OS-ELM

Online Sequential ELM updates the output layer as new chunks arrive without retraining on all historical data.

Math

The feature map is fixed after initialization:

H_i = g(X_iW + b)

The online head maintains weights β and covariance P. For each chunk, it applies recursive least squares:

K = P Hᵀ (I + H P Hᵀ)^(-1)
β ← β + K(T - Hβ)
P ← μ^(-1)(P - K H P)

When forgettingFactor = 1, this is ordinary OS-ELM.

API

feature_elm::OsElm<float> model(
    numInputs,
    numHiddenNodes,
    feature_elm::ActivationFunction::kSigmoid,
    feature_elm::Backend::kCpu,
    feature_elm::RlsOptions<float>{});

model.initialize(initialData, initialTargets, initialSamples, numOutputs);
model.update(newData, newTargets, newSamples);
auto prediction = model.predict(input);

Streaming flow

When to use

• Data arrives in chunks.
• Full batch retraining is too slow.
• You need a baseline for forgetting-factor drift adaptation.

Related

• ReOS-ELM and FOS-ELM for regularization and forgetting.
• OS-CELM for class-distance constraints.