Categorical_crossentropy vs sparse_categorical_crossentropy - Which is better?

1.4K    Asked by CamelliaKleiber in Data Science , Asked on Feb 15, 2023

Which is better for accuracy or are they the same? Of course, if you use categorical_crossentropy you use one hot encoding, and if you use sparse_categorical_crossentropy you encode as normal integers. Additionally, when is one better than the other?

categorical_crossentropy vs sparse_categorical_crossentropy Use sparse categorical cross entropy when your classes are mutually exclusive (e.g. when each sample belongs exactly to one class) and categorical cross entropy when one sample can have multiple classes or labels are soft probabilities (like [0.5, 0.3, 0.2]).

Formula for categorical cross entropy (S - samples, C - classes, s∈c - sample belongs to class c) is:

For cases when classes are exclusive, you don't need to sum over them - for each sample only non-zero value is just −logp(s∈c) for true class c. This allows us to conserve time and memory. Consider the case of 10000 classes when they are mutually exclusive - just 1 log instead of summing up 10000 for each sample, just one integer instead of 10000 floats. Formula is the same in both cases, so no impact on accuracy should be there.

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Answer (1)

The choice between categorical_crossentropy and sparse_categorical_crossentropy in Keras or TensorFlow depends on the format of your target data and how it's represented.

Here's a brief explanation of each:

Categorical Crossentropy:

Use categorical_crossentropy when your targets are one-hot encoded.

One-hot encoding means that each target value is represented as a binary vector where only one bit is on (1) indicating the class, and all other bits are off (0).

For example, if you have three classes and the target for a sample is class 2, it would be represented as [0, 1, 0].

This loss function compares the distribution of predicted probabilities across all classes with the target distribution.

Sparse Categorical Crossentropy:

Use sparse_categorical_crossentropy when your targets are integers.

In this case, your target for each sample is an integer representing the class index directly.

For example, if you have three classes and the target for a sample is class 2, it would be represented as 2.

This loss function implicitly performs the one-hot encoding internally.

So, which one is better depends on how your target data is represented:

If your target data is already one-hot encoded, you should use categorical_crossentropy.

If your target data is represented as integers (class indices), you should use sparse_categorical_crossentropy.

There's no inherent "better" choice between the two; it's all about matching the loss function with the format of your target data. Using the appropriate loss function ensures that your model is trained correctly and effectively.

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