smile.neighbor

Class LSH<E>

java.lang.Object

smile.neighbor.LSH<E>

Type Parameters:

E - the type of data objects in the hash table.

All Implemented Interfaces:

java.io.Serializable, KNNSearch<double[],E>, NearestNeighborSearch<double[],E>, RNNSearch<double[],E>

Direct Known Subclasses:

MPLSH, MutableLSH

public class LSH<E>
extends java.lang.Object
implements NearestNeighborSearch<double[],E>, KNNSearch<double[],E>, RNNSearch<double[],E>, java.io.Serializable

Locality-Sensitive Hashing. LSH is an efficient algorithm for approximate nearest neighbor search in high dimensional spaces by performing probabilistic dimension reduction of data. The basic idea is to hash the input items so that similar items are mapped to the same buckets with high probability (the number of buckets being much smaller than the universe of possible input items).

By default, the query object (reference equality) is excluded from the neighborhood.

References

1. Alexandr Andoni and Piotr Indyk. Near-Optimal Hashing Algorithms for Near Neighbor Problem in High Dimensions. FOCS, 2006.
2. Alexandr Andoni, Mayur Datar, Nicole Immorlica, Piotr Indyk, and Vahab Mirrokni. Locality-Sensitive Hashing Scheme Based on p-Stable Distributions. 2004.

See Also:

MPLSH, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected java.util.ArrayList<E>	data The data objects.
protected int	H The size of hash table.
protected java.util.List<Hash>	hash Hash functions.
protected int	k The number of random projections per hash value.
protected java.util.ArrayList<double[]>	keys The keys of data objects.
protected double	w The width of projection.

Constructor Summary

Constructors

Constructor and Description
LSH(double[][] keys, E[] data, double w) Constructor.
LSH(double[][] keys, E[] data, double w, int H) Constructor.
LSH(int d, int L, int k, double w) Constructor.
LSH(int d, int L, int k, double w, int H) Constructor.

Method Summary

Modifier and Type	Method and Description
protected void	initHashTable(int d, int L, int k, double w, int H) Initialize the hash tables.
Neighbor<double[],E>[]	knn(double[] q, int k) Search the k nearest neighbors to the query.
Neighbor<double[],E>	nearest(double[] q) Search the nearest neighbor to the given sample.
void	put(double[] key, E value) Insert an item into the hash table.
void	range(double[] q, double radius, java.util.List<Neighbor<double[],E>> neighbors) Search the neighbors in the given radius of query object, i.e.
java.lang.String	toString()

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Field Detail

keys

protected java.util.ArrayList<double[]> keys

The keys of data objects.

data

protected java.util.ArrayList<E> data

The data objects.

hash

protected java.util.List<Hash> hash

Hash functions.

H

protected int H

The size of hash table.

k

protected int k

The number of random projections per hash value.

w

protected double w

The width of projection. The hash function is defined as floor((a * x + b) / w). The value of w determines the bucket interval.

Constructor Detail

LSH

public LSH(double[][] keys,
           E[] data,
           double w)

Constructor.

Parameters:

keys - the keys of data objects.

data - the data objects.

w - the width of random projections. It should be sufficiently away from 0. But we should not choose an w value that is too large, which will increase the query time.

LSH

public LSH(double[][] keys,
           E[] data,
           double w,
           int H)

Constructor.

Parameters:

keys - the keys of data objects.

data - the data objects.

w - the width of random projections. It should be sufficiently away from 0. But we should not choose an w value that is too large, which will increase the query time.

H - the size of universal hash tables.

LSH

public LSH(int d,
           int L,
           int k,
           double w)

Constructor.

Parameters:

d - the dimensionality of data.

L - the number of hash tables.

k - the number of random projection hash functions, which is usually set to log(N) where N is the dataset size.

w - the width of random projections. It should be sufficiently away from 0. But we should not choose an w value that is too large, which will increase the query time.

LSH

public LSH(int d,
           int L,
           int k,
           double w,
           int H)

Constructor.

Parameters:

d - the dimensionality of data.

L - the number of hash tables.

k - the number of random projection hash functions, which is usually set to log(N) where N is the dataset size.

w - the width of random projections. It should be sufficiently away from 0. But we should not choose an w value that is too large, which will increase the query time.

H - the size of universal hash tables.

Method Detail

initHashTable

protected void initHashTable(int d,
                             int L,
                             int k,
                             double w,
                             int H)

Initialize the hash tables.

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

put

public void put(double[] key,
                E value)

Insert an item into the hash table.

nearest

public Neighbor<double[],E> nearest(double[] q)

Description copied from interface: NearestNeighborSearch

Search the nearest neighbor to the given sample.

Specified by:

nearest in interface NearestNeighborSearch<double[],E>

Parameters:

q - the query key.

Returns:

the nearest neighbor

knn

public Neighbor<double[],E>[] knn(double[] q,
                                  int k)

Description copied from interface: KNNSearch

Search the k nearest neighbors to the query.

Specified by:

knn in interface KNNSearch<double[],E>

Parameters:

q - the query key.

k - the number of nearest neighbors to search for.

range

public void range(double[] q,
                  double radius,
                  java.util.List<Neighbor<double[],E>> neighbors)

Description copied from interface: RNNSearch

Search the neighbors in the given radius of query object, i.e. d(q, v) ≤ radius.

Specified by:

range in interface RNNSearch<double[],E>

Parameters:

q - the query key.

radius - the radius of search range from target.

neighbors - the list to store found neighbors in the given range on output.