Here are some kernels I like to use for Machine Learning related projects.

kernels.py

#!/usr/bin/python
# -*- coding: utf-8 -*-

__author__ = ('Kaan Akşit')
__version__ = '0.1'

# Importing necessary libraries.
try:
    import sys,glob,time,copy
    import numpy as np
    from numpy.linalg import pinv
    from math import e
except ImportError, err:
    print "couldn't load module. %s" % (err)
    sys.exit()

# Cosine distance calculation in between two vectors.
def CosDis(a,b):
    dividend    = np.dot(a,b)
    denominator = np.linalg.norm(a,2)*np.linalg.norm(b,2)
    return dividend*1./denominator

# Minkowski distance calculation in between two vectors.
def MinDis(a,b,p):
    return np.linalg.norm(a-b,p)

# Chessboard distance calculation in between two vectors.
def ChessDis(a,b):
    return np.amax(abs(a-b))

# Bray curtis distance calculation in between two vectors.
def BrayDis(a,b):
    dividend    = np.sum(abs(a-b))
    denominator = np.sum(abs(a+b))
    return dividend*1./denominator

# Canberra distance calculation in between two vectors.
def CanberraDis(a,b):
    dividend    = abs(a-b)
    denominator = abs(a)+abs(b)
    return np.sum(dividend*1./denominator)

# Manhattan distance calculation in between two vectors.
def ManhattanDis(a,b):
    return np.sum(abs(a-b))

# Those kernel are learned from http://crsouza.com/2010/03/kernel-functions-for-machine-learning-applications/

# Radial basis calculation in between two vectors.
def RadialBasis(a,b,sigma=2.):
    gamma = 1./2./sigma**2
    return np.exp(-gamma*np.sqrt(np.sum((a-b)**2)))

# Exponential kernel calculation in between two vectors.
def Exponential(a,b,sigma=2.):
    gamma = 1./2./sigma**2
    return np.exp(-gamma*np.sqrt(np.sum((a-b))))

# Laplacian kernel calculation in between two vectors.
def Laplacian(a,b,sigma=2.):
    gamma = 1./sigma
    return np.exp(-gamma*np.sqrt(np.sum((a-b))))

# Linear kernel calculation in between two vectors.
def Linear(a,b,sigma=0.):
    return np.dot(a,b.T)+sigma

# Bare call response.
if __name__ == '__main__':
     pass