# Computes the alpha balanced focal crossentropy loss.

Source:`R/losses.R`

`loss_categorical_focal_crossentropy.Rd`

Use this crossentropy loss function when there are two or more label
classes and if you want to handle class imbalance without using
`class_weights`

. We expect labels to be provided in a `one_hot`

representation.

According to Lin et al., 2018, it helps to apply a focal factor to down-weight easy examples and focus more on hard examples. The general formula for the focal loss (FL) is as follows:

`FL(p_t) = (1 - p_t)^gamma * log(p_t)`

where `p_t`

is defined as follows:
`p_t = output if y_true == 1, else 1 - output`

`(1 - p_t)^gamma`

is the `modulating_factor`

, where `gamma`

is a focusing
parameter. When `gamma`

= 0, there is no focal effect on the cross entropy.
`gamma`

reduces the importance given to simple examples in a smooth manner.

The authors use alpha-balanced variant of focal loss (FL) in the paper:
`FL(p_t) = -alpha * (1 - p_t)^gamma * log(p_t)`

where `alpha`

is the weight factor for the classes. If `alpha`

= 1, the
loss won't be able to handle class imbalance properly as all
classes will have the same weight. This can be a constant or a list of
constants. If alpha is a list, it must have the same length as the number
of classes.

The formula above can be generalized to:
`FL(p_t) = alpha * (1 - p_t)^gamma * CrossEntropy(y_true, y_pred)`

where minus comes from `CrossEntropy(y_true, y_pred)`

(CE).

Extending this to multi-class case is straightforward:
`FL(p_t) = alpha * (1 - p_t) ** gamma * CategoricalCE(y_true, y_pred)`

In the snippet below, there is `num_classes`

floating pointing values per
example. The shape of both `y_pred`

and `y_true`

are
`(batch_size, num_classes)`

.

## Usage

```
loss_categorical_focal_crossentropy(
y_true,
y_pred,
alpha = 0.25,
gamma = 2,
from_logits = FALSE,
label_smoothing = 0,
axis = -1L,
...,
reduction = "sum_over_batch_size",
name = "categorical_focal_crossentropy"
)
```

## Arguments

- y_true
Tensor of one-hot true targets.

- y_pred
Tensor of predicted targets.

- alpha
A weight balancing factor for all classes, default is

`0.25`

as mentioned in the reference. It can be a list of floats or a scalar. In the multi-class case, alpha may be set by inverse class frequency by using`compute_class_weight`

from`sklearn.utils`

.- gamma
A focusing parameter, default is

`2.0`

as mentioned in the reference. It helps to gradually reduce the importance given to simple examples in a smooth manner. When`gamma`

= 0, there is no focal effect on the categorical crossentropy.- from_logits
Whether

`output`

is expected to be a logits tensor. By default, we consider that`output`

encodes a probability distribution.- label_smoothing
Float in

`[0, 1].`

When > 0, label values are smoothed, meaning the confidence on label values are relaxed. For example, if`0.1`

, use`0.1 / num_classes`

for non-target labels and`0.9 + 0.1 / num_classes`

for target labels.- axis
The axis along which to compute crossentropy (the features axis). Defaults to

`-1`

.- ...
For forward/backward compatability.

- reduction
Type of reduction to apply to the loss. In almost all cases this should be

`"sum_over_batch_size"`

. Supported options are`"sum"`

,`"sum_over_batch_size"`

or`NULL`

.- name
Optional name for the loss instance.

## Examples

```
y_true <- rbind(c(0, 1, 0), c(0, 0, 1))
y_pred <- rbind(c(0.05, 0.95, 0), c(0.1, 0.8, 0.1))
loss <- loss_categorical_focal_crossentropy(y_true, y_pred)
loss
```

Standalone usage:

```
y_true <- rbind(c(0, 1, 0), c(0, 0, 1))
y_pred <- rbind(c(0.05, 0.95, 0), c(0.1, 0.8, 0.1))
# Using 'auto'/'sum_over_batch_size' reduction type.
cce <- loss_categorical_focal_crossentropy()
cce(y_true, y_pred)
```

```
# Using 'sum' reduction type.
cce <- loss_categorical_focal_crossentropy(reduction = "sum")
cce(y_true, y_pred)
```

```
# Using 'none' reduction type.
cce <- loss_categorical_focal_crossentropy(reduction = NULL)
cce(y_true, y_pred)
```

Usage with the `compile()`

API:

```
model %>% compile(
optimizer = 'adam',
loss = loss_categorical_focal_crossentropy())
```

## See also

Other losses: `Loss()`

`loss_binary_crossentropy()`

`loss_binary_focal_crossentropy()`

`loss_categorical_crossentropy()`

`loss_categorical_hinge()`

`loss_cosine_similarity()`

`loss_ctc()`

`loss_dice()`

`loss_hinge()`

`loss_huber()`

`loss_kl_divergence()`

`loss_log_cosh()`

`loss_mean_absolute_error()`

`loss_mean_absolute_percentage_error()`

`loss_mean_squared_error()`

`loss_mean_squared_logarithmic_error()`

`loss_poisson()`

`loss_sparse_categorical_crossentropy()`

`loss_squared_hinge()`

`loss_tversky()`

`metric_binary_crossentropy()`

`metric_binary_focal_crossentropy()`

`metric_categorical_crossentropy()`

`metric_categorical_focal_crossentropy()`

`metric_categorical_hinge()`

`metric_hinge()`

`metric_huber()`

`metric_kl_divergence()`

`metric_log_cosh()`

`metric_mean_absolute_error()`

`metric_mean_absolute_percentage_error()`

`metric_mean_squared_error()`

`metric_mean_squared_logarithmic_error()`

`metric_poisson()`

`metric_sparse_categorical_crossentropy()`

`metric_squared_hinge()`