C ++支持向量机（SVM）模板库？

Question

I have a dataset from custom abstract objects and a custom distance function. Is there any good SVM libraries that allows me to train on my custom objects (not 2d points) and my custom distance function?

I searched the answers in this similar stackoverflow question , but none of them allows me to use custom objects and distance functions.

Answer 1

First things first.

SVM does not work on distance functions , it only accepts dot products . So your distance function (actually similarity, but usually 1-distance is similarity) has to:

• be symmetric s(a,b)=s(b,a)
• be positive definite s(a,a)>=0, s(a,a)=0 <=> a=0
• be linear in first argument s(ka, b) = ks(a,b) and s(a+b,c) = s(a,c) + s(b,c)

This can be tricky to check, as you actually ask "is there a function from my objects to some vector space, phi such that s(phi(x), phi(y)) " is a dot-product, thus leading to definition of so called kernel , K(x,y)=s(phi(x), phi(y)) . If your objects are themselves elements of vector space, then sometimes it is enough to put phi(x)=x thus K=s , but it is not true in general.

Once you have this kind of similarity nearly any SVM library (for example libSVM ) works with providing Gram matrix . Which is simply defined as

G_ij = K(x_i, x_j)

Thus requiring O(N^2) memory and time. Consequently it does not matter what are your objects, as SVM only works on pairwise dot-products , nothing more.

If you look appropriate mathematical tools to show this property, what can be done is to look for kernel learning from similarity . These methods are able to create valid kernel which behaves similarly to your similarity.

Answer 2

Check out the following:

• MLPack : a lightweight library that provides lots of functionality.
• DLib : a very popular toolkit that is used both in industry and academia.

Apart from these, you can also use Python packages, but import them from C++.