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?
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2 Answers
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Use sparse categorical crossentropy when your classes are mutually exclusive (e.g. when each sample belongs exactly to one class) and categorical crossentropy when one sample can have multiple classes or labels are soft probabilities (like [0.5, 0.3, 0.2]).
Formula for categorical crossentropy (S - samples, C - classess, $s \in c $ - sample belongs to class c) is:
$$ -\frac{1}{N} \sum_{s\in S} \sum_{c \in C} 1_{s\in c} log {p(s \in c)} $$
For case when classes are exclusive, you don't need to sum over them - for each sample only non-zero value is just $-log p(s \in c)$ for true class c.
This allows to conserve time and memory. Consider 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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1$\begingroup$ Do they impact the accuracy differently, for example on mnist digits dataset? $\endgroup$– Master MDec 1, 2018 at 8:47
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1$\begingroup$ Mathematically there is no difference. If there is significant difference in values computed by implementations (say tensorflow or pytorch), then this sounds like a bug. Simple comparison on random data (1000 classes, 10 000 samples) show no difference. $\endgroup$ Dec 1, 2018 at 14:20
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$\begingroup$ Dear frenzykryger, I guess you forgot a minus for the one sample case only: "for each sample only non-zero value is just -log(p(s $\in$ c))". For the rest, nice answer. $\endgroup$– NicgSep 13, 2019 at 12:48
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$\begingroup$ @frenzykryger I am working on multi-output problem. I have 3 seperate output
o1,o2,o3and each one have167,11,7classes respectively. I've read your answer that it'll make no difference but is there any difference if I usesparse__or not. Can I go forcategoricalfor the last 2 andsparsefor the first one as there are 167 classes in the first class? $\endgroup$– DeshwalJan 8, 2020 at 4:58
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The answer, in a nutshell
If your targets are one-hot encoded, use categorical_crossentropy.
Examples of one-hot encodings:
[1,0,0]
[0,1,0]
[0,0,1]
But if your targets are integers, use sparse_categorical_crossentropy.
Examples of integer encodings (for the sake of completion):
1
2
3
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2$\begingroup$ Do I need a single output node for
sparse_categorical_crossentropy? And what does thefrom_logitsargument mean? $\endgroup$– LeevoDec 15, 2019 at 17:01 -
3$\begingroup$ @Leevo
from_logits=Truetells the loss function that an activation function (e.g.softmax) was not applied on the last layer, in which case your output needs to be as the number of classes. This is equivalent to using asoftmaxandfrom_logits=False. However, if you end up usingsparse_categorical_crossentropy, make sure your target values are 1D. E.g.[1, 1, 0, 1, ...](and not[[1], [1], [0], [1], ...]). On the other hand, if you usecategorical_crossentropyand your target values are 1D, you need to applykeras.utils(targets)on them first to convert them to 2D. $\endgroup$– Alaa M.Jul 3, 2021 at 13:04 -
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$\begingroup$ I experienced vastly different results between the two losses and finally saw here that the last dimension needs to be removed. Thanks! $\endgroup$– N4ppeLDec 6, 2022 at 18:05