Source code for librosa.segment

#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Temporal segmentation
=====================

Recurrence and self-similarity
------------------------------
.. autosummary::
    :toctree: generated/

    cross_similarity
    recurrence_matrix
    recurrence_to_lag
    lag_to_recurrence
    timelag_filter
    path_enhance

Temporal clustering
-------------------
.. autosummary::
    :toctree: generated/

    agglomerative
    subsegment
"""

from decorator import decorator

import numpy as np
import scipy
import scipy.signal
import scipy.ndimage

import sklearn
import sklearn.cluster
import sklearn.feature_extraction
import sklearn.neighbors

from ._cache import cache
from . import util
from .filters import diagonal_filter
from .util.exceptions import ParameterError

__all__ = [
    "cross_similarity",
    "recurrence_matrix",
    "recurrence_to_lag",
    "lag_to_recurrence",
    "timelag_filter",
    "agglomerative",
    "subsegment",
    "path_enhance",
]


[docs]@cache(level=30) def cross_similarity( data, data_ref, *, k=None, metric="euclidean", sparse=False, mode="connectivity", bandwidth=None, ): """Compute cross-similarity from one data sequence to a reference sequence. The output is a matrix ``xsim``, where ``xsim[i, j]`` is non-zero if ``data_ref[..., i]`` is a k-nearest neighbor of ``data[..., j]``. Parameters ---------- data : np.ndarray [shape=(..., d, n)] A feature matrix for the comparison sequence. If the data has more than two dimensions (e.g., for multi-channel inputs), the leading dimensions are flattened prior to comparison. For example, a stereo input with shape `(2, d, n)` is automatically reshaped to `(2 * d, n)`. data_ref : np.ndarray [shape=(..., d, n_ref)] A feature matrix for the reference sequence If the data has more than two dimensions (e.g., for multi-channel inputs), the leading dimensions are flattened prior to comparison. For example, a stereo input with shape `(2, d, n_ref)` is automatically reshaped to `(2 * d, n_ref)`. k : int > 0 [scalar] or None the number of nearest-neighbors for each sample Default: ``k = 2 * ceil(sqrt(n_ref))``, or ``k = 2`` if ``n_ref <= 3`` metric : str Distance metric to use for nearest-neighbor calculation. See `sklearn.neighbors.NearestNeighbors` for details. sparse : bool [scalar] if False, returns a dense type (ndarray) if True, returns a sparse type (scipy.sparse.csc_matrix) mode : str, {'connectivity', 'distance', 'affinity'} If 'connectivity', a binary connectivity matrix is produced. If 'distance', then a non-zero entry contains the distance between points. If 'affinity', then non-zero entries are mapped to ``exp( - distance(i, j) / bandwidth)`` where ``bandwidth`` is as specified below. bandwidth : None or float > 0 If using ``mode='affinity'``, this can be used to set the bandwidth on the affinity kernel. If no value is provided, it is set automatically to the median distance to the k'th nearest neighbor of each ``data[:, i]``. Returns ------- xsim : np.ndarray or scipy.sparse.csc_matrix, [shape=(n_ref, n)] Cross-similarity matrix See Also -------- recurrence_matrix recurrence_to_lag librosa.feature.stack_memory sklearn.neighbors.NearestNeighbors scipy.spatial.distance.cdist Notes ----- This function caches at level 30. Examples -------- Find nearest neighbors in CQT space between two sequences >>> hop_length = 1024 >>> y_ref, sr = librosa.load(librosa.ex('pistachio')) >>> y_comp, sr = librosa.load(librosa.ex('pistachio'), offset=10) >>> chroma_ref = librosa.feature.chroma_cqt(y=y_ref, sr=sr, hop_length=hop_length) >>> chroma_comp = librosa.feature.chroma_cqt(y=y_comp, sr=sr, hop_length=hop_length) >>> # Use time-delay embedding to get a cleaner recurrence matrix >>> x_ref = librosa.feature.stack_memory(chroma_ref, n_steps=10, delay=3) >>> x_comp = librosa.feature.stack_memory(chroma_comp, n_steps=10, delay=3) >>> xsim = librosa.segment.cross_similarity(x_comp, x_ref) Or fix the number of nearest neighbors to 5 >>> xsim = librosa.segment.cross_similarity(x_comp, x_ref, k=5) Use cosine similarity instead of Euclidean distance >>> xsim = librosa.segment.cross_similarity(x_comp, x_ref, metric='cosine') Use an affinity matrix instead of binary connectivity >>> xsim_aff = librosa.segment.cross_similarity(x_comp, x_ref, metric='cosine', mode='affinity') Plot the feature and recurrence matrices >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(ncols=2, sharex=True, sharey=True) >>> imgsim = librosa.display.specshow(xsim, x_axis='s', y_axis='s', ... hop_length=hop_length, ax=ax[0]) >>> ax[0].set(title='Binary cross-similarity (symmetric)') >>> imgaff = librosa.display.specshow(xsim_aff, x_axis='s', y_axis='s', ... cmap='magma_r', hop_length=hop_length, ax=ax[1]) >>> ax[1].set(title='Cross-affinity') >>> ax[1].label_outer() >>> fig.colorbar(imgsim, ax=ax[0], orientation='horizontal', ticks=[0, 1]) >>> fig.colorbar(imgaff, ax=ax[1], orientation='horizontal') """ data_ref = np.atleast_2d(data_ref) data = np.atleast_2d(data) if not np.allclose(data_ref.shape[:-1], data.shape[:-1]): raise ParameterError( "data_ref.shape={} and data.shape={} do not match on leading dimension(s)".format( data_ref.shape, data.shape ) ) # swap data axes so the feature axis is last data_ref = np.swapaxes(data_ref, -1, 0) n_ref = data_ref.shape[0] # Use F-ordering for reshape to preserve leading axis data_ref = data_ref.reshape((n_ref, -1), order="F") data = np.swapaxes(data, -1, 0) n = data.shape[0] data = data.reshape((n, -1), order="F") if mode not in ["connectivity", "distance", "affinity"]: raise ParameterError( ( "Invalid mode='{}'. Must be one of " "['connectivity', 'distance', " "'affinity']" ).format(mode) ) if k is None: k = min(n_ref, 2 * np.ceil(np.sqrt(n_ref))) k = int(k) if bandwidth is not None: if bandwidth <= 0: raise ParameterError( "Invalid bandwidth={}. " "Must be strictly positive.".format(bandwidth) ) # Build the neighbor search object # `auto` mode does not work with some choices of metric. Rather than special-case # those here, we instead use a fall-back to brute force if auto fails. try: knn = sklearn.neighbors.NearestNeighbors( n_neighbors=min(n_ref, k), metric=metric, algorithm="auto" ) except ValueError: knn = sklearn.neighbors.NearestNeighbors( n_neighbors=min(n_ref, k), metric=metric, algorithm="brute" ) knn.fit(data_ref) # Get the knn graph if mode == "affinity": # sklearn's nearest neighbor doesn't support affinity, # so we use distance here and then do the conversion post-hoc kng_mode = "distance" else: kng_mode = mode xsim = knn.kneighbors_graph(X=data, mode=kng_mode).tolil() # Retain only the top-k links per point for i in range(n): # Get the links from point i links = xsim[i].nonzero()[1] # Order them ascending idx = links[np.argsort(xsim[i, links].toarray())][0] # Everything past the kth closest gets squashed xsim[i, idx[k:]] = 0 # Convert a compressed sparse row (CSR) format xsim = xsim.tocsr() xsim.eliminate_zeros() if mode == "connectivity": xsim = xsim.astype(np.bool) elif mode == "affinity": if bandwidth is None: bandwidth = np.nanmedian(xsim.max(axis=1).data) xsim.data[:] = np.exp(xsim.data / (-1 * bandwidth)) # Transpose to n_ref by n xsim = xsim.T if not sparse: xsim = xsim.toarray() return xsim
