{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\"FMP\"\n", "\"AudioLabs\"\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\"C7\"\n", "

Diagonal Matching

\n", "
\n", "\n", "
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\n", "Following Section 7.2.2 of [Müller, FMP, Springer 2015], we discuss in this notebook a simple diagonal matching strategy for comparing a short sequence with subsequences of a longer sequence. This procedure has been used for audio matching in the following article.\n", "

\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Matching Function\n", "\n", "The following subsequence matching technique is motivated by the task of [**audio matching**](../C7/C7S2_AudioMatching.html), which was introduced in the [FMP notbook on content-based audio retrieval](../C7/C7_ContentBasedAudioRetrieval.html). Recall that the goal of audio matching is to retrieve all audio excerpts that musically correspond to a short query audio clip. From an abstract point of view, let $X=(x_1,x_2,\\ldots,x_N)$ and $Y=(y_1,y_2,\\ldots,y_M)$ be two feature sequences, representing a query $\\mathcal{Q}$ and a document $\\mathcal{D}$, respectively. The length $N$ of the query is typically short in comparison with the length $M$ of the database document. To see if and where the query $\\mathcal{Q}$ is somehow \"contained\" in $\\mathcal{D}$, we shift the sequence $X$ over the sequence $Y$ and locally compare $X$ with suitable subsequences of $Y$. Every subsequence of $Y$ that is similar or, equivalently, has a small distance to $X$ is considered a **match** for the query. \n", "\n", "There are many ways for locally comparing $X$ with subsequences of $Y$. We now introduce a simple procedure, which is referred to as **diagonal matching**. First of all, we need to fix a local cost measure (or local distance measure) to compare the chroma vectors of the sequences $X$ and $Y$. In the following, we assume that all features are normalized with regard to the [**Euclidean norm**](../C3/C3S1_FeatureNormalization.html) and then use the distance measure $c$ based on the **inner product** (or **dot product**):\n", "\n", "\\begin{equation}\n", "c(x,y) = 1- \\langle x,y\\rangle = 1 - \\sum_{k=1}^K x(k)y(k)\n", "\\end{equation}\n", "\n", "for two $K$-dimensional vectors $x\\in\\mathbb{R}^K$ and $y\\in\\mathbb{R}^K$ with $\\|x\\|_2=\\|y\\|_2=1$. Furthermore, assuming that all feature vectors have **non-negative entries**, we have $c(x,y)\\in[0,1]$ with $c(x,y)=0$ if and only if $x=y$. One simple way for comparing two feature sequences that share\n", "the same length is to compute the average distance between corresponding vectors of the two sequences. Doing so, we compare the query sequence $X=(x_1,\\ldots,x_N)$ with all subsequences $(y_{1+m},\\ldots,y_{N+m})$ of $Y$ having the same length $N$ as the query, where $m\\in[0:M-N]$ denotes the shift index. This procedure yields a **matching function** $\\Delta_\\mathrm{Diag}:[0:M-N]\\to\\mathbb{R}$ defined by \n", "\n", "\\begin{equation}\n", " \\Delta_\\mathrm{Diag}(m) := \\frac{1}{N}\\sum_{n=1}^{N} c(x_n,y_{n+m}).\n", "\\end{equation}\n", "\n", "We now slightly reformulate the way this matching function is computed. Let $\\mathbf{C}\\in\\mathbb{R}^{N\\times M}$ be \n", "the **cost matrix** given by\n", "\n", "\\begin{equation}\n", "\\mathbf{C}(n,m):=c(x_n,y_m)\n", "\\end{equation}\n", "\n", "for $n\\in[1:N]$ and $m\\in[1:M]$. Then the value $\\Delta_\\mathrm{Diag}(m)$ is obtained (up to the normalization by the query length) by summing up diagonals of the matrix $\\mathbf{C}$ as illustrated by the next figure. This explains why this procedure is denoted as \"diagonal\" matching.