RBF features

RBF features are center-based radial basis functions. In v2, RBF is a FeatureMap, not an activation enum.

Math

Each RBF node computes:

φ_i(x) = exp(-||x - c_i||² / (2σ²))

where c_i is a center and σ is the shared width.

API

feature_elm::RbfMap<float> rbfMap(
    inputDim,
    numCenters,
    0.75f,
    feature_elm::RbfCenterInit::kKMeans,
    42u);

rbfMap.fit(trainData, numSamples);

std::vector<float> features;
rbfMap.transform(trainData, numSamples, &features);

Center initialization

Mode	Behavior	Use
kRandom	Centers are sampled from the data range	Fast, deterministic ablations
kKMeans	Centers are selected with k-means++ style sampling	Better coverage of data support

Width selection

• Small σ creates local, narrow basis functions.
• Large σ makes nodes overlap and behave more globally.
• Start near the median nearest-neighbor distance when the scale is unknown.

When to use

• Inputs have meaningful Euclidean geometry.
• Classes form local clusters.
• A single additive ELM layer struggles with concentric or local boundaries.

When not to use

• Inputs are high-dimensional and sparse without a meaningful distance metric.
• You need a cheap linear baseline: use IdentityMap.
• You need learned feature extraction: use ELM-AE and ML-ELM.