[docs]@cache(level=30) def recurrence_matrix( data, *, k=None, width=1, metric="euclidean", sym=False, sparse=False, mode="connectivity", bandwidth=None, self=False, axis=-1, ): """Compute a recurrence matrix from a data matrix. ``rec[i, j]`` is non-zero if ``data[..., i]`` is a k-nearest neighbor of ``data[..., j]`` and ``|i - j| >= width`` The specific value of ``rec[i, j]`` can have several forms, governed by the ``mode`` parameter below: - Connectivity: ``rec[i, j] = 1 or 0`` indicates that frames ``i`` and ``j`` are repetitions - Affinity: ``rec[i, j] > 0`` measures how similar frames ``i`` and ``j`` are. This is also known as a (sparse) self-similarity matrix. - Distance: ``rec[i, j] > 0`` measures how distant frames ``i`` and ``j`` are. This is also known as a (sparse) self-distance matrix. The general term *recurrence matrix* can refer to any of the three forms above. Parameters ---------- data : np.ndarray [shape=(..., d, n)] A feature matrix. If the data has more than two dimensions (e.g., for multi-channel inputs), the leading dimensions are flattened prior to comparison. For example, a stereo input with shape `(2, d, n)` is automatically reshaped to `(2 * d, n)`. k : int > 0 [scalar] or None the number of nearest-neighbors for each sample Default: ``k = 2 * ceil(sqrt(t - 2 * width + 1))``, or ``k = 2`` if ``t <= 2 * width + 1`` width : int >= 1 [scalar] only link neighbors ``(data[..., i], data[..., j])`` if ``|i - j| >= width`` ``width`` cannot exceed the length of the data. metric : str Distance metric to use for nearest-neighbor calculation. See `sklearn.neighbors.NearestNeighbors` for details. sym : bool [scalar] set ``sym=True`` to only link mutual nearest-neighbors sparse : bool [scalar] if False, returns a dense type (ndarray) if True, returns a sparse type (scipy.sparse.csc_matrix) mode : str, {'connectivity', 'distance', 'affinity'} If 'connectivity', a binary connectivity matrix is produced. If 'distance', then a non-zero entry contains the distance between points. If 'affinity', then non-zero entries are mapped to ``exp( - distance(i, j) / bandwidth)`` where ``bandwidth`` is as specified below. bandwidth : None or float > 0 If using ``mode='affinity'``, this can be used to set the bandwidth on the affinity kernel. If no value is provided, it is set automatically to the median distance between furthest nearest neighbors. self : bool If ``True``, then the main diagonal is populated with self-links: 0 if ``mode='distance'``, and 1 otherwise. If ``False``, the main diagonal is left empty. axis : int The axis along which to compute recurrence. By default, the last index (-1) is taken. Returns ------- rec : np.ndarray or scipy.sparse.csc_matrix, [shape=(t, t)] Recurrence matrix See Also -------- sklearn.neighbors.NearestNeighbors scipy.spatial.distance.cdist librosa.feature.stack_memory recurrence_to_lag Notes ----- This function caches at level 30. Examples -------- Find nearest neighbors in CQT space >>> y, sr = librosa.load(librosa.ex('nutcracker')) >>> hop_length = 1024 >>> chroma = librosa.feature.chroma_cqt(y=y, sr=sr, hop_length=hop_length) >>> # Use time-delay embedding to get a cleaner recurrence matrix >>> chroma_stack = librosa.feature.stack_memory(chroma, n_steps=10, delay=3) >>> R = librosa.segment.recurrence_matrix(chroma_stack) Or fix the number of nearest neighbors to 5 >>> R = librosa.segment.recurrence_matrix(chroma_stack, k=5) Suppress neighbors within +- 7 frames >>> R = librosa.segment.recurrence_matrix(chroma_stack, width=7) Use cosine similarity instead of Euclidean distance >>> R = librosa.segment.recurrence_matrix(chroma_stack, metric='cosine') Require mutual nearest neighbors >>> R = librosa.segment.recurrence_matrix(chroma_stack, sym=True) Use an affinity matrix instead of binary connectivity >>> R_aff = librosa.segment.recurrence_matrix(chroma_stack, metric='cosine', ... mode='affinity') Plot the feature and recurrence matrices >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(ncols=2, sharex=True, sharey=True) >>> imgsim = librosa.display.specshow(R, x_axis='s', y_axis='s', ... hop_length=hop_length, ax=ax[0]) >>> ax[0].set(title='Binary recurrence (symmetric)') >>> imgaff = librosa.display.specshow(R_aff, x_axis='s', y_axis='s', ... hop_length=hop_length, cmap='magma_r', ax=ax[1]) >>> ax[1].set(title='Affinity recurrence') >>> ax[1].label_outer() >>> fig.colorbar(imgsim, ax=ax[0], orientation='horizontal', ticks=[0, 1]) >>> fig.colorbar(imgaff, ax=ax[1], orientation='horizontal') """ data = np.atleast_2d(data) # Swap observations to the first dimension and flatten the rest data = np.swapaxes(data, axis, 0) t = data.shape[0] # Use F-ordering here to preserve leading axis layout data = data.reshape((t, -1), order="F") if width < 1 or width > t: raise ParameterError( "width={} must be at least 1 and at most data.shape[{}]={}".format( width, axis, t ) ) if mode not in ["connectivity", "distance", "affinity"]: raise ParameterError( ( "Invalid mode='{}'. Must be one of " "['connectivity', 'distance', " "'affinity']" ).format(mode) ) if k is None: if t > 2 * width + 1: k = 2 * np.ceil(np.sqrt(t - 2 * width + 1)) else: k = 2 if bandwidth is not None: if bandwidth <= 0: raise ParameterError( "Invalid bandwidth={}. " "Must be strictly positive.".format(bandwidth) ) k = int(k) # Build the neighbor search object try: knn = sklearn.neighbors.NearestNeighbors( n_neighbors=min(t - 1, k + 2 * width), metric=metric, algorithm="auto" ) except ValueError: knn = sklearn.neighbors.NearestNeighbors( n_neighbors=min(t - 1, k + 2 * width), metric=metric, algorithm="brute" ) knn.fit(data) # Get the knn graph if mode == "affinity": kng_mode = "distance" else: kng_mode = mode rec = knn.kneighbors_graph(mode=kng_mode).tolil() # Remove connections within width for diag in range(-width + 1, width): rec.setdiag(0, diag) # Retain only the top-k links per point for i in range(t): # Get the links from point i links = rec[i].nonzero()[1] # Order them ascending idx = links[np.argsort(rec[i, links].toarray())][0] # Everything past the kth closest gets squashed rec[i, idx[k:]] = 0 if self: if mode == "connectivity": rec.setdiag(1) elif mode == "affinity": # we need to keep the self-loop in here, but not mess up the # bandwidth estimation # # using negative distances here preserves the structure without changing # the statistics of the data rec.setdiag(-1) # symmetrize if sym: # Note: this operation produces a CSR (compressed sparse row) matrix! # This is why we have to do it after filling the diagonal in self-mode rec = rec.minimum(rec.T) rec = rec.tocsr() rec.eliminate_zeros() if mode == "connectivity": rec = rec.astype(np.bool) elif mode == "affinity": if bandwidth is None: bandwidth = np.nanmedian(rec.max(axis=1).data) # Set all the negatives back to 0 # Negatives are temporarily inserted above to preserve the sparsity structure # of the matrix without corrupting the bandwidth calculations rec.data[rec.data < 0] = 0.0 rec.data[:] = np.exp(rec.data / (-1 * bandwidth)) # Transpose to be column-major rec = rec.T if not sparse: rec = rec.toarray() return rec
[docs]def 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 [#]_. .. [#] 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 ---------- rec : np.ndarray, or scipy.sparse.spmatrix [shape=(n, n)] A (binary) recurrence matrix, as returned by `recurrence_matrix` pad : bool 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. axis : int The axis to keep as the ``time`` axis. The alternate axis will be converted to lag coordinates. Returns ------- lag : np.ndarray The recurrence matrix in (lag, time) (if ``axis=1``) or (time, lag) (if ``axis=0``) coordinates Raises ------ ParameterError : if ``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)') """ axis = np.abs(axis) if rec.ndim != 2 or rec.shape[0] != rec.shape[1]: raise ParameterError( "non-square recurrence matrix shape: " "{}".format(rec.shape) ) sparse = scipy.sparse.issparse(rec) if sparse: fmt = rec.format t = rec.shape[axis] if pad: if sparse: padding = np.asarray([[1, 0]], dtype=rec.dtype).swapaxes(axis, 0) if axis == 0: rec_fmt = "csr" else: rec_fmt = "csc" rec = scipy.sparse.kron(padding, rec, format=rec_fmt) else: padding = [(0, 0), (0, 0)] padding[(1 - axis)] = (0, t) rec = np.pad(rec, padding, mode="constant") lag = util.shear(rec, factor=-1, axis=axis) if sparse: lag = lag.asformat(fmt) return lag
