librosa.decompose.decompose

librosa.decompose.decompose(S, n_components=None, transformer=None, sort=False, fit=True, **kwargs)

Decompose a feature matrix.

Given a spectrogram S, produce a decomposition into components and activations such that S ~= components.dot(activations).

By default, this is done with with non-negative matrix factorization (NMF), but any sklearn.decomposition-type object will work.

Parameters:

S : np.ndarray [shape=(n_features, n_samples), dtype=float]

The input feature matrix (e.g., magnitude spectrogram)

n_components : int > 0 [scalar] or None

number of desired components

if None, then n_features components are used

transformer : None or object

If None, use sklearn.decomposition.NMF

Otherwise, any object with a similar interface to NMF should work. transformer must follow the scikit-learn convention, where input data is (n_samples, n_features).

transformer.fit_transform() will be run on S.T (not S), the return value of which is stored (transposed) as activations

The components will be retrieved as transformer.components_.T

S ~= np.dot(activations, transformer.components_).T

or equivalently: S ~= np.dot(transformer.components_.T, activations.T)

sort : bool

If True, components are sorted by ascending peak frequency.

Note

If used with transformer, sorting is applied to copies of the decomposition parameters, and not to transformer’s internal parameters.

fit : bool

If True, components are estimated from the input S.

If False, components are assumed to be pre-computed and stored in transformer, and are not changed.

kwargs : Additional keyword arguments to the default transformer

sklearn.decomposition.NMF

Returns:

components: np.ndarray [shape=(n_features, n_components)]

matrix of components (basis elements).

activations: np.ndarray [shape=(n_components, n_samples)]

transformed matrix/activation matrix

Raises:

ParameterError

if fit is False and no transformer object is provided.

See also

sklearn.decomposition

SciKit-Learn matrix decomposition modules

Examples

Decompose a magnitude spectrogram into 32 components with NMF

>>> y, sr = librosa.load(librosa.util.example_audio_file())
>>> S = np.abs(librosa.stft(y))
>>> comps, acts = librosa.decompose.decompose(S, n_components=8)
>>> comps
array([[  1.876e-01,   5.559e-02, ...,   1.687e-01,   4.907e-02],
       [  3.148e-01,   1.719e-01, ...,   2.314e-01,   9.493e-02],
       ...,
       [  1.561e-07,   8.564e-08, ...,   7.167e-08,   4.997e-08],
       [  1.531e-07,   7.880e-08, ...,   5.632e-08,   4.028e-08]])
>>> acts
array([[  4.197e-05,   8.512e-03, ...,   3.056e-05,   9.159e-06],
       [  9.568e-06,   1.718e-02, ...,   3.322e-05,   7.869e-06],
       ...,
       [  5.982e-05,   1.311e-02, ...,  -0.000e+00,   6.323e-06],
       [  3.782e-05,   7.056e-03, ...,   3.290e-05,  -0.000e+00]])

Sort components by ascending peak frequency

>>> comps, acts = librosa.decompose.decompose(S, n_components=16,
...                                           sort=True)

Or with sparse dictionary learning

>>> import sklearn.decomposition
>>> T = sklearn.decomposition.MiniBatchDictionaryLearning(n_components=16)
>>> scomps, sacts = librosa.decompose.decompose(S, transformer=T, sort=True)

>>> import matplotlib.pyplot as plt
>>> plt.figure(figsize=(10,8))
>>> plt.subplot(3, 1, 1)
>>> librosa.display.specshow(librosa.amplitude_to_db(S,
...                                                  ref=np.max),
...                          y_axis='log', x_axis='time')
>>> plt.title('Input spectrogram')
>>> plt.colorbar(format='%+2.0f dB')
>>> plt.subplot(3, 2, 3)
>>> librosa.display.specshow(librosa.amplitude_to_db(comps,
...                                                  ref=np.max),
...                          y_axis='log')
>>> plt.colorbar(format='%+2.0f dB')
>>> plt.title('Components')
>>> plt.subplot(3, 2, 4)
>>> librosa.display.specshow(acts, x_axis='time')
>>> plt.ylabel('Components')
>>> plt.title('Activations')
>>> plt.colorbar()
>>> plt.subplot(3, 1, 3)
>>> S_approx = comps.dot(acts)
>>> librosa.display.specshow(librosa.amplitude_to_db(S_approx,
...                                                  ref=np.max),
...                          y_axis='log', x_axis='time')
>>> plt.colorbar(format='%+2.0f dB')
>>> plt.title('Reconstructed spectrogram')
>>> plt.tight_layout()

(Source code)