Induction is argument by analogy.
- We see X holds in case A
- Case B is similar enough to case A in relevant characteristics
- Thus, we think X will hold in case B too.
That is induction, and also analogy.
Another word for analogy is "pattern-matching." We see that X holds in case A, and case A matches pattern P; case B also matches pattern P; thus, we think X will hold in case B too.
A neuron does nothing but match patterns. It fires under some circumstances, and not under others. The circumstances under which it fires are the pattern recognized by the neuron. We might equivalently say that the neuron is constantly inspecting the surrounding circumstances to see if they are similar enough to the circumstances under which it should fire, and if so, it fires.
Because neurons just match patterns, arguably practically everything the brain is doing is analogy.
More specifically, in regard to your question, the argument from analogy for other minds could also be called induction, or pattern-matching, whichever you want to call it. And it does provide some partial (probabilistic) evidence for other minds.
The SEP article lists the objection to the argument from analogy, that other minds cannot be directly checked. Well, neither can the presence of a table!
- We look at the table (it sure looks like a table; an analogy.)
- We touch the table (yes, it feels like a table; an analogy.)
- We disassemble the table (yes, those look and feel like parts of a table! an analogy)
But we can never directly check that there is a table there. Only that it looks and feels like a table, perhaps also smells and tastes like a table, weighs the same as a table, appears to hold plates like a table, and on and on. All by analogy. There is always the possibility that the apparent table might be some clever illusion, that we could be trapped in a dream, or something like that. This is precisely the same situation we are in when it comes to other minds.
All confirmations are probabilistic, never perfectly definite. Everything we know about the empirical world is by analogy/induction/pattern-matching. The argument from analogy for other minds has no more difficulty in this regard than any other claim about the world.