sklvq.distances.AdaptiveSquaredEuclidean

class sklvq.distances.AdaptiveSquaredEuclidean[source]

Adaptive squared Euclidean distance

Class that holds the adaptive squared Euclidean distance function and its gradient as described in [1] and [2].

Parameters:
force_all_finite{True, False, “allow-nan”}

Parameter to indicate that NaNLVQ distance variant should be used. If true no nans are allowed. If False or “allow-nan”, nans are allowed.

See also

Euclidean, SquaredEuclidean, LocalAdaptiveSquaredEuclidean

Notes

Compatible with the GMLVQ algorithm (only).

References

[1] Schneider, P. (2010). Advanced methods for prototype-based classification. Groningen.

[2] Schneider, P., Biehl, M., & Hammer, B. (2009). Adaptive Relevance Matrices in Learning Vector Quantization. Neural Computation, 21(12), 3532-3561.

__call__(data: ndarray, model: GMLVQ) → ndarray[source]

Computes the adaptive squared Euclidean distance:

d^{\Lambda}(\mathbf{w}, \mathbf{x}) = (\mathbf{x} - \mathbf{w})^{\top} \Lambda (\mathbf{x} - \mathbf{w})

with the relevance matrix \Lambda = \Omega^{\top} \Omega, the prototype \mathbf{w}, and sample \mathbf{x}.

Parameters:
datandarray with shape (n_samples, n_features)

The data for which the distance gradient to the prototypes of the model need to be computed.

modelGMLVQ

The model instance, containing the prototypes and relevance matrix.

Returns:
ndarray with shape (n_samples, n_prototypes)

Evaluation of the distance between each sample in the data and prototype of the model.

gradient(data: ndarray, model: GMLVQ, i_prototype: int) → ndarray[source]

Computes the gradient of the adaptive squared euclidean distance function, with respect to a single prototype:

\frac{\partial d}{\partial \mathbf{w_i}} = -2 \Lambda (\mathbf{x} - \mathbf{w_i}),

and the omega matrix (per element):

\frac{\partial d}{\partial \Omega_{lm}} = 2 \sum_i (x^i - w^i) \Omega_{li} (x^m - w^m)

Parameters:
datandarray with shape (n_samples, n_features)

The data for which the distance gradient to the prototypes of the model need to be computed.

modelGMLVQ

The model instance, containing the prototypes and relevance matrix.

i_prototypeint

An integer index value of the relevant prototype

Returns:
ndarray with shape (n_samples, n_features + n_omega_elements)

The gradient of the prototype and omega matrix with respect to each data sample.