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Pearson Class Reference

Shrunk Pearson correlation for rating data More...

Inheritance diagram for Pearson:
SymmetricCorrelationMatrix IRatingCorrelationMatrix SymmetricSparseMatrix< T > ICorrelationMatrix ICorrelationMatrix SparseMatrix< T > IMatrix< T > IMatrix< T > IMatrix< T >

Public Member Functions

void AddEntity (int entity_id)
 Add an entity to the ICorrelationMatrix by growing it to the requested size.
float ComputeCorrelation (IRatings ratings, EntityType entity_type, int i, int j)
 Computes the correlation of two rating vectors
float ComputeCorrelation (IRatings ratings, EntityType entity_type, IList< Tuple< int, float >> entity_ratings, int j)
 Compute correlation between two entities for given ratings
void ComputeCorrelations (IRatings ratings, EntityType entity_type)
 Compute the correlations for a given entity type from a rating dataset
override IMatrix< T > CreateMatrix (int num_rows, int num_columns)
 Create a matrix with a given number of rows and columns
 Pearson (int num_entities, float shrinkage)
 Constructor. Create a Pearson correlation matrix
override void Resize (int size)
 Resize to the given size
void Resize (int num_rows, int num_cols)
 Grows or shrinks the matrix to the requested size, if necessary
 SparseMatrix (int num_rows, int num_cols)
 Create a sparse matrix with a given number of rows
 SymmetricSparseMatrix (int dimension)
 Create a symmetric sparse matrix with a given dimension
virtual IMatrix< T > Transpose ()
 Get the transpose of the matrix, i.e. a matrix where rows and columns are interchanged
void Write (StreamWriter writer)
 Write out the correlations to a StreamWriter

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, set]
override int NumberOfNonEmptyEntries [get]
int NumberOfRows [get]
int NumEntities [get, set]
 Number of entities the correlation is defined over
float Shrinkage [get, set]
 shrinkage parameter, if set to 0 we have the standard Pearson correlation without shrinkage
override T this[int x, int y] [get, set]
 Access the elements of the sparse matrix
Dictionary< int, T > this[int x] [get]
 Get a row of the matrix

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:

Constructor & Destructor Documentation

Pearson ( int  num_entities,
float  shrinkage 
)
inline

Constructor. Create a Pearson correlation matrix

Parameters
num_entitiesthe number of entities
shrinkageshrinkage 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_idthe 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
ratingsthe rating data
entity_typethe entity type, either USER or ITEM
ithe ID of the first entity
jthe 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
ratingsthe rating data
entity_typethe entity type, either USER or ITEM
entity_ratingsratings identifying the first entity
jthe 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
ratingsthe rating data
entity_typethe EntityType - either USER or ITEM

Implements IRatingCorrelationMatrix.

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

Create a matrix with a given number of rows and columns

Parameters
num_rowsthe number of rows
num_columnsthe number of columns
Returns
A matrix with num_rows rows and num_column columns

Reimplemented from SparseMatrix< T >.

Reimplemented in SkewSymmetricSparseMatrix.

override void Resize ( int  size)
inlineinherited

Resize to the given size

Parameters
sizethe size

Implements ICorrelationMatrix.

void Resize ( int  num_rows,
int  num_cols 
)
inlineinherited

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

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

Parameters
num_rowsthe number of rows
num_colsthe number of columns

Implements IMatrix< T >.

SparseMatrix ( int  num_rows,
int  num_cols 
)
inlineinherited

Create a sparse matrix with a given number of rows

Parameters
num_rowsthe number of rows
num_colsthe number of columns
SymmetricSparseMatrix ( int  dimension)
inlineinherited

Create a symmetric sparse matrix with a given dimension

Parameters
dimensionthe dimension (number of rows/columns)
virtual IMatrix<T> Transpose ( )
inlinevirtualinherited

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

Returns
the transpose of the matrix (copy)

Implements IMatrix< T >.

void Write ( StreamWriter  writer)
inlineinherited

Write out the correlations to a StreamWriter

Parameters
writerA StreamWriter

Implements ICorrelationMatrix.

Property Documentation

int NumEntities
getsetinherited

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
xthe row ID
ythe column ID
Dictionary<int, T> this[int x]
getinherited

Get a row of the matrix

Parameters
xthe row ID

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