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librosa.segment.recurrence_to_lag

librosa.segment.recurrence_to_lag(rec, pad=True, axis=- 1)

Convert a recurrence matrix into a lag matrix.

lag[i, j] == rec[i+j, j]

This transformation turns diagonal structures in the recurrence matrix into horizontal structures in the lag matrix. These horizontal structures can be used to infer changes in the repetition structure of a piece, e.g., the beginning of a new section as done in 1.

1

Serra, J., Müller, M., Grosche, P., & Arcos, J. L. (2014). Unsupervised music structure annotation by time series structure features and segment similarity. IEEE Transactions on Multimedia, 16(5), 1229-1240.

Parameters

recnp.ndarray, or scipy.sparse.spmatrix [shape=(n, n)]

A (binary) recurrence matrix, as returned by recurrence_matrix

padbool

If False, lag matrix is square, which is equivalent to assuming that the signal repeats itself indefinitely.

If True, lag is padded with n zeros, which eliminates the assumption of repetition.

axisint

The axis to keep as the time axis. The alternate axis will be converted to lag coordinates.

Returns

lagnp.ndarray

The recurrence matrix in (lag, time) (if axis=1) or (time, lag) (if axis=0) coordinates

Raises

ParameterErrorif rec is non-square

See also

recurrence_matrix

lag_to_recurrence

util.shear

Examples

>>> y, sr = librosa.load(librosa.ex('nutcracker'))
>>> hop_length = 1024
>>> chroma = librosa.feature.chroma_cqt(y=y, sr=sr, hop_length=hop_length)
>>> chroma_stack = librosa.feature.stack_memory(chroma, n_steps=10, delay=3)
>>> recurrence = librosa.segment.recurrence_matrix(chroma_stack)
>>> lag_pad = librosa.segment.recurrence_to_lag(recurrence, pad=True)
>>> lag_nopad = librosa.segment.recurrence_to_lag(recurrence, pad=False)

>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(nrows=2, sharex=True)
>>> librosa.display.specshow(lag_pad, x_axis='time', y_axis='lag',
...                          hop_length=hop_length, ax=ax[0])
>>> ax[0].set(title='Lag (zero-padded)')
>>> ax[0].label_outer()
>>> librosa.display.specshow(lag_nopad, x_axis='time', y_axis='lag',
...                          hop_length=hop_length, ax=ax[1])
>>> ax[1].set(title='Lag (no padding)')