com.aliasi.matrix.KernelFunction Maven / Gradle / Ivy
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/*
* LingPipe v. 4.1.0
* Copyright (C) 2003-2011 Alias-i
*
* This program is licensed under the Alias-i Royalty Free License
* Version 1 WITHOUT ANY WARRANTY, without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the Alias-i
* Royalty Free License Version 1 for more details.
*
* You should have received a copy of the Alias-i Royalty Free License
* Version 1 along with this program; if not, visit
* http://alias-i.com/lingpipe/licenses/lingpipe-license-1.txt or contact
* Alias-i, Inc. at 181 North 11th Street, Suite 401, Brooklyn, NY 11211,
* +1 (718) 290-9170.
*/
package com.aliasi.matrix;
import com.aliasi.util.Proximity;
/**
* A KernelFunction computes real-valued proximities
* between vectors. Note that proximity runs in the reverse direction
* from distance: the more similar two vectors are,
* the greater their proximity.
*
* Implementations of the standard kernel functions used for
* machine learning are provided in this package, including {@link
* DotProductKernel}, {@link PolynomialKernel}, {@link
* GaussianRadialBasisKernel}, and {@link HyperbolicTangentKernel}.
* See those classes' documentation for definitions of the specific
* kernel functions.
*
*
Typically kernel functions will be functions that could,
* in theory, be represented by inner products of vectors
* f(v), where f maps an n-dimensional
* input vector to an m-dimensional or even infinite-dimensional
* vector f(v). The kernel function is then
* defined as kernel(v1,v2) = f(v1) * f(v2), where
* f(v) is the embedding function and *
* represents the dot-product.
*
*
The use of kernel functions is usually for the so-called
* "kernel trick", which allows classification or clustering
* in high-dimensional spaces by embedding a lower-dimensional space
* and then working with linear combinations of kernel function
* results.
*
*
*
* @author Bob Carpenter
* @version 3.1
* @since LingPipe3.1
*/
public interface KernelFunction extends Proximity {
/**
* Return the result of applying the kernel function to the
* specified pair of vectors.
*
* @param v1 First vector.
* @param v2 Second vector.
* @return Kernel function applied to the vectors.
*/
public double proximity(Vector v1, Vector v2);
}