Keras - Difference between categorical_accuracy and sparse_categorical_accuracy

The sparse_categorical_accuracy expects sparse targets:

[[0], [1], [2]]

For instance:

import tensorflow as tf

sparse = [[0], [1], [2]]
logits = [[.8, .1, .1], [.5, .3, .2], [.2, .2, .6]]

sparse_cat_acc = tf.metrics.SparseCategoricalAccuracy()
sparse_cat_acc(sparse, logits)

<tf.Tensor: shape=(), dtype=float64, numpy=0.6666666666666666>

---

categorical_accuracy expects one hot encoded targets:

[[1., 0., 0.],  [0., 1., 0.], [0., 0., 1.]]

For instance:

onehot = [[1., 0., 0.],  [0., 1., 0.], [0., 0., 1.]]
logits = [[.8, .1, .1], [.5, .3, .2], [.2, .2, .6]]

cat_acc = tf.metrics.CategoricalAccuracy()
cat_acc(sparse, logits)

<tf.Tensor: shape=(), dtype=float64, numpy=0.6666666666666666>

Looking at the source

def categorical_accuracy(y_true, y_pred):
    return K.cast(K.equal(K.argmax(y_true, axis=-1),
                          K.argmax(y_pred, axis=-1)),
                  K.floatx())


def sparse_categorical_accuracy(y_true, y_pred):
    return K.cast(K.equal(K.max(y_true, axis=-1),
                          K.cast(K.argmax(y_pred, axis=-1), K.floatx())),
K.floatx())

categorical_accuracy checks to see if the index of the maximal true value is equal to the index of the maximal predicted value.

sparse_categorical_accuracy checks to see if the maximal true value is equal to the index of the maximal predicted value.

From Marcin's answer above the categorical_accuracy corresponds to a one-hot encoded vector for y_true.

So in categorical_accuracy you need to specify your target (y) as one-hot encoded vector (e.g. in case of 3 classes, when a true class is second class, y should be (0, 1, 0). In sparse_categorical_accuracy you need should only provide an integer of the true class (in the case from previous example - it would be 1 as classes indexing is 0-based).