Pearson Class Reference

Shrunk Pearson correlation for rating data. More...

Inheritance diagram for Pearson:
RatingCorrelationMatrix CorrelationMatrix

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.
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.
 Pearson (int num_entities)
 Constructor. Create a Pearson correlation matrix.
double SumUp (int entity_id, ICollection< int > entities)
 Sum up the correlations between a given entity and the entities in a collection.
void Write (StreamWriter writer)
 Write out the correlations to a StreamWriter.

Static Public Member Functions

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

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

Properties

override bool IsSymmetric [get]
 returns true if the matrix is symmetric, which is generally the case for similarity matrices
float Shrinkage [get, set]
 shrinkage parameter, if set to 0 we have the standard Pearson correlation without shrinkage

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_entities the 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_id the numerical ID of the entity
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:
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
shrinkage the shrinkage parameter, set to 0 for the standard Pearson correlation without shrinkage
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:
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
shrinkage the 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:
ratings the rating data
entity_type the 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_entities the 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:
ratings the ratings data
entity_type the entity type, either USER or ITEM
shrinkage the shrinkage parameter, set to 0 for the standard Pearson correlation without shrinkage
Returns:
the complete Pearson correlation matrix
int [] GetNearestNeighbors ( int  entity_id,
uint  k 
) [inline, inherited]

Get the k nearest neighbors of a given entity.

Parameters:
entity_id the numerical ID of the entity
k the 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_id the entity ID
Returns:
a sorted list of all entities that are positively correlated to entitiy_id
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:
reader the StreamReader to read from
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_id the numerical ID of the entity
entities a collection containing the numerical IDs of the entities to compare to
Returns:
the correlation sum
void Write ( StreamWriter  writer  )  [inline, inherited]

Write out the correlations to a StreamWriter.

Parameters:
writer A StreamWriter

Member Data Documentation

int num_entities [protected, inherited]

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


Property Documentation

float Shrinkage [get, set]

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


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