Shrunk Pearson correlation for rating data More...

Inheritance diagram for Pearson:

Public Member Functions
void	AddEntity (int entity_id)
	Add an entity to the ICorrelationMatrix by growing it to the requested size. More...

float	ComputeCorrelation (IRatings ratings, EntityType entity_type, int i, int j)
	Computes the correlation of two rating vectors More...

float	ComputeCorrelation (IRatings ratings, EntityType entity_type, IList< Tuple< int, float >> entity_ratings, int j)
	Compute correlation between two entities for given ratings More...

void	ComputeCorrelations (IRatings ratings, EntityType entity_type)
	Compute the correlations for a given entity type from a rating dataset More...

IMatrix< T >	CreateMatrix (int num_rows, int num_columns)
	Create a matrix with a given number of rows and columns More...

IMatrix< T >	CreateMatrix (int num_rows, int num_columns)
	Create a matrix with a given number of rows and columns More...

override IMatrix< T >	CreateMatrix (int num_rows, int num_columns)
	Create a matrix with a given number of rows and columns More...

	Pearson (int num_entities, float shrinkage)
	Constructor. Create a Pearson correlation matrix More...

void	Resize (int num_rows, int num_cols)
	Grows or shrinks the matrix to the requested size, if necessary More...

void	Resize (int num_rows, int num_cols)
	Grows or shrinks the matrix to the requested size, if necessary More...

override void	Resize (int size)
	Resize to the given size More...

IMatrix< T >	Transpose ()
	Get the transpose of the matrix, i.e. a matrix where rows and columns are interchanged More...

IMatrix< T >	Transpose ()
	Get the transpose of the matrix, i.e. a matrix where rows and columns are interchanged More...

void	Write (StreamWriter writer)
	Write out the correlations to a StreamWriter More...

Protected Member Functions
virtual float	ComputeCorrelation (double i_sum, double j_sum, double ii_sum, double jj_sum, double ij_sum, int n)

virtual double	GetDenominator (double i_sum, double j_sum, double ii_sum, double jj_sum, int n)

virtual double	GetNumerator (double i_sum, double j_sum, double ij_sum, int n)

Properties
override bool	IsSymmetric `[get]`
	returns true if the matrix is symmetric, which is generally the case for similarity matrices

override IList< Tuple< int, int > >	NonEmptyEntryIDs `[get]`

int	NumberOfColumns `[get]`
	The number of columns of the matrix More...

int	NumberOfColumns `[get]`
	The number of columns of the matrix More...

override int	NumberOfNonEmptyEntries `[get]`

int	NumberOfRows `[get]`
	The number of rows of the matrix More...

int	NumberOfRows `[get]`
	The number of rows of the matrix More...

int	NumEntities `[get]`
	Number of entities the correlation is defined over More...

float	Shrinkage `[get, set]`
	shrinkage parameter, if set to 0 we have the standard Pearson correlation without shrinkage More...

override T	this[int x, int y] `[get, set]`
	Access the elements of the sparse matrix More...

T	this[int x, int y] `[get, set]`
	The value at (i,j) More...

T	this[int x, int y] `[get, set]`
	The value at (i,j) More...

Detailed Description

Shrunk Pearson correlation for rating data

The correlation values are shrunk towards zero, depending on the number of ratings the estimate is based on. Otherwise, we would give too much weight to similarities estimated from just a few examples.

http://en.wikipedia.org/wiki/Pearson_correlation

We apply shrinkage as in formula (5.16) of chapter 5 of the Recommender Systems Handbook. Note that the shrinkage formula has changed betweem the two publications. It is now based on the assumption that the true correlations are normally distributed; the shrunk estimate is the posterior mean of the empirical estimate.

Literature:

Yehuda Koren: Factor in the Neighbors: Scalable and Accurate Collaborative Filtering, Transactions on Knowledge Discovery from Data (TKDD), 2009. http://public.research.att.com/~volinsky/netflix/factorizedNeighborhood.pdf
Yehuda Koren, Robert Bell: Advances in Collaborative Filtering, Chapter 5 of the Recommender Systems Handbook, Springer, 2011. http://research.yahoo.net/files/korenBellChapterSpringer.pdf

Constructor & Destructor Documentation

Pearson	(	int	num_entities,
		float	shrinkage
	)

inline

Constructor. Create a Pearson correlation matrix

Parameters

num_entities	the number of entities
shrinkage	shrinkage parameter

Member Function Documentation

void AddEntity ( int entity_id )

inlineinherited

Add an entity to the ICorrelationMatrix by growing it to the requested size.

Note that you still have to correctly compute and set the entity's correlation values

Parameters

entity_id the numerical ID of the entity

Implements ICorrelationMatrix.

float ComputeCorrelation	(	IRatings	ratings,
		EntityType	entity_type,
		int	i,
		int	j
	)

inline

Computes the correlation of two rating vectors

Parameters

ratings	the rating data
entity_type	the entity type, either USER or ITEM
i	the ID of the first entity
j	the ID of the second entity

Returns: the correlation of the two vectors

Implements IRatingCorrelationMatrix.

float ComputeCorrelation	(	IRatings	ratings,
		EntityType	entity_type,
		IList< Tuple< int, float >>	entity_ratings,
		int	j
	)

inline

Compute correlation between two entities for given ratings

Parameters

ratings	the rating data
entity_type	the entity type, either USER or ITEM
entity_ratings	ratings identifying the first entity
j	the ID of second entity

Implements IRatingCorrelationMatrix.

void ComputeCorrelations	(	IRatings	ratings,
		EntityType	entity_type
	)

inline

Compute the correlations for a given entity type from a rating dataset

Parameters

ratings	the rating data
entity_type	the EntityType - either USER or ITEM

Implements IRatingCorrelationMatrix.

IMatrix<T> CreateMatrix	(	int	num_rows,
		int	num_columns
	)

inherited

Create a matrix with a given number of rows and columns

Parameters

num_rows	the number of rows
num_columns	the number of columns

Returns: A matrix with num_rows rows and num_column columns

IMatrix<T> CreateMatrix	(	int	num_rows,
		int	num_columns
	)

inherited

Create a matrix with a given number of rows and columns

Parameters

num_rows	the number of rows
num_columns	the number of columns

Returns: A matrix with num_rows rows and num_column columns

override IMatrix<T> CreateMatrix	(	int	num_rows,
		int	num_columns
	)

inlineinherited

Create a matrix with a given number of rows and columns

Parameters

num_rows	the number of rows
num_columns	the number of columns

Returns: A matrix with num_rows rows and num_column columns

void Resize	(	int	num_rows,
		int	num_cols
	)

inherited

Grows or shrinks the matrix to the requested size, if necessary

The new entries are filled with zeros. Obsolete entries are removed.

Parameters

num_rows	the number of rows
num_cols	the number of columns

void Resize	(	int	num_rows,
		int	num_cols
	)

inherited

Grows or shrinks the matrix to the requested size, if necessary

The new entries are filled with zeros. Obsolete entries are removed.

Parameters

num_rows	the number of rows
num_cols	the number of columns

override void Resize ( int size )

inlineinherited

Resize to the given size

Parameters

size the size

Implements ICorrelationMatrix.

IMatrix<T> Transpose ( )

inherited

Get the transpose of the matrix, i.e. a matrix where rows and columns are interchanged

Returns: the transpose of the matrix (copy)

IMatrix<T> Transpose ( )

inherited

Get the transpose of the matrix, i.e. a matrix where rows and columns are interchanged

Returns: the transpose of the matrix (copy)

void Write ( StreamWriter writer )

inlineinherited

Write out the correlations to a StreamWriter

Parameters

writer A StreamWriter

Implements ICorrelationMatrix.

Property Documentation

int NumberOfColumns

getinherited

The number of columns of the matrix

int NumberOfColumns

getinherited

The number of columns of the matrix

int NumberOfRows

getinherited

The number of rows of the matrix

int NumberOfRows

getinherited

The number of rows of the matrix

int NumEntities

getinherited

Number of entities the correlation is defined over

float Shrinkage

getset

shrinkage parameter, if set to 0 we have the standard Pearson correlation without shrinkage

override T this[int x, int y]

getsetinherited

Access the elements of the sparse matrix

Parameters

x	the row ID
y	the column ID

T this[int x, int y]

getsetinherited

The value at (i,j)

Parameters

x	the row ID
y	the column ID

T this[int x, int y]

getsetinherited

The value at (i,j)

Parameters

x	the row ID
y	the column ID

The documentation for this class was generated from the following file:

Pearson.cs

Public Member Functions

Protected Member Functions

Properties

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Property Documentation