\n", "\n", "\"FMP_C7_F11.png\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementation\n", "\n", "In the following code cell, we implement the diagonal matching procedure and apply it, as a simple example, to synthetically generated sequences $X$ and $Y$. In the subsequent example, the sequence $Y$ contains five subsequences that are similar to $X$ (starting at positions $m=20$, $40$, $60$, $80$, $100$, respectively):\n", "\n", "* The first occurrence starting at $m=20$ is an exact copy of $X$.\n", "* The occurrences at $m=40$ and $m=60$ are noisy versions of $X$. \n", "* The occurrence at $m=80$ is a stretched (slower) version of $X$.\n", "* The occurrence at $m=100$ is a compressed (faster) version of $X$.\n", "\n", "As can be seen in the following figure, the matching function $\\Delta_\\mathrm{Diag}$ reveals local minima at the expected positions. While the first minimum at $m=20$ is zero, the next two minima at $m=40$ and $m=60$ are still pronounced (with a matching value being close to zero). However, due to the stretching and compression, the diagonal matching procedure is not capable of capturing well the last two subsequences at $m=80$ and $m=100$." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T08:40:36.474215Z", "iopub.status.busy": "2024-02-15T08:40:36.473963Z", "iopub.status.idle": "2024-02-15T08:40:39.631805Z", "shell.execute_reply": "2024-02-15T08:40:39.631247Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import sys\n", "import numpy as np\n", "import scipy\n", "import librosa\n", "import matplotlib.pyplot as plt\n", "from matplotlib import patches\n", "\n", "sys.path.append('..')\n", "import libfmp.b\n", "%matplotlib inline\n", "\n", "def scale_tempo_sequence(X, factor=1):\n", " \"\"\"Scales a sequence (given as feature matrix) along time (second dimension)\n", "\n", " Notebook: C7/C7S2_DiagonalMatching.ipynb\n", "\n", " Args:\n", " X (np.ndarray): Feature sequences (given as K x N matrix)\n", " factor (float): Scaling factor (resulting in length \"round(factor * N)\"\") (Default value = 1)\n", "\n", " Returns:\n", " X_new (np.ndarray): Scaled feature sequence\n", " N_new (int): Length of scaled feature sequence\n", " \"\"\"\n", " N = X.shape[1]\n", " t = np.linspace(0, 1, num=N, endpoint=True)\n", " N_new = np.round(factor * N).astype(int)\n", " t_new = np.linspace(0, 1, num=N_new, endpoint=True)\n", " X_new = scipy.interpolate.interp1d(t, X, axis=1)(t_new)\n", " return X_new, N_new\n", "\n", "def cost_matrix_dot(X, Y):\n", " \"\"\"Computes cost matrix via dot product\n", "\n", " Notebook: C7/C7S2_DiagonalMatching.ipynb\n", "\n", " Args:\n", " X (np.ndarray): First sequence (K x N matrix)\n", " Y (np.ndarray): Second sequence (K x M matrix)\n", "\n", " Returns:\n", " C (np.ndarray): Cost matrix\n", " \"\"\"\n", " return 1 - np.dot(X.T, Y)\n", "\n", "def matching_function_diag(C, cyclic=False):\n", " \"\"\"Computes diagonal matching function\n", "\n", " Notebook: C7/C7S2_DiagonalMatching.ipynb\n", "\n", " Args:\n", " C (np.ndarray): Cost matrix\n", " cyclic (bool): If \"True\" then matching is done cyclically (Default value = False)\n", "\n", " Returns:\n", " Delta (np.ndarray): Matching function\n", " \"\"\"\n", " N, M = C.shape\n", " assert N <= M, \"N <= M is required\"\n", " Delta = C[0, :]\n", " for n in range(1, N):\n", " Delta = Delta + np.roll(C[n, :], -n)\n", " Delta = Delta / N\n", " if cyclic is False:\n", " Delta[M-N+1:M] = np.inf\n", " return Delta\n", "\n", "# Create snythetic example for sequences X and Y\n", "N = 15\n", "M = 130\n", "feature_dim = 12\n", "np.random.seed(2)\n", "X = np.random.random((feature_dim, N))\n", "Y = np.random.random((feature_dim, M))\n", "Y[:, 20:20+N] = X\n", "Y[:, 40:40+N] = X + 0.5 * np.random.random((feature_dim, N))\n", "Y[:, 60:60+N] = X + 0.8 * np.random.random((feature_dim, N))\n", "X_slow, N_slow = scale_tempo_sequence(X, factor=1.25)\n", "Y[:, 80:80+N_slow] = X_slow\n", "X_fast, N_fast = scale_tempo_sequence(X, factor=0.8)\n", "Y[:, 100:100+N_fast] = X_fast\n", "Y = librosa.util.normalize(Y, norm=2)\n", "X = librosa.util.normalize(X, norm=2)\n", "\n", "# Compute cost matrix and matching function\n", "C = cost_matrix_dot(X, Y)\n", "Delta = matching_function_diag(C)\n", "\n", "# Visualization\n", "fig, ax = plt.subplots(2, 2, gridspec_kw={'width_ratios': [1, 0.02], \n", " 'height_ratios': [1, 1]}, figsize=(8, 4)) \n", "cmap = libfmp.b.compressed_gray_cmap(alpha=-10, reverse=True)\n", "libfmp.b.plot_matrix(C, title='Cost matrix', xlabel='Time (samples)', ylabel='Time (samples)', \n", " ax=[ax[0, 0], ax[0, 1]], colorbar=True, cmap=cmap)\n", "\n", "libfmp.b.plot_signal(Delta, ax=ax[1,0], xlabel='Time (samples)', ylabel='',\n", " title = 'Matching function', color='k')\n", "ax[1, 0].grid()\n", "ax[1, 1].axis('off')\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Retrieval Procedure\n", "\n", "We now discuss how the matching function can be applied for retrieving all matches that are similar to the query fragment. In the following, we assume that the database is represented by a single document $\\mathcal{D}$ (e.g., by concatenating all document sequences). To determine the best match between $\\mathcal{Q}$ and $\\mathcal{D}$, we simply look for the index $m^\\ast\\in[0:M-N]$ that minimizes the matching function $\\Delta_\\mathrm{Diag}$:\n", "\n", "\\begin{equation}\n", " m^\\ast := \\underset{m\\in[0:M-N]}{\\mathrm{argmin}} \\,\\,\\Delta_\\mathrm{Diag}(m).\n", "\\end{equation}\n", "\n", "The best match is then given by the subsequence\n", "\n", "\\begin{equation}\n", " Y(1+m^\\ast:N+m^\\ast) := (y_{1+m^\\ast},\\ldots,y_{N+m^\\ast}).\n", "\\end{equation}\n", "\n", "To obtain further matches, we exclude a neighborhood of the best match from further considerations. For example, one may exclude a neighborhood of $\\rho= \\lfloor N/2 \\rfloor$ around $m^\\ast$, e.g., by setting $\\Delta_\\mathrm{Diag}(m)=\\infty$ for $m\\in [m^\\ast-\\rho:m^\\ast+\\rho]\\cap [0:M-N]$. This ensures that the subsequent matches do not overlap by more than half the query length. To find subsequent matches, the latter procedure is repeated until a certain number of matches is obtained or a specified distance threshold is exceeded.\n", "\n", "In the following code cell, we implement this retrieval procedure. Besides the parameter $\\rho$, we introduce a parameter $\\tau$ for restricting the matching values (i.e., we require $\\Delta_\\mathrm{Diag}(m^\\ast)\\leq \\tau$) and a parameters that specifies the maximum number of matches to be retrieved. Continuing with our synthetic example, we indicate in the visualization the minimizing matching positions (using a red dot) and the matching subsequence (using a transparent red rectangle)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T08:40:39.663352Z", "iopub.status.busy": "2024-02-15T08:40:39.662939Z", "iopub.status.idle": "2024-02-15T08:40:39.787677Z", "shell.execute_reply": "2024-02-15T08:40:39.787129Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def