///
public float ComputeCorrelation(IRatings ratings, EntityType entity_type, IList <Tuple <int, float> > entity_ratings, int j)
{
IList <int> indexes2 = (entity_type == EntityType.USER) ? ratings.ByUser[j] : ratings.ByItem[j];
// get common ratings for the two entities
var e1 = new HashSet <int>(from pair in entity_ratings select pair.Item1);
var e2 = (entity_type == EntityType.USER) ? ratings.GetItems(indexes2) : ratings.GetUsers(indexes2);
e1.IntersectWith(e2);
var ratings1 = new Dictionary <int, float>();
for (int index = 0; index < entity_ratings.Count; index++)
{
if (e1.Contains(entity_ratings[index].Item1))
{
ratings1.Add(entity_ratings[index].Item1, entity_ratings[index].Item2);
}
}
int n = e1.Count;
if (n < 2)
{
return(0);
}
// single-pass variant
double i_sum = 0;
double j_sum = 0;
double ij_sum = 0;
double ii_sum = 0;
double jj_sum = 0;
foreach (int other_entity_id in e1)
{
// get ratings
float r1 = ratings1[other_entity_id];
float r2 = 0;
if (entity_type == EntityType.USER)
{
r2 = ratings.Get(j, other_entity_id, indexes2);
}
else
{
r2 = ratings.Get(other_entity_id, j, indexes2);
}
// update sums
i_sum += r1;
j_sum += r2;
ij_sum += r1 * r2;
ii_sum += r1 * r1;
jj_sum += r2 * r2;
}
return(ComputeCorrelation(i_sum, j_sum, ii_sum, jj_sum, ij_sum, n));
}
///
public float ComputeCorrelation(IRatings ratings, EntityType entity_type, int i, int j)
{
if (i == j)
{
return(1);
}
IList <int> indexes1 = (entity_type == EntityType.USER) ? ratings.ByUser[i] : ratings.ByItem[i];
IList <int> indexes2 = (entity_type == EntityType.USER) ? ratings.ByUser[j] : ratings.ByItem[j];
// get common ratings for the two entities
var e1 = (entity_type == EntityType.USER) ? ratings.GetItems(indexes1) : ratings.GetUsers(indexes1);
var e2 = (entity_type == EntityType.USER) ? ratings.GetItems(indexes2) : ratings.GetUsers(indexes2);
e1.IntersectWith(e2);
int n = e1.Count;
if (n < 2)
{
return(0);
}
// single-pass variant
double i_sum = 0;
double j_sum = 0;
double ij_sum = 0;
double ii_sum = 0;
double jj_sum = 0;
foreach (int other_entity_id in e1)
{
// get ratings
float r1 = 0;
float r2 = 0;
if (entity_type == EntityType.USER)
{
r1 = ratings.Get(i, other_entity_id, indexes1);
r2 = ratings.Get(j, other_entity_id, indexes2);
}
else
{
r1 = ratings.Get(other_entity_id, i, indexes1);
r2 = ratings.Get(other_entity_id, j, indexes2);
}
// update sums
i_sum += r1;
j_sum += r2;
ij_sum += r1 * r2;
ii_sum += r1 * r1;
jj_sum += r2 * r2;
}
return(ComputeCorrelation(i_sum, j_sum, ii_sum, jj_sum, ij_sum, n));
}
/// <summary>Performs user-wise fold-in evaluation, but instead of folding in perform incremental training with the new data</summary>
/// <remarks>
/// </remarks>
/// <returns>the evaluation results</returns>
/// <param name='recommender'>a rating predictor capable of performing a user fold-in</param>
/// <param name='update_data'>the rating data used to represent the users</param>
/// <param name='eval_data'>the evaluation data</param>
static public RatingPredictionEvaluationResults EvaluateFoldInIncrementalTraining(this IncrementalRatingPredictor recommender, IRatings update_data, IRatings eval_data)
{
double rmse = 0;
double mae = 0;
double cbd = 0;
int rating_count = 0;
foreach (int user_id in update_data.AllUsers)
{
if (eval_data.AllUsers.Contains(user_id))
{
var local_recommender = (IncrementalRatingPredictor)recommender.Clone();
// add ratings and perform incremental training
var user_ratings = new RatingsProxy(update_data, update_data.ByUser[user_id]);
local_recommender.AddRatings(user_ratings);
var items_to_rate = (from index in eval_data.ByUser[user_id] select eval_data.Items[index]).ToArray();