[docs]def lag_to_recurrence(lag, *, axis=-1): """Convert a lag matrix into a recurrence matrix. Parameters ---------- lag : np.ndarray or scipy.sparse.spmatrix A lag matrix, as produced by ``recurrence_to_lag`` axis : int The axis corresponding to the time dimension. The alternate axis will be interpreted in lag coordinates. Returns ------- rec : np.ndarray or scipy.sparse.spmatrix [shape=(n, n)] A recurrence matrix in (time, time) coordinates For sparse matrices, format will match that of ``lag``. Raises ------ ParameterError : if ``lag`` does not have the correct shape See Also -------- recurrence_to_lag 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) >>> rec_pad = librosa.segment.lag_to_recurrence(lag_pad) >>> rec_nopad = librosa.segment.lag_to_recurrence(lag_nopad) >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(nrows=2, ncols=2, sharex=True) >>> librosa.display.specshow(lag_pad, x_axis='s', y_axis='lag', ... hop_length=hop_length, ax=ax[0, 0]) >>> ax[0, 0].set(title='Lag (zero-padded)') >>> ax[0, 0].label_outer() >>> librosa.display.specshow(lag_nopad, x_axis='s', y_axis='time', ... hop_length=hop_length, ax=ax[0, 1]) >>> ax[0, 1].set(title='Lag (no padding)') >>> ax[0, 1].label_outer() >>> librosa.display.specshow(rec_pad, x_axis='s', y_axis='time', ... hop_length=hop_length, ax=ax[1, 0]) >>> ax[1, 0].set(title='Recurrence (with padding)') >>> librosa.display.specshow(rec_nopad, x_axis='s', y_axis='time', ... hop_length=hop_length, ax=ax[1, 1]) >>> ax[1, 1].set(title='Recurrence (without padding)') >>> ax[1, 1].label_outer() """ if axis not in [0, 1, -1]: raise ParameterError("Invalid target axis: {}".format(axis)) axis = np.abs(axis) if lag.ndim != 2 or ( lag.shape[0] != lag.shape[1] and lag.shape[1 - axis] != 2 * lag.shape[axis] ): raise ParameterError("Invalid lag matrix shape: {}".format(lag.shape)) # Since lag must be 2-dimensional, abs(axis) = axis t = lag.shape[axis] rec = util.shear(lag, factor=+1, axis=axis) sub_slice = [slice(None)] * rec.ndim sub_slice[1 - axis] = slice(t) return rec[tuple(sub_slice)]
[docs]def timelag_filter(function, pad=True, index=0): """Filtering in the time-lag domain. This is primarily useful for adapting image filters to operate on `recurrence_to_lag` output. Using `timelag_filter` is equivalent to the following sequence of operations: >>> data_tl = librosa.segment.recurrence_to_lag(data) >>> data_filtered_tl = function(data_tl) >>> data_filtered = librosa.segment.lag_to_recurrence(data_filtered_tl) Parameters ---------- function : callable The filtering function to wrap, e.g., `scipy.ndimage.median_filter` pad : bool Whether to zero-pad the structure feature matrix index : int >= 0 If ``function`` accepts input data as a positional argument, it should be indexed by ``index`` Returns ------- wrapped_function : callable A new filter function which applies in time-lag space rather than time-time space. Examples -------- Apply a 31-bin median filter to the diagonal of a recurrence matrix. With default, parameters, this corresponds to a time window of about 0.72 seconds. >>> y, sr = librosa.load(librosa.ex('nutcracker'), duration=30) >>> chroma = librosa.feature.chroma_cqt(y=y, sr=sr) >>> chroma_stack = librosa.feature.stack_memory(chroma, n_steps=3, delay=3) >>> rec = librosa.segment.recurrence_matrix(chroma_stack) >>> from scipy.ndimage import median_filter >>> diagonal_median = librosa.segment.timelag_filter(median_filter) >>> rec_filtered = diagonal_median(rec, size=(1, 31), mode='mirror') Or