`sklvq.objectives`.GeneralizedLearningObjective

class sklvq.objectives.GeneralizedLearningObjective(activation_type: str | type, activation_params: dict, discriminant_type: str | type, discriminant_params: dict)[source]

Generalized learning objective

Class that holds the generalized learning objective function and its gradient as described in [1].

Parameters:

activation_type{“identity”, “sigmoid”, “soft-plus”, “swish”} or type: If string needs to be one of the indicated options. If not a string needs to be a custom activation class. See sklvq.activations.ActivationBaseClass.
activation_paramsdict or None: The dictionary with the parameters for the activation function or None if it doesn’t require any parameters.
discriminant_type: {“relative-distance”} or type: Can only be the relative distance. If not a string it can be a custom class. See sklvq.discriminants.DiscriminantBaseClass.
discriminant_paramsdict or None: The dictionary with the parameters for the discriminant function or None if it doesn’t require any parameters.

Notes

Compatible and used within the following models: GLVQ, GMLVQ, and LGMLVQ.

References

[1] Sato, A., and Yamada, K. (1996) “Generalized Learning Vector Quantization.” Advances in Neural Network Information Processing Systems, 423-429, 1996.

__call__(model: LVQBaseClass, data: np.ndarray, labels: np.ndarray) → np.ndarray[source]

Computes the generalized learning objective:

$E = \sum_{i=1}^{N} f(\mu(d_0(\mathbf{x}_i), d_1(\mathbf{x}_i))$

with $\mu(\cdot)$ the discriminative function, $f(\cdot)$ the activation function, and $d_0(\mathbf{x}_i)$ and $d_1(\mathbf{x}_i)$ the shortest distance to a prototype with a different and the same label respectively.

Parameters:

modelLVQBaseClass: The model which can be any LVQBaseClass compatible with this objective function.
data: ndarray with shape (n_samples, n_features): The data.
labels: ndarray with shape (n_samples): The labels of the samples in the data.

Returns:

float:: The cost

gradient(model: LVQBaseClass, data: np.ndarray, labels: np.ndarray) → np.ndarray[source]

Computes the generalized learning objective’s gradient with respect to the prototype with a different label:

$\frac{\partial E}{\partial \mathbf{w}_0} = \frac{\partial f}{\partial \mu} \frac{\partial \mu}{\partial d_0} \frac{\partial d_0}{\partial \mathbf{w}_0}$

with $\mathbf{w}_0$ the prototype with a different label than the data and $d_0$ the distance to that prototype.

$\frac{\partial E}{\partial \mathbf{w}_1} = \frac{\partial f}{\partial \mu} \frac{\partial \mu}{\partial d_1} \frac{\partial d_1}{\partial \mathbf{w}_1}$

with $\mathbf{w}_1$ the prototype with the same label as the data and $d_1$ the distance to that prototype.

Parameters:

modelLVQBaseClass: The model which can be any LVQBaseClass compatible with this objective function.
data: ndarray with shape (n_samples, n_features): The data.
labels: ndarray with shape (n_samples): The labels of the samples in the data.

Returns:

ndarray with the same shape as the model variables array (depending on the model): The generalized learning objective function’s gradient

sklvq.objectives.GeneralizedLearningObjective

`sklvq.objectives`.GeneralizedLearningObjective