Shrunk Pearson correlation for rating data
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Public Member Functions |
void | AddEntity (int entity_id) |
| Add an entity to the ICorrelationMatrix by growing it to the requested size.
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float | ComputeCorrelation (IRatings ratings, EntityType entity_type, int i, int j) |
| Computes the correlation of two rating vectors
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float | ComputeCorrelation (IRatings ratings, EntityType entity_type, IList< Tuple< int, float >> entity_ratings, int j) |
| Compute correlation between two entities for given ratings
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void | ComputeCorrelations (IRatings ratings, EntityType entity_type) |
| Compute the correlations for a given entity type from a rating dataset
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override IMatrix< T > | CreateMatrix (int num_rows, int num_columns) |
| Create a matrix with a given number of rows and columns
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| Pearson (int num_entities, float shrinkage) |
| Constructor. Create a Pearson correlation matrix
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override void | Resize (int size) |
| Resize to the given size
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void | Resize (int num_rows, int num_cols) |
| Grows or shrinks the matrix to the requested size, if necessary
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| SparseMatrix (int num_rows, int num_cols) |
| Create a sparse matrix with a given number of rows
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| SymmetricSparseMatrix (int dimension) |
| Create a symmetric sparse matrix with a given dimension
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virtual IMatrix< T > | Transpose () |
| Get the transpose of the matrix, i.e. a matrix where rows and columns are interchanged
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void | Write (StreamWriter writer) |
| Write out the correlations to a StreamWriter
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Properties |
override bool | IsSymmetric [get] |
| returns true if the matrix is symmetric, which is generally the case for similarity matrices
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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
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float | Shrinkage [get, set] |
| shrinkage parameter, if set to 0 we have the standard Pearson correlation without shrinkage
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override T | this[int x, int y] [get, set] |
| Access the elements of the sparse matrix
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Dictionary< int, T > | this[int x] [get] |
| Get a row of the matrix
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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 |
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int |
num_entities, |
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float |
shrinkage |
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) |
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inline |
Constructor. Create a Pearson correlation matrix
- Parameters
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num_entities | the number of entities |
shrinkage | shrinkage parameter |
Member Function Documentation
void AddEntity |
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int |
entity_id | ) |
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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
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entity_id | the numerical ID of the entity |
Implements ICorrelationMatrix.
Computes the correlation of two rating vectors
- Parameters
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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 |
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IRatings |
ratings, |
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EntityType |
entity_type, |
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IList< Tuple< int, float >> |
entity_ratings, |
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int |
j |
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) |
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inline |
Compute correlation between two entities for given ratings
- Parameters
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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.
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.
override IMatrix<T> CreateMatrix |
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int |
num_rows, |
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int |
num_columns |
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) |
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inlinevirtualinherited |
Create a matrix with a given number of rows and columns
- Parameters
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num_rows | the number of rows |
num_columns | the number of columns |
- Returns
- A matrix with num_rows rows and num_column columns
Reimplemented from SparseMatrix< T >.
Reimplemented in SkewSymmetricSparseMatrix.
override void Resize |
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int |
size | ) |
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inlineinherited |
void Resize |
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int |
num_rows, |
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int |
num_cols |
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) |
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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_rows | the number of rows |
num_cols | the number of columns |
Implements IMatrix< T >.
SparseMatrix |
( |
int |
num_rows, |
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int |
num_cols |
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) |
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inlineinherited |
Create a sparse matrix with a given number of rows
- Parameters
-
num_rows | the number of rows |
num_cols | the number of columns |
SymmetricSparseMatrix |
( |
int |
dimension | ) |
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inlineinherited |
Create a symmetric sparse matrix with a given dimension
- Parameters
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dimension | the dimension (number of rows/columns) |
virtual IMatrix<T> Transpose |
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| ) |
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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 |
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StreamWriter |
writer | ) |
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inlineinherited |
Property Documentation
Number of entities the correlation is defined over
shrinkage parameter, if set to 0 we have the standard Pearson correlation without shrinkage
override T this[int x, int y] |
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getsetinherited |
Access the elements of the sparse matrix
- Parameters
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x | the row ID |
y | the column ID |
Dictionary<int, T> this[int x] |
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getinherited |
Get a row of the matrix
- Parameters
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The documentation for this class was generated from the following file: