BaseL2Kernel (Java Statistical Analysis Tool 0.0.8 API)

java.lang.Object
- jsat.distributions.kernels.BaseL2Kernel

All Implemented Interfaces:

Serializable, Cloneable, KernelTrick, Parameterized

Direct Known Subclasses:

PukKernel, RationalQuadraticKernel, RBFKernel
```
public abstract class BaseL2Kernel
extends Object
implements KernelTrick
```
Many Kernels can be described in terms the L2 norm with some operations performed on it. For example, the RBFKernel and RationalQuadraticKernel can both be expressed in terms of the L₂ norm of the two inputs. To simplify the addition of other kernels based on the same norm, this base class exists.

All Kernels extending this base kernel support acceleration. This is done making use of the fact that || x - y ||² = x x' +y y' - 2 x y'
Thus the cached value for each vector is its self dot product.

Author:

Edward Raff

See Also:

Serialized Form

Constructor Summary

Constructors
Constructor and Description

BaseL2Kernel()

Constructors
Constructor and Description
`BaseL2Kernel()`

Method Summary

All Methods Instance Methods Abstract Methods Concrete Methods
Modifier and Type	Method and Description
`void`	`addToCache(Vec newVec, List<Double> cache)` Appends the new cache values for the given vector to the list of cache values.
`abstract KernelTrick`	`clone()`
`abstract double`	`eval(int a, int b, List<? extends Vec> trainingSet, List<Double> cache)` Produces the correct kernel evaluation given the training set and the cache generated by `KernelTrick.getAccelerationCache(List)`.
`abstract double`	`eval(int a, Vec b, List<Double> qi, List<? extends Vec> vecs, List<Double> cache)` Computes the kernel product between one vector in the original list of vectors with that of another vector not from the original list, but had information generated by `KernelTrick.getQueryInfo(jsat.linear.Vec)`.
`abstract double`	`eval(Vec a, Vec b)` Evaluate this kernel function for the two given vectors.
`double`	`evalSum(List<? extends Vec> finalSet, List<Double> cache, double[] alpha, Vec y, int start, int end)` Performs an efficient summation of kernel products of the form ∑ α_i k(x_i, y) where x are the final set of vectors, and α the associated scalar multipliers
`double`	`evalSum(List<? extends Vec> finalSet, List<Double> cache, double[] alpha, Vec y, List<Double> qi, int start, int end)` Performs an efficient summation of kernel products of the form ∑ α_i k(x_i, y) where x are the final set of vectors, and α the associated scalar multipliers
`List<Double>`	`getAccelerationCache(List<? extends Vec> trainingSet)` Creates a new list cache values from a given list of training set vectors.
`Parameter`	`getParameter(String paramName)` Returns the parameter with the given name.
`List<Parameter>`	`getParameters()` Returns the list of parameters that can be altered for this learner.
`List<Double>`	`getQueryInfo(Vec q)` Pre computes query information that would have be generated if the query was a member of the original list of vectors when calling `KernelTrick.getAccelerationCache(java.util.List)` .
`protected double`	`getSqrdNorm(int i, int j, List<? extends Vec> vecs, List<Double> cache)` Returns the squared L² norm between two points from the cache values.
`protected double`	`getSqrdNorm(int i, List<? extends Vec> vecs, List<Double> cache)` Returns the squared L² norm of the given point from the cache
`protected double`	`getSqrdNorm(int i, Vec y, List<Double> qi, List<? extends Vec> vecs, List<Double> cache)` Returns the squared L² norm between a point in the cache and one with a provided qi value
`boolean`	`supportsAcceleration()` Indicates if this kernel supports building an acceleration cache using the `KernelTrick.getAccelerationCache(List)` and associated cache accelerated methods.

Methods inherited from class java.lang.Object
equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface jsat.distributions.kernels.KernelTrick
normalized, toString

- Constructor Detail
  - BaseL2Kernel
```
public BaseL2Kernel()
```
- Method Detail
  - eval
```
public abstract double eval(Vec a,
                            Vec b)
```
    Description copied from interface: KernelTrick
    
    Evaluate this kernel function for the two given vectors.
    
    Specified by:
    
    eval in interface KernelTrick
    
    Parameters:
    
    a - the first vector
    
    b - the first vector
    
    Returns:
    
    the evaluation
  - clone
```
public abstract KernelTrick clone()
```
    Specified by:
    
    clone in interface KernelTrick
    
    Overrides:
    
    clone in class Object
  - supportsAcceleration
```
public boolean supportsAcceleration()
```
    Description copied from interface: KernelTrick
    
    Indicates if this kernel supports building an acceleration cache using the KernelTrick.getAccelerationCache(List) and associated cache accelerated methods. By default this method will return false. If true, then a cache can be obtained from this matrix and used in conjunction with KernelTrick.eval(int, Vec, List, List, List) and KernelTrick.eval(int, int, List, List) to perform kernel products.
    
    Specified by:
    
    supportsAcceleration in interface KernelTrick
    
    Returns:
    
    true if cache acceleration is supported for this kernel, false otherwise.
  - getSqrdNorm
```
protected double getSqrdNorm(int i,
                             int j,
                             List<? extends Vec> vecs,
                             List<Double> cache)
```
    Returns the squared L² norm between two points from the cache values.
    
    Parameters:
    
    i - the first index in the vector list
    
    j - the second index in the vector list
    
    vecs - the list of vectors that make the collection
    
    cache - the cache of values for each vector in the collection
    
    Returns:
    
    the squared norm ||x_i-x_j||²
  - getSqrdNorm
```
protected double getSqrdNorm(int i,
                             List<? extends Vec> vecs,
                             List<Double> cache)
```
    Returns the squared L² norm of the given point from the cache
    
    Parameters:
    
    i - the index in the vector list to get the squared norm from
    
    vecs - the list of vectors that make the collection
    
    cache - the cache of values for each vector in the collection
    
    Returns:
    
    the squared norm ||x_i||²
  - getSqrdNorm
```
protected double getSqrdNorm(int i,
                             Vec y,
                             List<Double> qi,
                             List<? extends Vec> vecs,
                             List<Double> cache)
```
    Returns the squared L² norm between a point in the cache and one with a provided qi value
    
    Parameters:
    
    i - the index in the vector list
    
    y - the other vector
    
    qi - the acceleration values for the other vector
    
    vecs - the list of vectors to make the collection
    
    cache - the cache of values for each vector in the collection
    
    Returns:
    
    the squared norm ||x_i-y||²
  - getAccelerationCache
```
public List<Double> getAccelerationCache(List<? extends Vec> trainingSet)
```
    Description copied from interface: KernelTrick
    
    Creates a new list cache values from a given list of training set vectors. If this kernel does not support acceleration, null will be returned.
    
    Specified by:
    
    getAccelerationCache in interface KernelTrick
    
    Parameters:
    
    trainingSet - the list of training set vectors
    
    Returns:
    
    a list of cache values that may be used by this kernel
  - getQueryInfo
```
public List<Double> getQueryInfo(Vec q)
```
    Description copied from interface: KernelTrick
    
    Pre computes query information that would have be generated if the query was a member of the original list of vectors when calling KernelTrick.getAccelerationCache(java.util.List) . This can then be used if a large number of kernel computations are going to be done against points in the original set for a point that is outside the original space.
    
    If this kernel does not support acceleration, null will be returned.
    
    Specified by:
    
    getQueryInfo in interface KernelTrick
    
    Parameters:
    
    q - the query point to generate cache information for
    
    Returns:
    
    the cache information for the query point
  - addToCache
```
public void addToCache(Vec newVec,
                       List<Double> cache)
```
    Description copied from interface: KernelTrick
    
    Appends the new cache values for the given vector to the list of cache values. This method is present for online style kernel learning algorithms, where the set of vectors is not known in advance. When a vector is added to the set of kernel vectors, its cache values can be added using this method.
    
    The results of calling this sequentially on a lit of vectors starting with an empty double list is equivalent to getting the results from calling KernelTrick.getAccelerationCache(java.util.List)
    
    If this kernel does not support acceleration, this method call will function as a nop.
    