with affinity weights >>> rec_aff = librosa.segment.recurrence_matrix(chroma_stack, mode='affinity') >>> rec_aff_fil = diagonal_median(rec_aff, size=(1, 31), mode='mirror') >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(nrows=2, ncols=2, sharex=True, sharey=True) >>> librosa.display.specshow(rec, y_axis='s', x_axis='s', ax=ax[0, 0]) >>> ax[0, 0].set(title='Raw recurrence matrix') >>> ax[0, 0].label_outer() >>> librosa.display.specshow(rec_filtered, y_axis='s', x_axis='s', ax=ax[0, 1]) >>> ax[0, 1].set(title='Filtered recurrence matrix') >>> ax[0, 1].label_outer() >>> librosa.display.specshow(rec_aff, x_axis='s', y_axis='s', ... cmap='magma_r', ax=ax[1, 0]) >>> ax[1, 0].set(title='Raw affinity matrix') >>> librosa.display.specshow(rec_aff_fil, x_axis='s', y_axis='s', ... cmap='magma_r', ax=ax[1, 1]) >>> ax[1, 1].set(title='Filtered affinity matrix') >>> ax[1, 1].label_outer() """ def __my_filter(wrapped_f, *args, **kwargs): """Decorator to wrap the filter""" # Map the input data into time-lag space args = list(args) args[index] = recurrence_to_lag(args[index], pad=pad) # Apply the filtering function result = wrapped_f(*args, **kwargs) # Map back into time-time and return return lag_to_recurrence(result) return decorator(__my_filter, function)
[docs]@cache(level=30) def subsegment(data, frames, *, n_segments=4, axis=-1): """Sub-divide a segmentation by feature clustering. Given a set of frame boundaries (``frames``), and a data matrix (``data``), each successive interval defined by ``frames`` is partitioned into ``n_segments`` by constrained agglomerative clustering. .. note:: If an interval spans fewer than ``n_segments`` frames, then each frame becomes a sub-segment. Parameters ---------- data : np.ndarray Data matrix to use in clustering frames : np.ndarray [shape=(n_boundaries,)], dtype=int, non-negative] Array of beat or segment boundaries, as provided by `librosa.beat.beat_track`, `librosa.onset.onset_detect`, or `agglomerative`. n_segments : int > 0 Maximum number of frames to sub-divide each interval. axis : int Axis along which to apply the segmentation. By default, the last index (-1) is taken. Returns ------- boundaries : np.ndarray [shape=(n_subboundaries,)] List of sub-divided segment boundaries See Also -------- agglomerative : Temporal segmentation librosa.onset.onset_detect : Onset detection librosa.beat.beat_track : Beat tracking Notes ----- This function caches at level 30. Examples -------- Load audio, detect beat frames, and subdivide in twos by CQT >>> y, sr = librosa.load(librosa.ex('choice'), duration=10) >>> tempo, beats = librosa.beat.beat_track(y=y, sr=sr, hop_length=512) >>> beat_times = librosa.frames_to_time(beats, sr=sr, hop_length=512) >>> cqt = np.abs(librosa.cqt(y, sr=sr, hop_length=512)) >>> subseg = librosa.segment.subsegment(cqt, beats, n_segments=2) >>> subseg_t = librosa.frames_to_time(subseg, sr=sr, hop_length=512) >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots() >>> librosa.display.specshow(librosa.amplitude_to_db(cqt, ... ref=np.max), ... y_axis='cqt_hz', x_axis='time', ax=ax) >>> lims = ax.get_ylim() >>> ax.vlines(beat_times, lims[0], lims[1], color='lime', alpha=0.9, ... linewidth=2, label='Beats') >>> ax.vlines(subseg_t, lims[0], lims[1], color='linen', linestyle='--', ... linewidth=1.5, alpha=0.5, label='Sub-beats') >>> ax.legend() >>> ax.set(title='CQT + Beat and sub-beat markers') """ frames = util.fix_frames(frames, x_min=0, x_max=data.shape[axis], pad=True) if n_segments < 1: raise ParameterError("n_segments must be a positive integer") boundaries = [] idx_slices = [slice(None)] * data.ndim for seg_start, seg_end in zip(frames[:-1], frames[1:]): idx_slices[axis] = slice(seg_start, seg_end) boundaries.extend( seg_start + agglomerative( data[tuple(idx_slices)], min(seg_end - seg_start, n_segments), axis=axis ) ) return np.array(boundaries)