mininma_from_matching_function(Delta, rho=2, tau=0.2, num=None):\n", " \"\"\"Derives local minima positions of matching function in an iterative fashion\n", "\n", " Notebook: C7/C7S2_DiagonalMatching.ipynb\n", "\n", " Args:\n", " Delta (np.ndarray): Matching function\n", " rho (int): Parameter to exclude neighborhood of a matching position for subsequent matches (Default value = 2)\n", " tau (float): Threshold for maximum Delta value allowed for matches (Default value = 0.2)\n", " num (int): Maximum number of matches (Default value = None)\n", "\n", " Returns:\n", " pos (np.ndarray): Array of local minima\n", " \"\"\"\n", " Delta_tmp = Delta.copy()\n", " M = len(Delta)\n", " pos = []\n", " num_pos = 0\n", " rho = int(rho)\n", " if num is None:\n", " num = M\n", " while num_pos < num and np.sum(Delta_tmp < tau) > 0:\n", " m = np.argmin(Delta_tmp)\n", " pos.append(m)\n", " num_pos += 1\n", " Delta_tmp[max(0, m - rho):min(m + rho, M)] = np.inf\n", " pos = np.array(pos).astype(int)\n", " return pos\n", "\n", "def matches_diag(pos, Delta_N):\n", " \"\"\"Derives matches from positions in the case of diagonal matching\n", "\n", " Notebook: C7/C7S2_DiagonalMatching.ipynb\n", "\n", " Args:\n", " pos (np.ndarray or list): Starting positions of matches\n", " Delta_N (int or np.ndarray or list): Length of match (a single number or a list of same length as Delta)\n", "\n", " Returns:\n", " matches (np.ndarray): Array containing matches (start, end)\n", " \"\"\"\n", " matches = np.zeros((len(pos), 2)).astype(int)\n", " for k in range(len(pos)):\n", " s = pos[k]\n", " matches[k, 0] = s\n", " if isinstance(Delta_N, int):\n", " matches[k, 1] = s + Delta_N - 1\n", " else:\n", " matches[k, 1] = s + Delta_N[s] - 1\n", " return matches\n", "\n", "def plot_matches(ax, matches, Delta, Fs=1, alpha=0.2, color='r', s_marker='o', t_marker=''):\n", " \"\"\"Plots matches into existing axis\n", "\n", " Notebook: C7/C7S2_DiagonalMatching.ipynb\n", "\n", " Args:\n", " ax: Axis\n", " matches: Array of matches (start, end)\n", " Delta: Matching function\n", " Fs: Feature rate (Default value = 1)\n", " alpha: Transparency pramaeter for match visualization (Default value = 0.2)\n", " color: Color used to indicated matches (Default value = 'r')\n", " s_marker: Marker used to indicate start of matches (Default value = 'o')\n", " t_marker: Marker used to indicate end of matches (Default value = '')\n", " \"\"\"\n", " y_min, y_max = ax.get_ylim()\n", " for (s, t) in matches:\n", " ax.plot(s/Fs, Delta[s], color=color, marker=s_marker, linestyle='None')\n", " ax.plot(t/Fs, Delta[t], color=color, marker=t_marker, linestyle='None')\n", " rect = patches.Rectangle(((s-0.5)/Fs, y_min), (t-s+1)/Fs, y_max, facecolor=color, alpha=alpha)\n", " ax.add_patch(rect)\n", "\n", "pos = mininma_from_matching_function(Delta, rho=N//2, tau=0.12, num=None)\n", "matches = matches_diag(pos, N)\n", "\n", "fig, ax, line = libfmp.b.plot_signal(Delta, figsize=(8, 2), xlabel='Time (samples)', \n", " title = 'Matching function with retrieved matches', \n", " color='k')\n", "ax.grid()\n", "plot_matches(ax, matches, Delta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Matching Function Using Multiple Queries\n", "\n", "This basic matching procedure works well in the case that the tempo of the query roughly coincides with the tempo within the sections to be matched. However, as also indicated by the previous example, diagonal matching becomes problematic when the database subsequences are stretched or compressed versions of the query. To compensate for such tempo differences, one can apply a **multiple-query strategy**. The idea is as follows:\n", "\n", "* Generate multiple versions of a query by applying scaling operations that simulate different tempi.