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: $1.0 - 0.9 \frac{\text{dist}^2}{\max^2}\}$