mlpack
2.1.1

Table of Contents
 Introduction to the KernelType policy
 The KernelTraits trait class
 List of kernels and classes that use a
KernelType
Introduction to the KernelType policy
`Kernel methods' make up a large class of machine learning techniques. Each of these methods is characterized by its dependence on a kernel function. In rough terms, a kernel function is a general notion of similarity between two points, with its value large when objects are similar and its value small when objects are dissimilar (note that this is not the only interpretation of what a kernel is).
A kernel (or `Mercer kernel') takes two objects as input and returns some sort of similarity value. The specific details and properties of kernels are outside the scope of this documentation; for a better introduction to kernels and kernel methods, there are numerous better resources available, including http://www.erickim.net/erickimnet/posts/1/kernel_trick.html "Eric Kim's tutorial".
mlpack implements a number of kernel methods and, accordingly, each of these methods allows arbitrary kernels to be used via the KernelType
template parameter. Like the MetricType policy, the requirements are quite simple: a class implementing the KernelType
policy must have
 an
Evaluate()
function  a default constructor
The signature of the Evaluate()
function is straightforward:
The function takes two vector arguments, a
and b
, and returns a double
that is the evaluation of the kernel between the two arguments. So, for a particular kernel , the Evaluate()
function should return .
The arguments a
and b
, of types VecTypeA
and VecTypeB
, respectively, will be an Armadillolike vector type (usually arma::vec
, arma::sp_vec
, or similar). In general it should be valid to assume that VecTypeA
is a class with the same API as arma::vec
.
Note that for kernels that do not hold any state, the Evaluate()
method can be marked as static
.
Overall, the KernelType
template policy is quite simple (much like the MetricType policy). Below is an example kernel class, which outputs 1
if the vectors are close and 0
otherwise.
Then, this kernel may be easily used inside of mlpack algorithms. For instance, the code below runs kernel PCA (mlpack::kpca::KernelPCA
) on a random dataset using the ExampleKernel
. The results are saved to a file called results.csv
. (Note that this is simply an example to demonstrate usage, and this example kernel isn't actually likely to be useful in practice.)
The KernelTraits trait class
Some algorithms that use kernels can specialize if the kernel fulfills some certain conditions. An example of a condition might be that the kernel is shiftinvariant or that the kernel is normalized. In the case of fast maxkernel search (mlpack::fastmks::FastMKS), the computation can be accelerated if the kernel is normalized. For this reason, the KernelTraits
trait class exists. This allows a kernel to specify via a const
static
bool
when these types of conditions are satisfied. Note that a KernelTraits class is not required, but may be helpful.
The KernelTraits
trait class is a template class that takes a KernelType
as a parameter, and exposes const
static
bool
values that depend on the kernel. Setting these values is achieved by specialization. The code below provides an example, specializing KernelTraits
for the ExampleKernel
from earlier:
At this time, there is only one kernel trait that is used in mlpack code:
IsNormalized
(defaults tofalse
): if , then the kernel is normalized and this should be set to true.
List of kernels and classes that use a \c KernelType
mlpack comes with a number of prewritten kernels that satisfy the KernelType
policy:
 mlpack::kernel::LinearKernel
 mlpack::kernel::ExampleKernel – an example kernel with more documentation
 mlpack::kernel::GaussianKernel
 mlpack::kernel::HyperbolicTangentKernel
 mlpack::kernel::EpanechnikovKernel
 mlpack::kernel::CosineDistance
 mlpack::kernel::LaplacianKernel
 mlpack::kernel::PolynomialKernel
 mlpack::kernel::TriangularKernel
 mlpack::kernel::SphericalKernel
 mlpack::kernel::PSpectrumStringKernel – operates on strings, not vectors
These kernels (or a custom kernel) may be used in a variety of mlpack methods:
 mlpack::kpca::KernelPCA  kernel principal components analysis
 mlpack::fastmks::FastMKS  fast maxkernel search
 mlpack::kernel::NystroemMethod  the Nystroem method for sampling
 mlpack::metric::IPMetric  a metric built on a kernel
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