Sparse Categorical Crossentropy vs. Categorical Crossentropy
Last Updated :
26 Jul, 2025
When training a machine learning model for multi-class classification, selecting the right loss function is crucial. Two commonly used loss functions are Categorical Crossentropy and Sparse Categorical Crossentropy. Both serve the same core purpose of measuring how well the predicted class probabilities match the true class but differ in how the target labels are represented.
What is Categorical Crossentropy?
Categorical Crossentropy measures how well the predicted probabilities of each class align with the actual target labels. Its primary purpose is to evaluate a classification model's performance by comparing the model's predicted probabilities for each class with the actual class labels. Categorical Crossentropy requires the target labels to be in one-hot encoded format. This means that for each label, the correct class is represented by 1 while all other classes are represented by 0.
Example: If we are classifying animals into three categories- Dog, Cat and Rabbit and the correct label is "Cat",
- The one-hot encoded vector would be [0, 1, 0].
- Suppose the model predicts probabilities like [0.2, 0.7, 0.1] (20% Dog, 70% Cat, 10% Rabbit). The loss is calculated for the correct class (Cat) using the formula:
-log(predicted probability of correct class) = −log(0.7) ≈ 0.3567
- The lower the loss, the closer the model's prediction is to the true label. The model minimizes this loss during training to improve accuracy.
What is Sparse Categorical Crossentropy?
Sparse Categorical Crossentropy is functionally similar to Categorical Crossentropy but is designed for cases where the target labels are not one-hot encoded. Instead, the labels are represented as integers corresponding to the class indices. The true labels are integers where each integer represents the class index.
Example: If the correct label is "Cat", it would be represented as the integer 1 (since "Cat" is the second class, starting from 0).
- Suppose the model predicts probabilities like
[0.2, 0.7, 0.1]. - The loss is calculated for the correct class (
Cat) using the formula: -\log(0.7) - This again results in a loss of approximately 0.3567.
Sparse Categorical Crossentropy internally converts these integer labels into one-hot encoded format before calculating the loss. This approach can save memory and computational resources, especially when dealing with datasets containing a large number of classes.
Key Differences Between Categorical Crossentropy and Sparse Categorical Crossentropy
| Feature | Categorical Crossentropy | Sparse Categorical Crossentropy |
|---|
| Label Representation | Requires one-hot encoded labels(e.g., [0, 1, 0]) | Uses integer labels representing class indices(e.g., 1) |
|---|
| Memory Efficiency | Less efficient(due to full one-hot vectors) | More efficient(stores a single integer) |
|---|
| Use Cases | Suitable for smaller datasets with manageable class counts | Ideal for raw or large datasets with many classes |
|---|
| Performance | Slower due to one-hot encoding overhead | Faster |
|---|
| Loss Calculation | Compares predicted probabilities with one-hot encoded labels | Compares predicted probabilities with class indices |
|---|
Ease of Use | Requires label preprocessing | No extra preprocessing required |
|---|
Compatibility | Must match prediction shape exactly | More flexible with label format |
|---|
When to Use
Use Categorical Crossentropy if:
- Our labels are already one-hot encoded.
- We want precise control over label representation. For example, custom metrics or weighted classes.
Use Sparse Categorical Crossentropy if:
- Our labels are integers.
- We want faster training and better memory usage, especially with many classes.
Both Categorical and Sparse Categorical Crossentropy are equally effective for multi-class classification. The only real difference lies in the label format.
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