linkability()

audmetric.linkability(truth, prediction, omega=1.0, nbins=None)

Linkability for verification tasks.

Let $s$ be the provided prediction score for the similarity of the tested sample. The clipped local linkability metric is then defined as:

$$\text{max}(0, p(\text{mated} | s) - p(\text{non-mated} | s))$$

The higher the value, the more likely that an attacker can link two mated samples. The global linkability metric $D_\text{sys}$ is the mean value over all local scores,[1] and in the range $0$ and $1$.

Implementation is based on code from M. Maouche, which is licensed under LGPL.

[1]

M. Gomez-Barrero, J. Galbally, C. Rathgeb, and C. Busch. General framework to evaluate unlinkability in biometric template protection systems. IEEE Transactions on Information Forensics and Security, 13:1406–1420, 2017. doi:10.1109/TIFS.2017.2788000.

Parameters:

• truth (bool | int | Sequence[bool | int]) – ground truth classes

• prediction (bool | int | float | Sequence[bool | int | float]) – predicted classes or similarity scores

• omega (float) – prior ratio $\frac{p(\text{mated})}{p(\text{non-mated})}$

• nbins (int) – number of bins of the histograms that estimate the distributions of mated and non-mated scores. If None it is set to $\min(\frac{\text{len}(\text{mated})}{10}, 100)$

Return type:

float

Returns:

global linkability $D_\text{sys}$

Raises:

ValueError – if truth contains values different from 1, 0, True, False

Examples

>>> np.random.seed(1)
>>> samples = 10000
>>> truth = [1, 0] * int(samples / 2)
>>> prediction = []
>>> for _ in range(int(samples / 2)):
...     prediction.extend(
...         [np.random.uniform(0, 0.2), np.random.uniform(0.8, 1.0)]
...     )
>>> linkability(truth, prediction)
0.9747999999999999
>>> truth = [1, 0, 0, 0] * int(samples / 4)
>>> prediction = [np.random.uniform(0, 1) for _ in range(samples)]
>>> linkability(truth, prediction, omega=1 / 3)
0.0