var predicted_ratings = recommender.Recommend(user_id, candidate_items: items_to_rate);
foreach (var pred in predicted_ratings)
{
float prediction = pred.Item2;
float actual_rating = eval_data.Get(user_id, pred.Item1, eval_data.ByUser[user_id]);
float error = prediction - actual_rating;
rmse += error * error;
mae += Math.Abs(error);
cbd += Eval.Ratings.ComputeCBD(actual_rating, prediction, recommender.MinRating, recommender.MaxRating);
rating_count++;
}
// remove ratings again
local_recommender.RemoveRatings(user_ratings);
Console.Error.Write(".");
}
}
mae = mae / rating_count;
rmse = Math.Sqrt(rmse / rating_count);
cbd = cbd / rating_count;
var result = new RatingPredictionEvaluationResults();
result["RMSE"] = (float)rmse;
result["MAE"] = (float)mae;
result["NMAE"] = (float)mae / (recommender.MaxRating - recommender.MinRating);
result["CBD"] = (float)cbd;
return(result);
}
/// <summary>Performs user-wise fold-in evaluation</summary>
/// <returns>the evaluation results</returns>
/// <param name='recommender'>a rating predictor capable of performing a user fold-in</param>
/// <param name='update_data'>the rating data used to represent the users</param>
/// <param name='eval_data'>the evaluation data</param>
static public RatingPredictionEvaluationResults EvaluateFoldIn(this IFoldInRatingPredictor recommender, IRatings update_data, IRatings eval_data)
{
double rmse = 0;
double mae = 0;
double cbd = 0;
int rating_count = 0;
foreach (int user_id in update_data.AllUsers)
{
if (eval_data.AllUsers.Contains(user_id))
{
var known_ratings = (
from index in update_data.ByUser[user_id]
select Tuple.Create(update_data.Items[index], update_data[index])
).ToArray();
var items_to_rate = (from index in eval_data.ByUser[user_id] select eval_data.Items[index]).ToArray();
var predicted_ratings = recommender.ScoreItems(known_ratings, items_to_rate);
foreach (var pred in predicted_ratings)
{
float prediction = pred.Item2;
float actual_rating = eval_data.Get(user_id, pred.Item1, eval_data.ByUser[user_id]);
float error = prediction - actual_rating;
rmse += error * error;
mae += Math.Abs(error);
cbd += Eval.Ratings.ComputeCBD(actual_rating, prediction, recommender.MinRating, recommender.MaxRating);
rating_count++;
}
Console.Error.Write(".");
}
}
mae = mae / rating_count;
rmse = Math.Sqrt(rmse / rating_count);
cbd = cbd / rating_count;
var result = new RatingPredictionEvaluationResults();
result["RMSE"] = (float)rmse;
result["MAE"] = (float)mae;
result["NMAE"] = (float)mae / (recommender.MaxRating - recommender.MinRating);
result["CBD"] = (float)cbd;
return(result);
}
/// <summary>Performs user-wise fold-in evaluation</summary>
/// <returns>the evaluation results</returns>
/// <param name='recommender'>a rating predictor capable of performing a user fold-in</param>
/// <param name='update_data'>the rating data used to represent the users</param>
/// <param name='eval_data'>the evaluation data</param>
static public RatingPredictionEvaluationResults EvaluateFoldIn(this IFoldInRatingPredictor recommender, IRatings update_data, IRatings eval_data)
{
double rmse = 0;
double mae = 0;
double cbd = 0;
int rating_count = 0;
foreach (int user_id in update_data.AllUsers)
if (eval_data.AllUsers.Contains(user_id))
{
var known_ratings = (
from index in update_data.ByUser[user_id]
select Tuple.Create(update_data.Items[index], update_data[index])
).ToArray();
var items_to_rate = (from index in eval_data.ByUser[user_id] select eval_data.Items[index]).ToArray();
var predicted_ratings = recommender.ScoreItems(known_ratings, items_to_rate);
foreach (var pred in predicted_ratings)
{
float prediction = pred.Item2;
