Shift-Invariant NMF / Convolutive NMF / Sparse NMF

Definition

Extensions to standard NMF for audio that handle real-world variations: frequency shifts (same note at different pitches), time shifts (same sound at different times), and sparsity constraints (fewer active components at once).

Key Ideas

• Shift-invariant NMF: basis spectra can shift along frequency axis — handles pitch variations without needing a separate basis per note.
• Convolutive NMF: basis spectra convolved across time — handles temporal patterns (e.g., drum hits with different decays).
• Sparse NMF: adds L1 regularization on activations H — enforces that only a few components are active at any time, matching the sparsity of real audio.
• Together these address the primary limitations of vanilla NMF for audio tasks.

Relationships

• Builds on ../concepts/non-negative-matrix-factorization-audio
• Relevant to ../concepts/synthetic-mixing-pipelines — can generate training data via NMF-based decomposition
• Modern relevance: NMF variants can serve as interpretable front-ends or regularization for neural models

Sources

None ingested yet — seed batch setup.