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Public Member Functions | Protected Attributes | Properties
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 >

List of all members.

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.

Protected Attributes

internal List< List< int > > index_list = new List<List<int>>()
 List of lists that stores the column indices of the entries.
internal List< List< T > > value_list = new List<List<T>>()
 List of lists that stores the values of the entries.

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]
 The row and column IDs of non-empty entries in the matrix.
int NumberOfColumns [get, set]
 The number of columns of the matrix.
override int NumberOfNonEmptyEntries [get]
 The number of non-empty entries in the matrix.
int NumberOfRows [get]
 The number of rows of the matrix.
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) [inline, inherited]

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 
) [inline, virtual, inherited]

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) [inline, inherited]

Resize to the given size.

Parameters:
sizethe size

Implements ICorrelationMatrix.

void Resize ( int  num_rows,
int  num_cols 
) [inline, 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_rowsthe number of rows
num_colsthe number of columns

Implements IMatrix< T >.

SparseMatrix ( int  num_rows,
int  num_cols 
) [inline, inherited]

Create a sparse matrix with a given number of rows.

Parameters:
num_rowsthe number of rows
num_colsthe number of columns
SymmetricSparseMatrix ( int  dimension) [inline, inherited]

Create a symmetric sparse matrix with a given dimension.

Parameters:
dimensionthe dimension (number of rows/columns)
virtual IMatrix<T> Transpose ( ) [inline, virtual, inherited]

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) [inline, inherited]

Write out the correlations to a StreamWriter.

Parameters:
writerA StreamWriter

Implements ICorrelationMatrix.


Member Data Documentation

internal List<List<int> > index_list = new List<List<int>>() [protected, inherited]

List of lists that stores the column indices of the entries.

internal List<List<T> > value_list = new List<List<T>>() [protected, inherited]

List of lists that stores the values of the entries.


Property Documentation

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

The row and column IDs of non-empty entries in the matrix.

The row and column IDs of non-empty entries in the matrix

Reimplemented from SparseMatrix< T >.

int NumberOfColumns [get, set, inherited]

The number of columns of the matrix.

The number of columns of the matrix

Implements IMatrix< T >.

override int NumberOfNonEmptyEntries [get, inherited]

The number of non-empty entries in the matrix.

The number of non-empty entries in the matrix

Reimplemented from SparseMatrix< T >.

int NumberOfRows [get, inherited]

The number of rows of the matrix.

The number of rows of the matrix

Implements IMatrix< T >.

int NumEntities [get, set, inherited]

Number of entities the correlation is defined over.

Implements ICorrelationMatrix.

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, inherited]

Access the elements of the sparse matrix.

Parameters:
xthe row ID
ythe column ID

Reimplemented from SparseMatrix< T >.

Reimplemented in SkewSymmetricSparseMatrix.

Dictionary<int, T> this[int x] [get, inherited]

Get a row of the matrix.

Parameters:
xthe row ID

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