Calculates the Pearson Correlation Coefficient (PCC).

Formula:

loss = mean(l2norm(y_true - mean(y_true) * l2norm(y_pred - mean(y_pred)))

PCC measures the linear relationship between the true values (y_true) and the predicted values (y_pred). The coefficient ranges from -1 to 1, where a value of 1 implies a perfect positive linear correlation, 0 indicates no linear correlation, and -1 indicates a perfect negative linear correlation.

This metric is widely used in regression tasks where the strength of the linear relationship between predictions and true labels is an important evaluation criterion.

Usage

metric_pearson_correlation(
  y_true,
  y_pred,
  axis = -1L,
  ...,
  name = "pearson_correlation",
  dtype = NULL
)

Arguments

y_true: Tensor of true targets.
y_pred: Tensor of predicted targets.
axis: (Optional) integer or tuple of integers of the axis/axes along which to compute the metric. Defaults to -1.
...: For forward/backward compatability.
name: (Optional) string name of the metric instance.
dtype: (Optional) data type of the metric result.

Examples

pcc <- metric_pearson_correlation(axis = -1)
y_true <- rbind(c(0, 1, 0.5),
                c(1, 1, 0.2))
y_pred <- rbind(c(0.1, 0.9, 0.5),
                c(1, 0.9, 0.2))
pcc$update_state(y_true, y_pred)
pcc$result()

## tf.Tensor(0.99669963, shape=(), dtype=float32)

# equivalent operation using R's stats::cor()
mean(sapply(1:nrow(y_true), function(i) {
  cor(y_true[i, ], y_pred[i, ])
}))

## [1] 0.9966996

Usage with compile() API:

model |> compile(
  optimizer = 'sgd',
  loss = 'mean_squared_error',
  metrics = c(keras.metrics.PearsonCorrelation())
)

Other regression metrics:
metric_concordance_correlation()
metric_cosine_similarity()
metric_log_cosh_error()
metric_mean_absolute_error()
metric_mean_absolute_percentage_error()
metric_mean_squared_error()
metric_mean_squared_logarithmic_error()
metric_r2_score()
metric_root_mean_squared_error()

Other metrics:
Metric()
custom_metric()
metric_auc()
metric_binary_accuracy()
metric_binary_crossentropy()
metric_binary_focal_crossentropy()
metric_binary_iou()
metric_categorical_accuracy()
metric_categorical_crossentropy()
metric_categorical_focal_crossentropy()
metric_categorical_hinge()
metric_concordance_correlation()
metric_cosine_similarity()
metric_f1_score()
metric_false_negatives()
metric_false_positives()
metric_fbeta_score()
metric_hinge()
metric_huber()
metric_iou()
metric_kl_divergence()
metric_log_cosh()
metric_log_cosh_error()
metric_mean()
metric_mean_absolute_error()
metric_mean_absolute_percentage_error()
metric_mean_iou()
metric_mean_squared_error()
metric_mean_squared_logarithmic_error()
metric_mean_wrapper()
metric_one_hot_iou()
metric_one_hot_mean_iou()
metric_poisson()
metric_precision()
metric_precision_at_recall()
metric_r2_score()
metric_recall()
metric_recall_at_precision()
metric_root_mean_squared_error()
metric_sensitivity_at_specificity()
metric_sparse_categorical_accuracy()
metric_sparse_categorical_crossentropy()
metric_sparse_top_k_categorical_accuracy()
metric_specificity_at_sensitivity()
metric_squared_hinge()
metric_sum()
metric_top_k_categorical_accuracy()
metric_true_negatives()
metric_true_positives()

Usage

Arguments

Examples

See also