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Pearson Class Reference

Shrunk Pearson correlation for rating data. More...

Inheritance diagram for Pearson:
RatingCorrelationMatrix CorrelationMatrix SymmetricSparseMatrix< T > SparseMatrix< T > IMatrix< T >

List of all members.

Public Member Functions

void AddEntity (int entity_id)
 Add an entity to the CorrelationMatrix by growing it to the requested size.
override void ComputeCorrelations (IRatings ratings, EntityType entity_type)
 Compute correlations for given ratings.
override IMatrix< T > CreateMatrix (int num_rows, int num_columns)
 Create a matrix with a given number of rows and columns.
int[] GetNearestNeighbors (int entity_id, uint k)
 Get the k nearest neighbors of a given entity.
IList< int > GetPositivelyCorrelatedEntities (int entity_id)
 Get all entities that are positively correlated to an entity, sorted by correlation.
void Grow (int num_rows, int num_cols)
 Grows the matrix to the requested size, if necessary.
 Pearson (int num_entities)
 Constructor. Create a Pearson correlation matrix.
 SparseMatrix (int num_rows, int num_cols)
 Create a sparse matrix with a given number of rows.
double SumUp (int entity_id, ICollection< int > entities)
 Sum up the correlations between a given entity and the entities in a collection.
 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.

Static Public Member Functions

static float ComputeCorrelation (IRatings ratings, EntityType entity_type, int i, int j, float shrinkage)
 Compute correlation between two entities for given ratings.
static float ComputeCorrelation (IRatings ratings, EntityType entity_type, IList< Pair< int, float >> entity_ratings, int j, float shrinkage)
 Compute correlation between two entities for given ratings.
static CorrelationMatrix Create (int num_entities)
 Creates a correlation matrix.
static CorrelationMatrix Create (IRatings ratings, EntityType entity_type, float shrinkage)
 Create a Pearson correlation matrix from given data.
static CorrelationMatrix ReadCorrelationMatrix (StreamReader reader)
 Creates a CorrelationMatrix from the lines of a StreamReader.

Protected Attributes

internal List< List< int > > index_list = new List<List<int>>()
 List of lists that stores the column indices of the entries.
int num_entities
 Number of entities, e.g. users or items.
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< Pair< 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.
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) [inline]

Constructor. Create a Pearson correlation matrix.

Parameters:
num_entitiesthe number of entities

Member Function Documentation

void AddEntity ( int  entity_id) [inline, inherited]

Add an entity to the CorrelationMatrix 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
static float ComputeCorrelation ( IRatings  ratings,
EntityType  entity_type,
int  i,
int  j,
float  shrinkage 
) [inline, static]

Compute correlation between two entities for given ratings.

Parameters:
ratingsthe rating data
entity_typethe entity type, either USER or ITEM
ithe ID of the first entity
jthe ID of the second entity
shrinkagethe shrinkage parameter, set to 0 for the standard Pearson correlation without shrinkage
static float ComputeCorrelation ( IRatings  ratings,
EntityType  entity_type,
IList< Pair< int, float >>  entity_ratings,
int  j,
float  shrinkage 
) [inline, static]

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
shrinkagethe shrinkage parameter, set to 0 for the standard Pearson correlation without shrinkage
override void ComputeCorrelations ( IRatings  ratings,
EntityType  entity_type 
) [inline, virtual]

Compute correlations for given ratings.

Parameters:
ratingsthe rating data
entity_typethe entity type, either USER or ITEM

Implements RatingCorrelationMatrix.

static CorrelationMatrix Create ( int  num_entities) [inline, static, inherited]

Creates a correlation matrix.

Gives out a useful warning if there is not enough memory

Parameters:
num_entitiesthe number of entities
Returns:
the correlation matrix
static CorrelationMatrix Create ( IRatings  ratings,
EntityType  entity_type,
float  shrinkage 
) [inline, static]

Create a Pearson correlation matrix from given data.

Parameters:
ratingsthe ratings data
entity_typethe entity type, either USER or ITEM
shrinkagethe shrinkage parameter, set to 0 for the standard Pearson correlation without shrinkage
Returns:
the complete Pearson correlation matrix
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.

int [] GetNearestNeighbors ( int  entity_id,
uint  k 
) [inline, inherited]

Get the k nearest neighbors of a given entity.

Parameters:
entity_idthe numerical ID of the entity
kthe neighborhood size
Returns:
an array containing the numerical IDs of the k nearest neighbors
IList<int> GetPositivelyCorrelatedEntities ( int  entity_id) [inline, inherited]

Get all entities that are positively correlated to an entity, sorted by correlation.

Parameters:
entity_idthe entity ID
Returns:
a sorted list of all entities that are positively correlated to entitiy_id
void Grow ( int  num_rows,
int  num_cols 
) [inline, inherited]

Grows the matrix to the requested size, if necessary.

The new entries are filled with zeros.

Parameters:
num_rowsthe minimum number of rows
num_colsthe minimum number of columns

Implements IMatrix< T >.

static CorrelationMatrix ReadCorrelationMatrix ( StreamReader  reader) [inline, static, inherited]

Creates a CorrelationMatrix from the lines of a StreamReader.

In the first line, we expect to be the number of entities. All the other lines have the format

		      EntityID1 EntityID2 Correlation
		    

where EntityID1 and EntityID2 are non-negative integers and Correlation is a floating point number.

Parameters:
readerthe StreamReader to read from
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
double SumUp ( int  entity_id,
ICollection< int >  entities 
) [inline, inherited]

Sum up the correlations between a given entity and the entities in a collection.

Parameters:
entity_idthe numerical ID of the entity
entitiesa collection containing the numerical IDs of the entities to compare to
Returns:
the correlation sum
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

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.

int num_entities [protected, inherited]

Number of entities, e.g. users or items.

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<Pair<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 >.

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: