4 ms·
I'm an undergrad CS major in my fourth year, and I have no idea what you are writing about, although it sounds like it might be interesting or useful if I under
by Figs 16y ago
I'm an undergrad CS major in my fourth year, and I have no idea what you are writing about, although it sounds like it might be interesting or useful if I understood it. The first stumbling block came right away, since I don't know what the notation you used here is supposed to mean:
"In algebra (kernel of a linear transform, of a homomorphism, of a matrix), a kernel is the set of elements that map to the neutral element. T : V → W ker(T) = {v ∈ V | T.v = 0}"
What is T.v? Is 0 the "neutral element"? What is meant by neutral element? (I am not an expert at algebra, since I am a CS major, and my major has been focused more on things like compilers, machine architecture, programming languages, algorithms, etc. rather than machine learning) What does V -> W ker(T) mean? I assume you're saying something like "T is a kernel of a function that maps V to W if T.v (where v is a V) is the neutral element", but this means nothing to me. Aren't you trying to explain what a kernel is...? How is the reader supposed to understand this if they don't already know what it is?
- snippyhollow 16y agoT is a linear transform/map or (it is the same thing!) a homomorphism, or a matrix: an application between 2 vector spaces that preserves vector addition and scalar multiplication (i.e. f(x+y) = f(x)+f(y), f(a.x) = a.f(x)). T : V -> W is the signature of this homomorphism, whereas ker(T) = {v \in V | T.v = 0} means "ker of T is the set of vectors v in the vector space V such that T applied to v is the neutral element of W". The neutral element is noted 0 because, in a vector space, it is such that v + neutral_element = v. So neutral_element is the null vector. I learned algebra kernels in my first year of college, so I assumed wrongly. But that's not the point: I was not thinking about explaining what a kernel is but instead (higher level) trying to group what seemed to be scattered definitions into explaining why we call "kernel machines" this (and why a kernel trick involves a kernel). Now, I'm thinking about explaining (with pictures) what an algebra kernel is...
- snippyhollow 16y agoHere it is: http://i.imgur.com/8V7Xg.png http://i.imgur.com/8V7Xg.png
- ableal 16y agoI'd suggest tossing that figure into the original post. It's a nice visual hook.