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May 2, 2020 10:15
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Keras Pearson Correlation Loss
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| def l2_distance_matrix(x, exact=True): | |
| """ | |
| Calculate an L2 distance matrix from embedding vectors) | |
| :param | |
| x: embedding tensor size (batch_size, embedding_length) | |
| exact: if False, skip the final sqrt | |
| :return: l2 distance matrix tensor tensor size (batch_size, batch_size) | |
| """ | |
| r = K.sum(x*x, 1) | |
| r = K.reshape(r, [-1, 1]) # turn r into column vector | |
| dm = r - 2*K.dot(x, K.transpose(x)) + K.transpose(r) | |
| if exact: | |
| dm = K.sqrt(dm) | |
| return dm | |
| def cosine_distance_matrix(x): | |
| """ | |
| Calculate a Cosine distance matrix from embedding vectors) | |
| :param | |
| x: embedding tensor size (batch_size, embedding_length) | |
| :return: cosine distance matrix tensor tensor size (batch_size, batch_size) | |
| """ | |
| return K.dot(x, K.transpose(x)) | |
| def pearson_correlation_of_embeddings(y_true, y_pred, distance_matrix_function, normalized=False): | |
| """ | |
| Calculate pearson correlation loss | |
| :param y_true: embedding tensor size (batch_size, embedding_length) | |
| :param y_pred: embedding tensor size (batch_size, embedding_length) | |
| :param distance_matrix_function: callable that calculates a distance matrix from an embedding | |
| (batch_size, embedding_length) -> (batch_size, batch_size) | |
| :param normalized: if True, Softmax is applied to the distance matrix | |
| :return: loss tensor | |
| """ | |
| dm_true = distance_matrix_function(y_true) | |
| dm_pred = distance_matrix_function(y_pred) | |
| return pearson_correlation_of_distance_matrix(dm_true, dm_pred, normalized) | |
| def pearson_correlation_of_distance_matrix(y_true, y_pred, normalized=False): | |
| """ | |
| Calculate pearson correlation loss | |
| :param y_true: distance matrix tensor tensor size (batch_size, batch_size) | |
| :param y_pred: distance matrix tensor tensor size (batch_size, batch_size) | |
| :param normalized: if True, Softmax is applied to the distance matrix | |
| :return: loss tensor | |
| """ | |
| if normalized: | |
| y_true = K.softmax(y_true, axis=-1) | |
| y_pred = K.softmax(y_pred, axis=-1) | |
| sum_true = K.sum(y_true, axis=1) | |
| sum2_true = K.sum(K.square(y_true), axis=1) | |
| sum_pred = K.sum(y_pred, axis=1) | |
| sum2_pred = K.sum(K.square(y_pred), axis=1) | |
| prod = K.sum(y_true*y_pred, axis=1) | |
| n = K.cast(K.shape(y_true)[0], K.floatx()) | |
| corr = n*prod - sum_true*sum_pred | |
| corr /= K.sqrt(n * sum2_true - sum_true * sum_true + K.epsilon()) | |
| corr /= K.sqrt(n * sum2_pred - sum_pred * sum_pred + K.epsilon()) | |
| return -corr |
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