[docs]def agglomerative(data, k, *, clusterer=None, axis=-1): """Bottom-up temporal segmentation. Use a temporally-constrained agglomerative clustering routine to partition ``data`` into ``k`` contiguous segments. Parameters ---------- data : np.ndarray data to cluster k : int > 0 [scalar] number of segments to produce clusterer : sklearn.cluster.AgglomerativeClustering, optional An optional AgglomerativeClustering object. If `None`, a constrained Ward object is instantiated. axis : int axis along which to cluster. By default, the last axis (-1) is chosen. Returns ------- boundaries : np.ndarray [shape=(k,)] left-boundaries (frame numbers) of detected segments. This will always include `0` as the first left-boundary. See Also -------- sklearn.cluster.AgglomerativeClustering Examples -------- Cluster by chroma similarity, break into 20 segments >>> y, sr = librosa.load(librosa.ex('nutcracker'), duration=15) >>> chroma = librosa.feature.chroma_cqt(y=y, sr=sr) >>> bounds = librosa.segment.agglomerative(chroma, 20) >>> bound_times = librosa.frames_to_time(bounds, sr=sr) >>> bound_times array([ 0. , 0.65 , 1.091, 1.927, 2.438, 2.902, 3.924, 4.783, 5.294, 5.712, 6.13 , 7.314, 8.522, 8.916, 9.66 , 10.844, 11.238, 12.028, 12.492, 14.095]) Plot the segmentation over the chromagram >>> import matplotlib.pyplot as plt >>> import matplotlib.transforms as mpt >>> fig, ax = plt.subplots() >>> trans = mpt.blended_transform_factory( ... ax.transData, ax.transAxes) >>> librosa.display.specshow(chroma, y_axis='chroma', x_axis='time', ax=ax) >>> ax.vlines(bound_times, 0, 1, color='linen', linestyle='--', ... linewidth=2, alpha=0.9, label='Segment boundaries', ... transform=trans) >>> ax.legend() >>> ax.set(title='Power spectrogram') """ # Make sure we have at least two dimensions data = np.atleast_2d(data) # Swap data index to position 0 data = np.swapaxes(data, axis, 0) # Flatten the features n = data.shape[0] data = data.reshape((n, -1), order="F") if clusterer is None: # Connect the temporal connectivity graph grid = sklearn.feature_extraction.image.grid_to_graph(n_x=n, n_y=1, n_z=1) # Instantiate the clustering object clusterer = sklearn.cluster.AgglomerativeClustering( n_clusters=k, connectivity=grid, memory=cache.memory ) # Fit the model clusterer.fit(data) # Find the change points from the labels boundaries = [0] boundaries.extend(list(1 + np.nonzero(np.diff(clusterer.labels_))[0].astype(int))) return np.asarray(boundaries)
[docs]def path_enhance( R, n, *, window="hann", max_ratio=2.0, min_ratio=None, n_filters=7, zero_mean=False, clip=True, **kwargs, ): """Multi-angle path enhancement for self- and cross-similarity matrices. This function convolves multiple diagonal smoothing filters with a self-similarity (or recurrence) matrix R, and aggregates the result by an element-wise maximum. Technically, the output is a matrix R_smooth such that:: R_smooth[i, j] = max_theta (R * filter_theta)[i, j] where `*` denotes 2-dimensional convolution, and ``filter_theta`` is a smoothing filter at orientation theta. This is intended to provide coherent temporal smoothing of self-similarity matrices when there are changes in tempo. Smoothing filters are generated at evenly spaced orientations between min_ratio and max_ratio. This function is inspired by the multi-angle path enhancement of [#]_, but differs by modeling tempo differences in the space of similarity matrices rather than re-sampling the underlying features prior to generating the self-similarity matrix. .. [#] Müller, Meinard and Frank Kurth. "Enhancing similarity matrices for music audio analysis." 