# Package de.lmu.ifi.dbs.elki.math.linearalgebra.pca.weightfunctions

Weight functions used in weighted PCA via WeightedCovarianceMatrixBuilder

See: Description

• 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 The result is always 1.0
ErfcStddevWeight
Gaussian Error Function Weight function, scaled using stddev.
ErfcWeight
Gaussian Error Function Weight function, scaled such that the result it 0.1 at distance == max erfc(1.1630871536766736 * distance / max) The value of 1.1630871536766736 is erfcinv(0.1), to achieve the intended scaling.
ExponentialStddevWeight
Exponential Weight function, scaled such that the result it 0.1 at distance == max stddev * exp(-.5 * distance/stddev) This is similar to the Gaussian weight function, except distance/stddev is not squared.
ExponentialWeight
Exponential Weight function, scaled such that the result it 0.1 at distance == max exp(-2.3025850929940455 * distance/max) This is similar to the Gaussian weight function, except distance/max is not squared
GaussStddevWeight
Gaussian weight function, scaled using standard deviation $$1/\sqrt(2\pi) \exp(-\frac{\text{dist}^2}{2\sigma^2})$$
GaussWeight
Gaussian weight function, scaled such that the result it 0.1 at distance == max, using $$\exp(-2.3025850929940455 \frac{\text{dist}^2}{\max^2})$$.
InverseLinearWeight
Inverse Linear Weight Function.
InverseProportionalStddevWeight
Inverse proportional weight function, scaled using the standard deviation. 1 / (1 + distance/stddev)
InverseProportionalWeight
Inverse proportional weight function, scaled using the maximum. 1 / (1 + distance/max)
LinearWeight
Linear weight function, scaled using the maximum such that it goes from 1.0 to 0.1 1 - 0.9 * (distance/max)
Weight functions used in weighted PCA via WeightedCovarianceMatrixBuilder