smile.neighbor

Class MPLSH<E>

java.lang.Object

smile.neighbor.LSH<E>

smile.neighbor.MPLSH<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>

public class MPLSH<E>
extends LSH<E>

Multi-Probe 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). A drawback of LSH is the requirement for a large number of hash tables in order to achieve good search quality. Multi-probe LSH is designed to overcome this drawback. Multi-probe LSH intelligently probes multiple buckets that are likely to contain query results in a hash table.

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

References

1. Qin Lv, William Josephson, Zhe Wang, Moses Charikar, and Kai Li. Multi-probe LSH: efficient indexing for high-dimensional similarity search. VLDB, 2007.
2. Alexis Joly and Olivier Buisson. A posteriori multi-probe locality sensitive hashing. ACM international conference on Multimedia, 2008.

See Also:

LSH, Serialized Form

Field Summary

Fields inherited from class smile.neighbor.LSH

data, H, hash, k, keys, w

Constructor Summary

Constructors

Constructor and Description
MPLSH(int d, int L, int k, double w) Constructor.
MPLSH(int d, int L, int k, double w, int H) Constructor.

Method Summary

Modifier and Type	Method and Description
void	fit(RNNSearch<double[],double[]> range, double[][] samples, double radius) Fits the posteriori multiple probe algorithm.
void	fit(RNNSearch<double[],double[]> range, double[][] samples, double radius, int Nz) Fits the posteriori multiple probe algorithm.
void	fit(RNNSearch<double[],double[]> range, double[][] samples, double radius, int Nz, double sigma) Train the posteriori multiple probe algorithm.
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>[]	knn(double[] q, int k, double recall, int T) Returns the approximate k-nearest neighbors.
Neighbor<double[],E>	nearest(double[] q) Search the nearest neighbor to the given sample.
Neighbor<double[],E>	nearest(double[] q, double recall, int T) Returns the approximate nearest neighbor.
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.
void	range(double[] q, double radius, java.util.List<Neighbor<double[],E>> neighbors, double recall, int T) Search the neighbors in the given radius of query object, i.e.
java.lang.String	toString()

Methods inherited from class smile.neighbor.LSH

put

Methods inherited from class java.lang.Object

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

Constructor Detail

MPLSH

public MPLSH(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.

MPLSH

public MPLSH(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 r value that is too large, which will increase the query time.

H - the number of buckets of hash tables.

Method Detail

initHashTable

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

Description copied from class: LSH

Initialize the hash tables.

Overrides:

initHashTable in class LSH<E>

toString

public java.lang.String toString()

Overrides:

toString in class LSH<E>

fit

public void fit(RNNSearch<double[],double[]> range,
                double[][] samples,
                double radius)

Fits the posteriori multiple probe algorithm.

Parameters:

range - the neighborhood search data structure.

radius - the radius for range search.

samples - the training samples.

fit

public void fit(RNNSearch<double[],double[]> range,
                double[][] samples,
                double radius,
                int Nz)

Fits the posteriori multiple probe algorithm.

Parameters:

range - the neighborhood search data structure.

radius - the radius for range search.

Nz - the number of quantized values.

fit

public void fit(RNNSearch<double[],double[]> range,
                double[][] samples,
                double radius,
                int Nz,
                double sigma)

Train the posteriori multiple probe algorithm.

Parameters:

range - the neighborhood search data structure.

radius - the radius for range search.

Nz - the number of quantized values.

sigma - the Parzen window width.

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>

Overrides:

nearest in class LSH<E>

Parameters:

q - the query key.

Returns:

the nearest neighbor

nearest

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

Returns the approximate nearest neighbor. A posteriori multiple probe model has to be trained already.

Parameters:

q - the query object.

recall - the expected recall rate.

T - the maximum number of probes.

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>

Overrides:

knn in class LSH<E>

Parameters:

q - the query key.

k - the number of nearest neighbors to search for.

knn

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

Returns the approximate k-nearest neighbors. A posteriori multiple probe model has to be trained already.

Parameters:

q - the query object.

k - the number of nearest neighbors to search for.

recall - the expected recall rate.

T - the maximum number of probes.

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>

Overrides:

range in class LSH<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.

range

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

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

Parameters:

q - the query object.

radius - the radius of search range.

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

recall - the expected recall rate.

T - the maximum number of probes.