\n", "* Compute a separate matching function for each of the scaled versions using diagonal matching.\n", "* Minimize over all resulting matching functions, which results in a single matching function. \n", "\n", "Note that this idea is similar to the **multiple-filtering approach** for [enhancing the path structure of SSMs](../C4/C4S2_SSM-PathEnhancement.html). In the following implementation, we introduce a set $\\Theta$ that samples the range of expected relative tempo differences. In music retrieval, it rarely happens that the relative tempo difference between matching sections is larger than $50$ percent. Therefore, $\\Theta$ can be chosen to cover tempo variations of roughly $-50$ to $+50$ percent. For example, the set\n", "\n", "$$\n", "\\Theta=\\{0.66,0.81,1.00,1.22,1.50\\}\n", "$$\n", "\n", "(with logarithmically spaced tempo parameters) covers tempo variations of roughly $−50$ to $+50$ percent. (This set can be computed by the function `libfmp.c4.compute_tempo_rel_set`.)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T08:40:39.790937Z", "iopub.status.busy": "2024-02-15T08:40:39.790690Z", "iopub.status.idle": "2024-02-15T08:40:40.682433Z", "shell.execute_reply": "2024-02-15T08:40:40.681873Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def matching_function_diag_multiple(X, Y, tempo_rel_set=[1], cyclic=False):\n", " \"\"\"Computes diagonal matching function using multiple query strategy\n", "\n", " Notebook: C7/C7S2_DiagonalMatching.ipynb\n", "\n", " Args:\n", " X (np.ndarray): First sequence (K x N matrix)\n", " Y (np.ndarray): Second sequence (K x M matrix)\n", " tempo_rel_set (np.ndarray): Set of relative tempo values (scaling) (Default value = [1])\n", " cyclic (bool): If \"True\" then matching is done cyclically (Default value = False)\n", "\n", " Returns:\n", " Delta_min (np.ndarray): Matching function (obtained by from minimizing over several matching functions)\n", " Delta_N (np.ndarray): Query length of best match for each time position\n", " Delta_scale (np.ndarray): Set of matching functions (for each of the scaled versions of the query)\n", " \"\"\"\n", " M = Y.shape[1]\n", " num_tempo = len(tempo_rel_set)\n", " Delta_scale = np.zeros((num_tempo, M))\n", " N_scale = np.zeros(num_tempo)\n", " for k in range(num_tempo):\n", " X_scale, N_scale[k] = scale_tempo_sequence(X, factor=tempo_rel_set[k])\n", " C_scale = cost_matrix_dot(X_scale, Y)\n", " Delta_scale[k, :] = matching_function_diag(C_scale, cyclic=cyclic)\n", " Delta_min = np.min(Delta_scale, axis=0)\n", " Delta_argmin = np.argmin(Delta_scale, axis=0)\n", " Delta_N = N_scale[Delta_argmin]\n", " return Delta_min, Delta_N, Delta_scale\n", "\n", "\n", "# import libfmp.c4\n", "# tempo_rel_set = libfmp.c4.compute_tempo_rel_set(tempo_rel_min=0.66, tempo_rel_max=1.5, num=5) \n", "# print(tempo_rel_set)\n", "\n", "tempo_rel_set = [0.66, 0.81, 1.00, 1.22, 1.50]\n", "color_set = ['b', 'c', 'gray', 'r', 'g']\n", "num_tempo = len(tempo_rel_set)\n", "\n", "Delta_min, Delta_N, Delta_scale = matching_function_diag_multiple(X, Y, tempo_rel_set=tempo_rel_set,\n", " cyclic=False)\n", "\n", "for k in range(num_tempo):\n", " libfmp.b.plot_signal(Delta_scale[k,:], figsize=(8, 2), xlabel='Time (samples)',\n", " title = 'Matching function with scaling factor %.2f' % tempo_rel_set[k], \n", " color=color_set[k], ylim=[0, 0.3])\n", " plt.grid()\n", " \n", "fig, ax, line = libfmp.b.plot_signal(Delta_min, figsize=(8, 2), xlabel='Time (samples)',\n", " title = 'Matching function', color='k', ylim=[0,0.3], linewidth=3, label='min')\n", "ax.grid()\n", "for k in range(num_tempo):\n", " ax.plot(Delta_scale[k, :], linewidth=1, color=color_set[k], label=tempo_rel_set[k])\n", " \n", "plt.legend(loc='lower right', framealpha=1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the multiple-query matching function, the subsequences that correspond to stretched or compressed versions of the query are now revealed by local minima that have a value much closer to zero. As a result, our retrieval procedure from above (with the same parameter settings) now yields the expected matches. The length of the matching subsequence is derived from the scaled query that yields the minimal matching value over all query versions considered. Therefore, as also indicated in the subsequent figure, the length may differ from the length $N$ of the original (non-stretched) query. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T08:40:40.684987Z", "iopub.status.busy": "2024-02-15T08:40:40.684801Z", "iopub.status.idle": "2024-02-15T08:40:40.999032Z", "shell.execute_reply": "2024-02-15T08:40:40.998039Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pos = mininma_from_matching_function(Delta_min, rho=N//2, tau=0.12, num=None)\n", "matches = matches_diag(pos, Delta_N)\n", "\n", "fig, ax = plt.subplots(2, 2, gridspec_kw={'width_ratios': [1, 0.02], \n", " 'height_ratios': [3, 3]}, figsize=(8, 4)) \n", "cmap = libfmp.b.compressed_gray_cmap(alpha=-10, reverse=True)\n", "libfmp.b.plot_matrix(C, title='Cost matrix', xlabel='Time (samples)', ylabel='Time (samples)', \n", " ax=[ax[0, 0], ax[0, 1]], colorbar=True, cmap=cmap)\n", "\n", "libfmp.b.plot_signal(Delta_min, ax=ax[1, 0], xlabel='Time (samples)', \n", " title = 'Matching function with retrieved matches', color='k')\n", "\n", "ax[1,0].grid()\n", "plot_matches(ax[1, 0], matches, Delta_min)\n", "ax[1,1].axis('off')\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Further Notes\n", "\n", "In this notebook, we discussed a simple matching procedure that identifies database subsequences that are similar to a given query sequence. We have also shown how differences in tempo can be handled by using a multiple-query approach. \n", "\n", "* This matching strategy can be used for the task of [**audio matching**](../C7/C7S2_AudioMatching.html), which we introduced in the [FMP notebook on content-based audio retrieval](../C7/C7_ContentBasedAudioRetrieval.html).\n", "* The matching strategy based on multiple queries was used in combination with [CENS features](../C7/C7S2_CENS.html) in the original paper on audio matching. \n", "* As an alternative to diagonal matching, we introduce in the [FMP notebook on subsequence DTW](../C7/C7S2_SubsequenceDTW.html) an alternative that can handle local tempo variations using a variant of [dynamic time warping](../C3/C3S2_DTWbasic.html) (DTW).\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "Acknowledgment: This notebook was created by Meinard Müller and Frank Zalkow.\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n", "
\"C0\"\"C1\"\"C2\"\"C3\"\"C4\"\"C5\"\"C6\"\"C7\"\"C8\"
" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.16" } }, "nbformat": 4, "nbformat_minor": 1 }