float actual_rating = eval_data.Get(user_id, pred.Item1, eval_data.ByUser[user_id]);
float error = prediction - actual_rating;
rmse += error * error;
mae += Math.Abs(error);
cbd += Eval.Ratings.ComputeCBD(actual_rating, prediction, recommender.MinRating, recommender.MaxRating);
rating_count++;
}
Console.Error.Write(".");
}
mae = mae / rating_count;
rmse = Math.Sqrt(rmse / rating_count);
cbd = cbd / rating_count;
var result = new RatingPredictionEvaluationResults();
result["RMSE"] = (float) rmse;
result["MAE"] = (float) mae;
result["NMAE"] = (float) mae / (recommender.MaxRating - recommender.MinRating);
result["CBD"] = (float) cbd;
return result;
}
/// <summary>Compute correlations between two entities for given ratings</summary>
/// <param name="ratings">the rating data</param>
/// <param name="entity_type">the entity type, either USER or ITEM</param>
/// <param name="i">the ID of first entity</param>
/// <param name="j">the ID of second entity</param>
/// <param name="shrinkage">the shrinkage parameter</param>
public static float ComputeCorrelation(IRatings ratings, EntityType entity_type, int i, int j, float shrinkage)
{
if (i == j)
{
return(1);
}
IList <int> ratings1 = (entity_type == EntityType.USER) ? ratings.ByUser[i] : ratings.ByItem[i];
IList <int> ratings2 = (entity_type == EntityType.USER) ? ratings.ByUser[j] : ratings.ByItem[j];
// get common ratings for the two entities
HashSet <int> e1 = (entity_type == EntityType.USER) ? ratings.GetItems(ratings1) : ratings.GetUsers(ratings1);
HashSet <int> e2 = (entity_type == EntityType.USER) ? ratings.GetItems(ratings2) : ratings.GetUsers(ratings2);
e1.IntersectWith(e2);
int n = e1.Count;
if (n < 2)
{
return(0);
}
List <Ratings> ratings_by_other_entity = (entity_type == EntityType.USER) ? ratings.ByItem : ratings.ByUser;
double sum_ij = 0;
double sum_ii = 0;
double sum_jj = 0;
foreach (int other_entity_id in e1)
{
double average_rating = ratings_by_other_entity[other_entity_id].Average;
// get ratings
double r1 = 0;
double r2 = 0;
if (entity_type == EntityType.USER)
{
r1 = ratings.Get(i, other_entity_id, ratings1);
r2 = ratings.Get(j, other_entity_id, ratings2);
}
else
{
r1 = ratings.Get(other_entity_id, i, ratings1);
r2 = ratings.Get(other_entity_id, j, ratings2);
}
double dev_i = r1 - average_rating;
double dev_j = r2 - average_rating;
// update sums
sum_ij += dev_i * dev_j;
sum_ii += dev_i * dev_i;
sum_jj += dev_j * dev_j;
}
double denominator = Math.Sqrt(sum_ii * sum_jj);
if (denominator == 0)
{
return(0);
}
double adjusted_cosine = sum_ij / denominator;
return((float)adjusted_cosine * (n / (n + shrinkage)));
}
///
public float ComputeCorrelation(IRatings ratings, EntityType entity_type, int i, int j)
{
if (i == j)
return 1;
IList<int> indexes1 = (entity_type == EntityType.USER) ? ratings.ByUser[i] : ratings.ByItem[i];
IList<int> indexes2 = (entity_type == EntityType.USER) ? ratings.ByUser[j] : ratings.ByItem[j];
// get common ratings for the two entities
var e1 = (entity_type == EntityType.USER) ? ratings.GetItems(indexes1) : ratings.GetUsers(indexes1);
var e2 = (entity_type == EntityType.USER) ? ratings.GetItems(indexes2) : ratings.GetUsers(indexes2);
e1.IntersectWith(e2);
int n = e1.Count;
if (n < 2)
return 0;
// single-pass variant
double i_sum = 0;
double j_sum = 0;
double ij_sum = 0;
double ii_sum = 0;
double jj_sum = 0;
foreach (int other_entity_id in e1)
{
// get ratings
float r1 = 0;
float r2 = 0;
if (entity_type == EntityType.USER)
{
r1 = ratings.Get(i, other_entity_id, indexes1);
r2 = ratings.Get(j, other_entity_id, indexes2);
}
else
{
r1 = ratings.Get(other_entity_id, i, indexes1);