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings. Vol. 5. IEEE, 2006. .. note:: if using recurrence_matrix to construct the input similarity matrix, be sure to include the main diagonal by setting ``self=True``. Otherwise, the diagonal will be suppressed, and this is likely to produce discontinuities which will pollute the smoothing filter response. Parameters ---------- R : np.ndarray The self- or cross-similarity matrix to be smoothed. Note: sparse inputs are not supported. If the recurrence matrix is multi-dimensional, e.g. `shape=(c, n, n)`, then enhancement is conducted independently for each leading channel. n : int > 0 The length of the smoothing filter window : window specification The type of smoothing filter to use. See `filters.get_window` for more information on window specification formats. max_ratio : float > 0 The maximum tempo ratio to support min_ratio : float > 0 The minimum tempo ratio to support. If not provided, it will default to ``1/max_ratio`` n_filters : int >= 1 The number of different smoothing filters to use, evenly spaced between ``min_ratio`` and ``max_ratio``. If ``min_ratio = 1/max_ratio`` (the default), using an odd number of filters will ensure that the main diagonal (ratio=1) is included. zero_mean : bool By default, the smoothing filters are non-negative and sum to one (i.e. are averaging filters). If ``zero_mean=True``, then the smoothing filters are made to sum to zero by subtracting a constant value from the non-diagonal coordinates of the filter. This is primarily useful for suppressing blocks while enhancing diagonals. clip : bool If True, the smoothed similarity matrix will be thresholded at 0, and will not contain negative entries. **kwargs : additional keyword arguments Additional arguments to pass to `scipy.ndimage.convolve` Returns ------- R_smooth : np.ndarray, shape=R.shape The smoothed self- or cross-similarity matrix See Also -------- librosa.filters.diagonal_filter recurrence_matrix Examples -------- Use a 51-frame diagonal smoothing filter to enhance paths in a recurrence matrix >>> y, sr = librosa.load(librosa.ex('nutcracker')) >>> hop_length = 2048 >>> 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) >>> rec = librosa.segment.recurrence_matrix(chroma_stack, mode='affinity', self=True) >>> rec_smooth = librosa.segment.path_enhance(rec, 51, window='hann', n_filters=7) Plot the recurrence matrix before and after smoothing >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(ncols=2, sharex=True, sharey=True) >>> img = librosa.display.specshow(rec, x_axis='s', y_axis='s', ... hop_length=hop_length, ax=ax[0]) >>> ax[0].set(title='Unfiltered recurrence') >>> imgpe = librosa.display.specshow(rec_smooth, x_axis='s', y_axis='s', ... hop_length=hop_length, ax=ax[1]) >>> ax[1].set(title='Multi-angle enhanced recurrence') >>> ax[1].label_outer() >>> fig.colorbar(img, ax=ax[0], orientation='horizontal') >>> fig.colorbar(imgpe, ax=ax[1], orientation='horizontal') """ if min_ratio is None: min_ratio = 1.0 / max_ratio elif min_ratio > max_ratio: raise ParameterError( "min_ratio={} cannot exceed max_ratio={}".format(min_ratio, max_ratio) ) R_smooth = None for ratio in np.logspace( np.log2(min_ratio), np.log2(max_ratio), num=n_filters, base=2 ): kernel = diagonal_filter(window, n, slope=ratio, zero_mean=zero_mean) # Expand leading dimensions to match R # This way, if R has shape, eg, [2, 3, n, n] # the expanded kernel will have shape [1, 1, m, m] # The following is valid for numpy >= 1.18 # kernel = np.expand_dims(kernel, axis=list(np.arange(R.ndim - kernel.ndim))) # This is functionally equivalent, but works on numpy 1.17 shape = [1] * R.ndim shape[-2:] = kernel.shape kernel = np.reshape(kernel, shape) if R_smooth is None: R_smooth = scipy.ndimage.convolve(R, kernel, **kwargs) else: # Compute the point-wise maximum in-place np.maximum( R_smooth, scipy.ndimage.convolve(R, kernel, **kwargs), out=R_smooth ) if clip: # Clip the output in-place np.clip(R_smooth, 0, None, out=R_smooth) return R_smooth