Batch ELM

Batch ELM is a single hidden-layer feedforward network with random additive features and a closed-form output layer.

Math

For samples X, random additive features compute:

H = g(XW + b)

The output weights solve the regularized least-squares problem:

minβ ||Hβ - T||² + α||β||²

The CPU default solves the primal system when it is cheaper:

(HᵀH + αI)β = HᵀT

When samples are fewer than hidden nodes, BatchRidgeSolver can use the dual form:

(HHᵀ + αI)α_dual = T
β = Hᵀα_dual

API

feature_elm::BatchElm<float> model(
    numInputs,
    numHiddenNodes,
    feature_elm::ActivationFunction::kSigmoid,
    feature_elm::Backend::kCpu,
    1e-6f);

model.train(trainData, trainTargets, numSamples, numOutputs);
auto predictions = model.predictBatch(testData, testSamples);

BatchElm owns a RandomAdditiveMap and a BatchRidgeSolver. The constructor preserves the v1 shape while routing hidden computation through the feature-map layer.

When to use

• Strong deterministic baseline.
• Small or medium tabular datasets.
• GPU batch transforms when numSamples * numHiddenNodes is large.
• Comparison baseline for RBF and ML-ELM.

When not to use

• Data arrives continuously and full retraining is too expensive: use OS-ELM.
• The feature stack must be learned: use ML-ELM.
• The problem is clearly center-based and local: compare against RBF features.