`sklvq.discriminants`.RelativeDistance

class sklvq.discriminants.RelativeDistance[source]

Relative distance function

Class that holds the relative distance function and gradient as described in [1].

References

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

__call__(dist_same: ndarray, dist_diff: ndarray) → ndarray[source]

The relative distance discriminant function for a single sample ( $\mathbf{x}$ ):: $\mu(\mathbf{x}) = \frac{d(\mathbf{x}, \mathbf{w}_1) - d(\mathbf{x}, \mathbf{w}_0)}{d( \mathbf{x}, \mathbf{w}_1) + d(\mathbf{x}, \mathbf{w}_0)},$

with $\mathbf{w}_1$ the prototype with the same label and $\mathbf{w}_0$ the prototype with a different label.

Parameters:

dist_samendarray with shape (n_samples, 1), with n_samples >= 1: Shortest distance of n_samples to a prototype with the same label.
dist_diffndarray with shape (n_samples, 1), with n_samples >= 1: Shortest distance of n_samples to a prototype with a different label.

Returns:

ndarray with shape (n_samples, 1): Evaluation of the relative distance discriminative function.

gradient(dist_same: ndarray, dist_diff: ndarray, same_label: bool) → ndarray[source]

Computes the relative distance discriminant function’s gradient.

The partial derivative with respect to the closest prototypes with the same label (same_label=True):

$\frac{\partial \mu}{\partial \mathbf{w}_1} = \frac{2 \cdot d(\mathbf{x}, \mathbf{w}_0))}{(d(\mathbf{x}, \mathbf{w}_1) + d(\mathbf{x}, \mathbf{w}_0))^2}.$

The partial derivative with respect to the closest prototypes with a different label (same_label=False):

$\frac{\partial \mu}{\partial \mathbf{w}_0} = \frac{-2 \cdot d(\mathbf{x}, \mathbf{w}_1))}{(d(\mathbf{x}, \mathbf{w}_1) + d(\mathbf{x}, \mathbf{w}_0))^2},$

with $d(\mathbf{x}, \mathbf{w}_1)$ the distance to the prototype with the same label and $d(\mathbf{x}, \mathbf{w}_0)$ the distance to the closest prototype with a different label.

Parameters:

dist_samendarray with shape (n_samples, 1), with n_samples >= 1: Shortest distance of n_samples to a prototype with the same label.
dist_diffndarray with shape (n_samples, 1), with n_samples >= 1: Shortest distance of n_samples to a prototype with a different label.
same_labelbool: Indicating if the derivative with respect to a prototype with the same label (True) or a different label (False) needs to be calculated.

Returns:

ndarray with shape (n_samples, 1): Evaluation of the relative distance function’s gradient.

sklvq.discriminants.RelativeDistance

`sklvq.discriminants`.RelativeDistance