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ReOS-ELM and FOS-ELM

ReOS-ELM and FOS-ELM are not separate classes in v2. They are toggles on RlsOptions<FloatT>.

ReOS-ELM

ReOS-ELM regularizes the initial covariance used by the online solver.

feature_elm::RlsOptions<float> options;
options.regularization = 1e-2f;
options.forgettingFactor = 1.0f;
options.constraint = feature_elm::RlsConstraint::kNone;

Use it when:

  • The initial chunk is small.
  • The hidden feature matrix is ill-conditioned.
  • Early online updates produce unstable weights.

The extension is off when regularization = 0.

FOS-ELM

FOS-ELM applies a forgetting factor to down-weight stale data.

feature_elm::RlsOptions<float> options;
options.regularization = 0.0f;
options.forgettingFactor = 0.98f;
options.constraint = feature_elm::RlsConstraint::kNone;

Use it when:

  • The stream distribution changes over time.
  • Recent labels are more informative than old labels.
  • You need to compare against ordinary OS-ELM.

The extension is off when forgettingFactor = 1.

Drift comparison

xychart-beta
    title "Expected drift behavior"
    x-axis "Samples seen" [0, 250, 500, 750, 1000]
    y-axis "Accuracy" 0 --> 1
    line "OS-ELM" [0.92, 0.90, 0.72, 0.68, 0.66]
    line "FOS-ELM" [0.91, 0.89, 0.74, 0.82, 0.86]

FOS-ELM should recover faster after the configured drift point because older chunks receive lower weight.

References

  • Liang, Huang, Saratchandran, and Sundararajan. 2006. OS-ELM.
  • Online sequential learning and forgetting-factor variants in the ELM literature.