    Specified by:
    
    addToCache in interface KernelTrick
    
    Parameters:
    
    newVec - the new vector to add to the cache values
    
    cache - the original list of cache values to add to
  - eval
```
public abstract double eval(int a,
                            Vec b,
                            List<Double> qi,
                            List<? extends Vec> vecs,
                            List<Double> cache)
```
    Description copied from interface: KernelTrick
    
    Computes the kernel product between one vector in the original list of vectors with that of another vector not from the original list, but had information generated by KernelTrick.getQueryInfo(jsat.linear.Vec).
    If the cache input is null, then KernelTrick.eval(jsat.linear.Vec, jsat.linear.Vec) will be called directly.
    
    Specified by:
    
    eval in interface KernelTrick
    
    Parameters:
    
    a - the index of the vector in the cache
    
    b - the other vector
    
    qi - the query information about b
    
    vecs - the list of vectors used to build the cache
    
    cache - the cache associated with the given list of vectors
    
    Returns:
    
    the kernel product of the two vectors
  - eval
```
public abstract double eval(int a,
                            int b,
                            List<? extends Vec> trainingSet,
                            List<Double> cache)
```
    Description copied from interface: KernelTrick
    
    Produces the correct kernel evaluation given the training set and the cache generated by KernelTrick.getAccelerationCache(List). The training vectors should be in the same order.
    
    Specified by:
    
    eval in interface KernelTrick
    
    Parameters:
    
    a - the index of the first training vector
    
    b - the index of the second training vector
    
    trainingSet - the list of training set vectors
    
    cache - the double list of cache values generated by this kernel for the given training set
    
    Returns:
    
    the same kernel evaluation result as KernelTrick.eval(jsat.linear.Vec, jsat.linear.Vec)
  - evalSum
```
public double evalSum(List<? extends Vec> finalSet,
                      List<Double> cache,
                      double[] alpha,
                      Vec y,
                      int start,
                      int end)
```
    Description copied from interface: KernelTrick
    
    Performs an efficient summation of kernel products of the form
    ∑ α_i k(x_i, y)
    where x are the final set of vectors, and α the associated scalar multipliers
    
    Specified by:
    
    evalSum in interface KernelTrick
    
    Parameters:
    
    finalSet - the final set of vectors
    
    cache - the cache associated with the final set of vectors
    
    alpha - the coefficients associated with each vector
    
    y - the vector to perform the summed kernel products against
    
    start - the starting index (inclusive) to sum from
    
    end - the ending index (exclusive) to sum from
    
    Returns:
    
    the sum of the multiplied kernel products
  - evalSum
```
public double evalSum(List<? extends Vec> finalSet,
                      List<Double> cache,
                      double[] alpha,
                      Vec y,
                      List<Double> qi,
                      int start,
                      int end)
```
    Description copied from interface: KernelTrick
    
    Performs an efficient summation of kernel products of the form
    ∑ α_i k(x_i, y)
    where x are the final set of vectors, and α the associated scalar multipliers
    
    Specified by:
    
    evalSum in interface KernelTrick
    
    Parameters:
    
    finalSet - the final set of vectors
    
    cache - the cache associated with the final set of vectors
    
    alpha - the coefficients associated with each vector
    
    y - the vector to perform the summed kernel products against
    
    qi - the query information about y
    
    start - the starting index (inclusive) to sum from
    
    end - the ending index (exclusive) to sum from
    
    Returns:
    
    the sum of the multiplied kernel products
  - getParameters
```
public List<Parameter> getParameters()
```
    Description copied from interface: Parameterized
    
    Returns the list of parameters that can be altered for this learner.
    
    Specified by:
    
    getParameters in interface Parameterized
    
    Returns:
    
    the list of parameters that can be altered for this learner.
  - getParameter
```
public Parameter getParameter(String paramName)
```
    Description copied from interface: Parameterized
    
    Returns the parameter with the given name. Two different strings may map to a single Parameter object. An ASCII only string, and a Unicode style string.
    
    Specified by:
    
    getParameter in interface Parameterized
    
    Parameters:
    
    paramName - the name of the parameter to obtain
    
    Returns:
    
    the Parameter in question, or null if no such named Parameter exists.

Class BaseL2Kernel

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface jsat.distributions.kernels.KernelTrick

Constructor Detail

BaseL2Kernel

Method Detail

eval

clone

supportsAcceleration

getSqrdNorm

getSqrdNorm

getSqrdNorm

getAccelerationCache

getQueryInfo

addToCache

eval

eval

evalSum

evalSum

getParameters

getParameter