Hinge losses for "maximum-margin" classification

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Hinge class

keras.losses.Hinge(reduction="sum_over_batch_size", name="hinge", dtype=None)

Computes the hinge loss between y_true & y_pred.

Formula:

loss = maximum(1 - y_true * y_pred, 0)

y_true values are expected to be -1 or 1. If binary (0 or 1) labels are provided we will convert them to -1 or 1.

Arguments

• 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", "mean", "mean_with_sample_weight" or None. "sum" sums the loss, "sum_over_batch_size" and "mean" sum the loss and divide by the sample size, and "mean_with_sample_weight" sums the loss and divides by the sum of the sample weights. "none" and None perform no aggregation. Defaults to "sum_over_batch_size".
• name: Optional name for the loss instance.
• dtype: The dtype of the loss's computations. Defaults to None, which means using keras.backend.floatx(). keras.backend.floatx() is a "float32" unless set to different value (via keras.backend.set_floatx()). If a keras.DTypePolicy is provided, then the compute_dtype will be utilized.

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SquaredHinge class

keras.losses.SquaredHinge(
    reduction="sum_over_batch_size", name="squared_hinge", dtype=None
)

Computes the squared hinge loss between y_true & y_pred.

Formula:

loss = square(maximum(1 - y_true * y_pred, 0))

y_true values are expected to be -1 or 1. If binary (0 or 1) labels are provided we will convert them to -1 or 1.

Arguments

• 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", "mean", "mean_with_sample_weight" or None. "sum" sums the loss, "sum_over_batch_size" and "mean" sum the loss and divide by the sample size, and "mean_with_sample_weight" sums the loss and divides by the sum of the sample weights. "none" and None perform no aggregation. Defaults to "sum_over_batch_size".
• name: Optional name for the loss instance.
• dtype: The dtype of the loss's computations. Defaults to None, which means using keras.backend.floatx(). keras.backend.floatx() is a "float32" unless set to different value (via keras.backend.set_floatx()). If a keras.DTypePolicy is provided, then the compute_dtype will be utilized.

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CategoricalHinge class

keras.losses.CategoricalHinge(
    reduction="sum_over_batch_size", name="categorical_hinge", dtype=None
)

Computes the categorical hinge loss between y_true & y_pred.

Formula:

loss = maximum(neg - pos + 1, 0)

where neg=maximum((1-y_true)*y_pred) and pos=sum(y_true*y_pred)

Arguments

• 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", "mean", "mean_with_sample_weight" or None. "sum" sums the loss, "sum_over_batch_size" and "mean" sum the loss and divide by the sample size, and "mean_with_sample_weight" sums the loss and divides by the sum of the sample weights. "none" and None perform no aggregation. Defaults to "sum_over_batch_size".
• name: Optional name for the loss instance.
• dtype: The dtype of the loss's computations. Defaults to None, which means using keras.backend.floatx(). keras.backend.floatx() is a "float32" unless set to different value (via keras.backend.set_floatx()). If a keras.DTypePolicy is provided, then the compute_dtype will be utilized.

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hinge function

keras.losses.hinge(y_true, y_pred)

Computes the hinge loss between y_true & y_pred.

Formula:

loss = mean(maximum(1 - y_true * y_pred, 0), axis=-1)

Arguments

• y_true: The ground truth values. y_true values are expected to be -1 or 1. If binary (0 or 1) labels are provided they will be converted to -1 or 1 with shape = [batch_size, d0, .. dN].
• y_pred: The predicted values with shape = [batch_size, d0, .. dN].

Returns

Hinge loss values with shape = [batch_size, d0, .. dN-1].

Example

>>> y_true = np.random.choice([-1, 1], size=(2, 3))
>>> y_pred = np.random.random(size=(2, 3))
>>> loss = keras.losses.hinge(y_true, y_pred)

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squared_hinge function

keras.losses.squared_hinge(y_true, y_pred)

Computes the squared hinge loss between y_true & y_pred.

Formula:

loss = mean(square(maximum(1 - y_true * y_pred, 0)), axis=-1)

Arguments

• y_true: The ground truth values. y_true values are expected to be -1 or 1. If binary (0 or 1) labels are provided we will convert them to -1 or 1 with shape = [batch_size, d0, .. dN].
• y_pred: The predicted values with shape = [batch_size, d0, .. dN].

Returns

Squared hinge loss values with shape = [batch_size, d0, .. dN-1].

Example

>>> y_true = np.random.choice([-1, 1], size=(2, 3))
>>> y_pred = np.random.random(size=(2, 3))
>>> loss = keras.losses.squared_hinge(y_true, y_pred)

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categorical_hinge function

keras.losses.categorical_hinge(y_true, y_pred)

Computes the categorical hinge loss between y_true & y_pred.

Formula:

loss = maximum(neg - pos + 1, 0)

where neg=maximum((1-y_true)*y_pred) and pos=sum(y_true*y_pred)

Arguments

• y_true: The ground truth values. y_true values are expected to be either {-1, +1} or {0, 1} (i.e. a one-hot-encoded tensor) with shape = [batch_size, d0, .. dN].
• y_pred: The predicted values with shape = [batch_size, d0, .. dN].

Returns

Categorical hinge loss values with shape = [batch_size, d0, .. dN-1].

Example

>>> y_true = np.random.randint(0, 3, size=(2,))
>>> y_true = np.eye(np.max(y_true) + 1)[y_true]
>>> y_pred = np.random.random(size=(2, 3))
>>> loss = keras.losses.categorical_hinge(y_true, y_pred)