r2 = ratings.Get(other_entity_id, j, indexes2);
}
// update sums
i_sum += r1;
j_sum += r2;
ij_sum += r1 * r2;
ii_sum += r1 * r1;
jj_sum += r2 * r2;
}
return ComputeCorrelation (i_sum, j_sum, ii_sum, jj_sum, ij_sum, n);
}
///
public float ComputeCorrelation(IRatings ratings, EntityType entity_type, IList<Tuple<int, float>> entity_ratings, int j)
{
IList<int> indexes2 = (entity_type == EntityType.USER) ? ratings.ByUser[j] : ratings.ByItem[j];
// get common ratings for the two entities
var e1 = new HashSet<int>(from pair in entity_ratings select pair.Item1);
var e2 = (entity_type == EntityType.USER) ? ratings.GetItems(indexes2) : ratings.GetUsers(indexes2);
e1.IntersectWith(e2);
var ratings1 = new Dictionary<int, float>();
for (int index = 0; index < entity_ratings.Count; index++)
if (e1.Contains(entity_ratings[index].Item1))
ratings1.Add(entity_ratings[index].Item1, entity_ratings[index].Item2);
int n = e1.Count;
if (n < 2)
return 0;
// single-pass variant
double i_sum = 0;
double j_sum = 0;
double ij_sum = 0;
double ii_sum = 0;
double jj_sum = 0;
foreach (int other_entity_id in e1)
{
// get ratings
float r1 = ratings1[other_entity_id];
float r2 = 0;
if (entity_type == EntityType.USER)
r2 = ratings.Get(j, other_entity_id, indexes2);
else
r2 = ratings.Get(other_entity_id, j, indexes2);
// update sums
i_sum += r1;
j_sum += r2;
ij_sum += r1 * r2;
ii_sum += r1 * r1;
jj_sum += r2 * r2;
}
return ComputeCorrelation (i_sum, j_sum, ii_sum, jj_sum, ij_sum, n);
}
/// <summary>Performs user-wise fold-in evaluation, but instead of folding in perform incremental training with the new data</summary>
/// <remarks>
/// </remarks>
/// <returns>the evaluation results</returns>
/// <param name='recommender'>a rating predictor capable of performing a user fold-in</param>
/// <param name='update_data'>the rating data used to represent the users</param>
/// <param name='eval_data'>the evaluation data</param>
static public RatingPredictionEvaluationResults EvaluateFoldInIncrementalTraining(this IncrementalRatingPredictor recommender, IRatings update_data, IRatings eval_data)
{
double rmse = 0;
double mae = 0;
double cbd = 0;
int rating_count = 0;
foreach (int user_id in update_data.AllUsers)
if (eval_data.AllUsers.Contains(user_id))
{
var local_recommender = (IncrementalRatingPredictor) recommender.Clone();
// add ratings and perform incremental training
var user_ratings = new RatingsProxy(update_data, update_data.ByUser[user_id]);
local_recommender.AddRatings(user_ratings);
var items_to_rate = (from index in eval_data.ByUser[user_id] select eval_data.Items[index]).ToArray();
var predicted_ratings = recommender.Recommend(user_id, candidate_items:items_to_rate);
foreach (var pred in predicted_ratings)
{
float prediction = pred.Item2;
float actual_rating = eval_data.Get(user_id, pred.Item1, eval_data.ByUser[user_id]);
float error = prediction - actual_rating;
rmse += error * error;
mae += Math.Abs(error);
cbd += Eval.Ratings.ComputeCBD(actual_rating, prediction, recommender.MinRating, recommender.MaxRating);
rating_count++;
}
// remove ratings again
local_recommender.RemoveRatings(user_ratings);
Console.Error.Write(".");
}
mae = mae / rating_count;
rmse = Math.Sqrt(rmse / rating_count);
cbd = cbd / rating_count;
var result = new RatingPredictionEvaluationResults();
result["RMSE"] = (float) rmse;
result["MAE"] = (float) mae;
result["NMAE"] = (float) mae / (recommender.MaxRating - recommender.MinRating);
result["CBD"] = (float) cbd;
return result;
}
/// <summary>Compute correlations between two entities for given ratings</summary>
/// <param name="ratings">the rating data</param>
/// <param name="entity_type">the entity type, either USER or ITEM</param>
