions about the clustering.
It seemed to me that you either didn't understand these fundamentals (which seemed plausible considering its not your area of expertise) or you understood the fundamentals but had too low IQ to rationalize about the implications. You took it as a "win", lol. Instead you should've taken it as an invitation to learn the fundamentals and correct your misconception so that we may reach a higher level of debate and gain new insights. I am absolutely certain that you too hold knowledge where you can school me, probably also 1st year undergraduate stuff that I just OUGHT to know, but simply don't because we don't have the same background.
Engaging with you is an opportunity for me to learn, hopefully, and also an opportunity for you to learn, unless you're closeminded and think you know it all, despite that clearly not being the case.

But we have hardly even explored the anthropological assumptions in your argument. What are our preconceived ideas about race? How do you KNOW what the clusters are in advance? What is this information that you refuse to talk about? It is absolutely imperative to your argument. You keep saying it over and over, so obviously it is important. What are our preconceived ideas about race?

As a starting point we could use some of the race realist classifications from 200-100 years ago, knowing that they're outdated, wars have happend, genocides have happend and so on, but still we'll expect them to be mostly correct if we account for some historical changes and admixture events over this time period.
We will find that many of the ideas will be wrong but that the overall idea was correct.