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  1. For intra-cluster relationships, we applied mathematical optimisation to choose the best tree produced by neighbour joining method.

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  1. For intra-cluster relationships, we applied mathematical optimisation to choose the best tree produced by the neighbour joining method.

What is the rule for using "the" before mathematical methods in general?

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    If "neighbour joining method" names a specific technique being used, "the" should be placed in front of it. If not, I don't understand what the sentence is supposed to mean.
    – Hot Licks
    Commented Oct 28, 2015 at 23:02

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You have to use the if you use method. Consider this example:

We were studying neighbor joining. We applied mathematical optimisation to choose the best tree produced by the method.

If you remove the attributive noun phrase "neighbor joining," you need the definite article. Therefore, you also need the definite article if you include the phrase.

On the other hand, as Isaac Askew notes, you can use the noun phrase by itself as the object of the preposition, in which case, you would write we applied mathematical optimisation to choose the best tree produced by neighbor joining.

The best choice probably depends on the context.

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It's hard to find a lot of rules on the subject. I personally feel like both 'the' and 'method' should be stripped:

For intra-cluster relationships, we applied mathematical optimisation to choose the best tree produced by neighbour joining.

If neighbour joining is something that is unfamiliar to readers or if the method referred to is ambiguous (such as a one-word method that might be a common word), I would introduce the method beforehand, describing it as 'neighbour joining, a method characterized by...' then refer to it as 'neighbour joining' for the rest of the paper. Once people know the scope it would be less confusing.

It's purely speculation as I've never seen any rules on it. I personally think that just mentioning the method as in my blockquote above would be sufficient, but it would depend on the audience of the paper. If it was purely instructional, use 'the neighbour joining method' and describe what it is. If it's for a mathematically excellent audience, just 'neighbour joining' should work.

Using 'the' and 'rule' feels unnatural to me. Imagine people saying:

"To find the answer, we must first apply the L'Hôpital's Rule rule."

I know it's probably not helpful, as you probably need specifics for a journal or thesis. That's my 2 cents though; best of luck!

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    The L'Hôpital's Rule example is not terribly good because the name includes rule and, being a possessive phrase, does not take the definite article. How about the goal was disallowed because of the offside rule as opposed to the goal was disallowed because of offside? I far prefer the former.
    – phoog
    Commented Oct 28, 2015 at 22:48
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    Agree with @phoog -- L'Hôpital's Rule goes by different rules. Try "Golden Rule" instead and see what you get.
    – Hot Licks
    Commented Oct 28, 2015 at 23:04

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