/// <param name="i">the ID of first entity</param>
/// <param name="j">the ID of second entity</param>
/// <param name="shrinkage">the shrinkage parameter</param>
public static float ComputeCorrelation(IRatings ratings, EntityType entity_type, int i, int j, float shrinkage)
{
if (i == j)
return 1;
IList<int> ratings1 = (entity_type == EntityType.USER) ? ratings.ByUser[i] : ratings.ByItem[i];
IList<int> ratings2 = (entity_type == EntityType.USER) ? ratings.ByUser[j] : ratings.ByItem[j];
// get common ratings for the two entities
HashSet<int> e1 = (entity_type == EntityType.USER) ? ratings.GetItems(ratings1) : ratings.GetUsers(ratings1);
HashSet<int> e2 = (entity_type == EntityType.USER) ? ratings.GetItems(ratings2) : ratings.GetUsers(ratings2);
e1.IntersectWith(e2);
int n = e1.Count;
if (n < 2)
return 0;
List<Ratings> ratings_by_other_entity = (entity_type == EntityType.USER) ? ratings.ByItem : ratings.ByUser;
double sum_ij = 0;
double sum_ii = 0;
double sum_jj = 0;
foreach (int other_entity_id in e1)
{
double average_rating = ratings_by_other_entity[other_entity_id].Average;
// get ratings
double r1 = 0;
double r2 = 0;
if (entity_type == EntityType.USER)
{
r1 = ratings.Get(i, other_entity_id, ratings1);
r2 = ratings.Get(j, other_entity_id, ratings2);
}
else
{
r1 = ratings.Get(other_entity_id, i, ratings1);
r2 = ratings.Get(other_entity_id, j, ratings2);
}
double dev_i = r1 - average_rating;
double dev_j = r2 - average_rating;
// update sums
sum_ij += dev_i * dev_j;
sum_ii += dev_i * dev_i;
sum_jj += dev_j * dev_j;
}
double denominator = Math.Sqrt( sum_ii * sum_jj );
if (denominator == 0)
return 0;
double adjusted_cosine = sum_ij / denominator;
return (float) adjusted_cosine * (n / (n + shrinkage));
}
/// <summary>Compute correlations between two entities for given ratings</summary>
/// <param name="ratings">the rating data</param>
/// <param name="entity_type">the entity type, either USER or ITEM</param>
/// <param name="i">the ID of first entity</param>
/// <param name="j">the ID of second entity</param>
/// <param name="shrinkage">the shrinkage parameter</param>
public static float ComputeCorrelation(IRatings ratings, EntityType entity_type, int i, int j, float shrinkage)
{
if (i == j)
{
return(1);
}
IList <int> ratings1 = (entity_type == EntityType.USER) ? ratings.ByUser[i] : ratings.ByItem[i];
IList <int> ratings2 = (entity_type == EntityType.USER) ? ratings.ByUser[j] : ratings.ByItem[j];
// get common ratings for the two entities
HashSet <int> e1 = (entity_type == EntityType.USER) ? ratings.GetItems(ratings1) : ratings.GetUsers(ratings1);
HashSet <int> e2 = (entity_type == EntityType.USER) ? ratings.GetItems(ratings2) : ratings.GetUsers(ratings2);
e1.IntersectWith(e2);
int n = e1.Count;
if (n < 2)
{
return(0);
}
// single-pass variant
double i_sum = 0;
double j_sum = 0;
double ij_sum = 0;
double ii_sum = 0;
double jj_sum = 0;
foreach (int other_entity_id in e1)
{
// get ratings
double r1 = 0;
double r2 = 0;
if (entity_type == EntityType.USER)
{
r1 = ratings.Get(i, other_entity_id, ratings1);
r2 = ratings.Get(j, other_entity_id, ratings2);
}
else
{
r1 = ratings.Get(other_entity_id, i, ratings1);
r2 = ratings.Get(other_entity_id, j, ratings2);
}
// update sums
i_sum += r1;
j_sum += r2;
ij_sum += r1 * r2;
ii_sum += r1 * r1;
jj_sum += r2 * r2;
}
double denominator = Math.Sqrt((n * ii_sum - i_sum * i_sum) * (n * jj_sum - j_sum * j_sum));
if (denominator == 0)
{
return(0);
}
double pmcc = (n * ij_sum - i_sum * j_sum) / denominator;
return((float)pmcc * (n / (n + shrinkage)));
}
/// <summary>Compute correlations between two entities for given ratings</summary>
