TheAlgorithms · ZJUGuoShuai · Jan 13, 2024 · Jun 3, 2024 · tianyizheng02 · Jun 3, 2024
diff --git a/machine_learning/loss_functions.py b/machine_learning/loss_functions.py
@@ -663,6 +663,110 @@ def kullback_leibler_divergence(y_true: np.ndarray, y_pred: np.ndarray) -> float
     return np.sum(kl_loss)
 
 
+def connectionist_temporal_classification_loss(
+    y_true: np.ndarray, y_pred: np.ndarray, blank: int = 0
+):
+    """
+    Calculate the connectionist temporal classification (CTC) loss between the given
+    log probabilities and targets.
+
+    CTC loss is used in speech recognition, handwriting recognition and other sequence
+    problems. It's used to get around not knowing the alignment between the input and
+    the output.
+
+    References:
+    - https://en.wikipedia.org/wiki/Connectionist_temporal_classification
+    - https://pytorch.org/docs/stable/generated/torch.nn.CTCLoss.html
+
+    Parameters:
+    - y_true: True labels (containing class indices).
+    - y_pred: Predicted class probabilities for each input timestep.
+    - blank: Index of the blank token, default: 0.
+
+    Returns:
+    - CTC loss between y_true and y_pred.
+
+    >>> y_true = np.array([1, 2, 3])
+    >>> y_pred = np.array([[0.1, 0.6, 0.1, 0.2],
+    ...                    [0.2, 0.1, 0.5, 0.2],
+    ...                    [0.2, 0.1, 0.5, 0.2]])
+    >>> connectionist_temporal_classification_loss(y_true, y_pred)
+    2.8134107167600364
+
+    >>> y_true = np.array([1, 2, 3, 1])
+    >>> y_pred = np.random.rand(3, 4)
+    >>> connectionist_temporal_classification_loss(y_true, y_pred)
+    Traceback (most recent call last):
+        ...
+    ValueError: y_true cannot be longer than y_pred.
+
+    >>> y_true = np.array([[1, 2, 3]])
+    >>> y_pred = np.random.rand(3, 4)
+    >>> connectionist_temporal_classification_loss(y_true, y_pred)
+    Traceback (most recent call last):
+        ...
+    ValueError: y_true should be an 1D array.
+
+    >>> y_true = np.array([1, 2, 3])
+    >>> y_pred = np.array([0.1, 0.6, 0.1, 0.2])
+    >>> connectionist_temporal_classification_loss(y_true, y_pred)
+    Traceback (most recent call last):
+        ...
+    ValueError: y_pred should be a 2D array.
+
+    >>> y_true = np.array([1, 2, 3])
+    >>> y_pred = np.array([[0.1, 0.6, 0.1], [0.2, 0.1, 0.5], [0.2, 0.1, 0.5]])
+    >>> connectionist_temporal_classification_loss(y_true, y_pred)
+    Traceback (most recent call last):
+        ...
+    ValueError: Class indices in y_true should be less than y_pred.shape[1].
+    """
+    if len(y_true) > len(y_pred):
+        raise ValueError("y_true cannot be longer than y_pred.")
+
+    if y_true.ndim != 1:
+        raise ValueError("y_true should be an 1D array.")
+
+    if y_pred.ndim != 2:
+        raise ValueError("y_pred should be a 2D array.")
+
+    if np.max(y_true) >= y_pred.shape[1]:
+        raise ValueError("Class indices in y_true should be less than y_pred.shape[1].")
+
+    log_probs = np.log(y_pred)
+    input_len = log_probs.shape[0]  # Input sequence length
+    target_len = len(y_true)  # Target sequence length
+    target_len_extended = 2 * target_len + 1  # Target sequence length with blanks
+
+    # Initialize blank and target sequences
+    extended_targets = np.full(target_len_extended, blank)
+    extended_targets[1::2] = y_true
+
+    # Initialize alpha (forward variable)
+    alpha = np.full((input_len, target_len_extended), -np.inf)
+    alpha[0, 0] = log_probs[0, blank]  # Starting with blank
+    if target_len_extended > 1:
+        alpha[0, 1] = log_probs[0, extended_targets[1]]
+
+    # Dynamic programming to calculate alpha
+    for t in range(1, input_len):
+        for s in range(target_len_extended):
+            current_label = extended_targets[s]
+            alpha[t, s] = alpha[t - 1, s]
+            if s > 0:
+                alpha[t, s] = np.logaddexp(alpha[t, s], alpha[t - 1, s - 1])
+            if s > 1 and current_label != extended_targets[s - 2]:
+                alpha[t, s] = np.logaddexp(alpha[t, s], alpha[t - 1, s - 2])
+            alpha[t, s] += log_probs[t, current_label]
+
+    # CTC loss is the negative log probability of the target sequence
+    loss = -np.logaddexp(
+        alpha[input_len - 1, target_len_extended - 1],
+        alpha[input_len - 1, target_len_extended - 2],
+    )
+    return loss
+
+
 if __name__ == "__main__":
     import doctest