ELM-AE¶

ElmAutoEncoderLayer is a learned FeatureMap. It trains an ELM autoencoder with the input as its own target, then derives an encoder for downstream layers.

Math¶

An ELM-AE layer computes hidden activations:

Z = g(XW + b)

It solves output weights B for reconstruction:

minB ||ZB - X||² + α||B||²

The encoder used by downstream layers is derived from the learned autoencoder output weights using the implementation's transpose convention:

features = activation(Z_encoder * B_encoder + b_encoder)

The layer is still an ELM-style layer: input weights are random, but the output-side encoder is learned from data.

API¶

feature_elm::ElmAutoEncoderLayer<float> layer(
    inputDim,
    outputDim,
    feature_elm::ActivationKind::kSigmoid,
    42u,
    1e-6f);

layer.fit(trainData, numSamples);

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

Architecture¶

flowchart LR
    X[Input X] --> W[Random input weights]
    W --> Z[Hidden Z]
    Z --> B[Solve reconstruction B]
    B --> E[Encoder weights]
    E --> F[Encoded features]

When to use¶

• Learned feature extraction is needed.
• A single additive ELM layer underfits.
• You need a stackable layer for ML-ELM or H-OS-ELM.

Notes¶

• The layer reconstructs its input during fit.
• The encoder is frozen after fitting.
• Use ridgeAlpha to stabilize the autoencoder solve.