/// <param name="ratings">the rating data</param>
/// <param name="entity_type">the entity type, either USER or ITEM</param>
/// <param name="i">the ID of first entity</param>
/// <param name="j">the ID of second entity</param>
/// <param name="shrinkage">the shrinkage parameter</param>
public static float ComputeCorrelation(IRatings ratings, EntityType entity_type, int i, int j, float shrinkage)
{
if (i == j)
return 1;
IList<int> ratings1 = (entity_type == EntityType.USER) ? ratings.ByUser[i] : ratings.ByItem[i];
IList<int> ratings2 = (entity_type == EntityType.USER) ? ratings.ByUser[j] : ratings.ByItem[j];
// get common ratings for the two entities
HashSet<int> e1 = (entity_type == EntityType.USER) ? ratings.GetItems(ratings1) : ratings.GetUsers(ratings1);
HashSet<int> e2 = (entity_type == EntityType.USER) ? ratings.GetItems(ratings2) : ratings.GetUsers(ratings2);
e1.IntersectWith(e2);
int n = e1.Count;
if (n < 2)
return 0;
// single-pass variant
double i_sum = 0;
double j_sum = 0;
double ij_sum = 0;
double ii_sum = 0;
double jj_sum = 0;
foreach (int other_entity_id in e1)
{
// get ratings
double r1 = 0;
double r2 = 0;
if (entity_type == EntityType.USER)
{
r1 = ratings.Get(i, other_entity_id, ratings1);
r2 = ratings.Get(j, other_entity_id, ratings2);
}
else
{
r1 = ratings.Get(other_entity_id, i, ratings1);
r2 = ratings.Get(other_entity_id, j, ratings2);
}
// update sums
i_sum += r1;
j_sum += r2;
ij_sum += r1 * r2;
ii_sum += r1 * r1;
jj_sum += r2 * r2;
}
double denominator = Math.Sqrt( (n * ii_sum - i_sum * i_sum) * (n * jj_sum - j_sum * j_sum) );
if (denominator == 0)
return 0;
double pmcc = (n * ij_sum - i_sum * j_sum) / denominator;
return (float) pmcc * (n / (n + shrinkage));
}
/// <summary>Compute correlation between two entities for given ratings</summary>
/// <param name="ratings">the rating data</param>
/// <param name="entity_type">the entity type, either USER or ITEM</param>
/// <param name="entity_ratings">ratings identifying the first entity</param>
/// <param name="j">the ID of second entity</param>
/// <param name="shrinkage">the shrinkage parameter, set to 0 for the standard Pearson correlation without shrinkage</param>
public static float ComputeCorrelation(IRatings ratings, EntityType entity_type, IList<Pair<int, float>> entity_ratings, int j, float shrinkage)
{
IList<int> indexes2 = (entity_type == EntityType.USER) ? ratings.ByUser[j] : ratings.ByItem[j];
// get common ratings for the two entities
var e1 = new HashSet<int>(from pair in entity_ratings select pair.First);
var e2 = (entity_type == EntityType.USER) ? ratings.GetItems(indexes2) : ratings.GetUsers(indexes2);
e1.IntersectWith(e2);
var ratings1 = new Dictionary<int, float>();
for (int index = 0; index < entity_ratings.Count; index++)
if (e1.Contains(entity_ratings[index].First))
ratings1.Add(entity_ratings[index].First, entity_ratings[index].Second);
int n = e1.Count;
if (n < 2)
return 0;
// single-pass variant
double i_sum = 0;
double j_sum = 0;
double ij_sum = 0;
double ii_sum = 0;
double jj_sum = 0;
foreach (int other_entity_id in e1)
{
// get ratings
float r1 = ratings1[other_entity_id];
float r2 = 0;
if (entity_type == EntityType.USER)
r2 = ratings.Get(j, other_entity_id, indexes2);
else
r2 = ratings.Get(other_entity_id, j, indexes2);
// update sums
i_sum += r1;
j_sum += r2;
ij_sum += r1 * r2;
ii_sum += r1 * r1;
jj_sum += r2 * r2;
}
double denominator = Math.Sqrt( (n * ii_sum - i_sum * i_sum) * (n * jj_sum - j_sum * j_sum) );
if (denominator == 0)
return 0;
double pmcc = (n * ij_sum - i_sum * j_sum) / denominator;
return (float) pmcc * ((n - 1) / (n - 1 + shrinkage));
}