Package elki.math.linearalgebra.pca.weightfunctions
Weight functions used in weighted PCA via
WeightedCovarianceMatrixBuilder.-
Interface Summary Interface Description WeightFunction WeightFunction interface that allows the use of various distance-based weight functions. -
Class Summary Class Description ConstantWeight Constant weight function.ErfcStddevWeight Gaussian Error Function Weight function, scaled using stddev using: \( \text{erfc}(\frac{1}{\sqrt{2}} \frac{\text{distance}}{\sigma}) \).ErfcWeight Gaussian Error Function Weight function, scaled such that the result it 0.1 when the distance is the maximum using: \( \text{erfc}(1.1630871536766736 \frac{\text{distance}}{\max}) \).ExponentialStddevWeight Exponential Weight function, scaled using the standard deviation using: \( \sigma \exp(-\frac{1}{2} \frac{\text{distance}}{\sigma}) \).ExponentialWeight Exponential Weight function, scaled such that the result it 0.1 at distance equal max, so it does not completely disappear using: \( \exp(-2.3025850929940455 \frac{\text{distance}}{\max}) \)GaussStddevWeight Gaussian weight function, scaled using standard deviation \( \frac{1}{\sqrt{2\pi}} \exp(-\frac{\text{dist}^2}{2\sigma^2}) \)GaussWeight Gaussian weight function, scaled such that the result it 0.1 when distance equals the maximum, using \( \exp(-2.3025850929940455 \frac{\text{dist}^2}{\max^2}) \).InverseLinearWeight Inverse linear weight function using \(.1+0.9\frac{\text{distance}}{\max}\).InverseProportionalStddevWeight Inverse proportional weight function, scaled using the standard deviation using: \( 1 / (1 + \frac{distance}{\sigma}) \)InverseProportionalWeight Inverse proportional weight function, scaled using the maximum using: \( 1 / (1 + \frac{\text{distance}}{\max} ) \)LinearWeight Linear weight function, scaled using the maximum such that it goes from 1.0 to 0.1 using: \( 1 - 0.9 \frac{\text{distance}}{\max} \)QuadraticStddevWeight Quadratic weight function, scaled using the standard deviation: \( \max\{0.0, 1.0 - \frac{\text{dist}^2}{3\sigma^2} \} \).QuadraticWeight Quadratic weight function, scaled using the maximum to reach 0.1 at that point using: \( 1.0 - 0.9 \frac{\text{dist}^2}{\max^2}\} \)