# 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: $$1 - 0.9 \frac{\text{distance}}{\max}$$
Quadratic weight function, scaled using the standard deviation: $$\max\{0.0, 1.0 - \frac{\text{dist}^2}{3\sigma^2} \}$$.
Quadratic weight function, scaled using the maximum to reach 0.1 at that point using: $$1.0 - 0.9 \frac{\text{dist}^2}{\max^2}\}$$